Day 1 - Thursday June 27
Infrastructure & Public Policy
Chairperson: Maria Lavrutich (NTNU, Norway)
Infrastructure Investment with Conflicting Objectives under Uncertainty
Discussant: Motoh Tsujimura (Doshisha University, Japan)
We study optimal infrastructure investment decisions of a social planner (SP) that has to anticipate capacity investment of a private company (PC) in a market characterized by uncertain demand. The proposed model captures the investment decisions of the SP and PC and accounts for the conflicting objectives and game-theoretic interactions of the distinct agents. Taking an option-based approach allows us to study the effect of uncertainty on the investment decisions, and to take the agents' discretion over investment timing as well as size into account. We show, if and how the SP can align the decision of the PC with the social optimum using the fact that the PC is dependent on the infrastructure provided.
Financing with Price Externality: Public Transport in Hong Kong
Discussant: Maria Lavrutich (Norwegian University of Science and Technology, Norway)
Because of debt concerns, many cities face challenges in financing their infrastructure. Hong Kong's transit operator designed a model which allows it to exploit the positive externalities of public transport on real estate prices to finance the infrastructure. We develop a Stackelberg leader-follower game of timing under uncertainty to explore this rationale. Our main findings are that internalizing positive externalities provides additional revenue sources for defraying the overall costs of infrastructure investments, thereby accelerating the delivery of infrastructure; in a multi-player stopping game, the equilibrium investment times are not typical first-hitting times. This study provides theoretical insight into infrastructure planning and financing based on compound (growth) options.
Abatement Planning when Abatement Technology is Ambiguous
Discussant: Benoit Chevalier-Roignant (Cranfield University, United Kingdom)
In this paper, we analyze a pollutant abatement investment strategy when the central planner does not have confidence with the dynamics of abatement technology. The central planner maximizes social welfare under the abatement technology ambiguity by choosing a consumption level and an investment share for the abatement activity. Due to the existence of abatement technology ambiguity, we adopt the HS type robust control approach to solve the central planner's problem. We obtain the nonlinear partial difference equation (PDE), which derives the optimal abatement investment strategy. Because the PDE is nonlinear, it has to be solved numerically. We leave the numerical calculation for future work.
Mining, Oil & Gas
Chairperson: Yuri Lawryshyn ( U of Toronto, Canada)
of Tailings Dam Failure in Mining Operations
Discussant: Luis Alfredo Mogollon (Ecopetrol, Colombia)
Traditional mining projects store the byproducts of mining operations behind a tailings dam. When the wall of a tailings dam is breached, it causes serious environmental damage and often loss of life. Most studies on tailings dam failures focus on the technical causes of the dam failure, or on the loss of life and the environmental damage. Investing in the safety of tailings dams or in alternative mine designs devoid of such dams should be the preferred option from both financial and environmental point of views. This work focuses on the evaluation of the financial impact of such disasters within a real option framework for the mining companies. We establish a closed-form formula for the expected value of a conventional mining project subject to the risk of tailings dam failure. The stochastic components considered are the metal price, the occurrence of a tailings dam failure, the penalty cost and recovery period after such a failure. These components are calibrated to the available statistical data on tailings dam failures. We analyse two dynamic options available to mining companies: to perform preventive maintenance and temporary repairs, and to retrofit the mine with an alternative design such as dry processing. We obtain a semi-analytic value for these two real options by a dynamic programming numerical scheme combined with Monte Carlo simulations of the dynamic risk factors. We analyse the results and discuss the factors that could lead to a growing recourse to dry processing in the future.
Boundary-based Simulation with Application to Multi-Option Mining Investments
Discussant: Wen Chen (CSIRO, Australia)
The new RO approach based on simulation and exercise boundary fitting, that was recently presented on a few simplified cases (Bashiri, Davison, & Lawryshyn, 2018), in this research is extended to more realistic and complex setups of mining investment. The two models are developed that provide insights into optimal investment patterns of multiple real option combinations. In the presence of single price uncertainty, the investment patterns are shown to depend heavily on the choice of a stochastic process and its parameters. In particular, GBM incentivizes RO to delay investment, whereas, under MRP, ceteris paribus, the optimal decision is to invest at the earliest. Investing not full size is only reasonable when full extraction is possible within the license term. The RO to stage the investment becomes relevant only when the learning process about the total ore amount is introduced. The added value of learning during extraction surpasses the otherwise suboptimal investment timing. The models presented are the work in progress and require further development.
Estimation of Exploratory Projects in Unconventional Oil & Gas
Discussant: Mariia Kozlova (Lappeenranta University of Technology, Finland)
This paper mainly seeks to show the use of volatility calculation in exploratory projects of unconventional, can, when compared to traditional methods, lead to improved decision-making. For such purpose, a new methodology involving the Monte Carlo simulation and the volatility calculation is presented, based on volatility calculation method that allows to define which ones the options in each project are. To develop such application, a hypothetical area of "Play" of "shale" of a basin Middle Magdalena Valley (VMM)" of Colombia is considered, framed by a decision tree, according to the following stages: 1) Prospective area evaluation; 2) Productivity verification; 3) Commercial viability and 4) Development, including technical and economic uncertainties at every stage, allowing volatility calculation, and the expected value with the objective of forming the portfolio that allows this to make the optimal decisions of the exploratory investment. In addition, it was analyzed, using the "waiting option", which allowed to define which project to start with.
Chairperson: Mikael Collan (Lappeenranta U of Technology, Finland)
Expansion and Term Extension in Public Infrastructure Concessions
Discussant: Jyrki Savolainen (LUT University, Finland)
Infrastructure projects have as characteristics a long maturation period and high capital investments, which generates significant risks. Government Grants or Concessions, as well as Public Private Partnerships (PPPs), are usually bound by a time term defined in the contract, during which the private party must get its payback and return on invested capital. Although the objectives of both sides (public and private) are oppositely different, they need not be antagonistic as they both get to profit from the other in the project involved. When well designed, the contract rules should guarantee the smooth development of the concession, bringing about a win-win partnership. Capacity expansion, especially in infrastructure concessions such as roads, ports, trains, airports, among others, should be driven by the demand and decided by the concessionaire, since it is an intensive capital decision and is subject to a time frame limit. We argue in this research that in order to optimize such a financial decision, which finally should be beneficial to both parties involved, an investment in capacity expansion should not only be decided by the concessionaire, evidently under previously designed contract rules, but also permit extension of the time grant in order to turn it financially viable for the investor, even if close to the end of the contract term. In this sense, the purpose of this article is to model, through the real options approach, different policies of capacity expansion option in governmental concession grants
Construction Projects: Applying Fuzzy Logic and System Dynamics
Discussant: Carlos Bastian-Pinto (PUC-Rio, Brazil)
Phasing construction projects is an interesting possibility that has received only limited attention in the academic literature, especially the quantification of benefits from phasing and the effect phasing has on project risk have not been fully explored. This paper presents two approaches to analyze the effects of phasing in the context of construction projects: a simple fuzzy logic-based method for preliminary analyses and a system dynamic simulation-approach for deeper analysis with timing. Both approaches are illustrated with a numerical example case. The presented results are new in academic literature and of practical relevance to managers and investors working with construction projects.
Petroleum Models I
Chairperson: Gonzalo Cortazar (PUC - Chile)
Price Process and Sequential Exploration with Geologically Dependent Prospects
In a group of exploration prospects with common geological features, drilling a well reveals information about chances of success in others. With such dependencies, where do we drill first and what comes next given success or failure in previous wells? In addition, oil prices vary during the exploration campaign and with them so do the economics of wells and the optimal decision to drill. The grand problem then becomes a valuation of a group of prospects given geological dependencies and uncertain oil prices. Using a joint distribution for geological outcomes (a result of using information-theoretic methods) and a two-factor stochastic price process in a two-dimensional binomial sequence, we propose a Markov decision process that solves the optimal exploration problem. An Excel VBA software implementation of this algorithm also accompanies this paper.
Term Structure of Oil Risk Premiums
Discussant: Babak Jafarizadeh (Heriot-Watt University)
This paper proposes to extract time-varying commodity risk premiums from multi-factor models using futures prices and analyst's forecasts of future prices. The model is calibrated for oil using a 3-factor stochastic commodity-pricing model with an affine risk-premium specification. WTI futures price data is from NYMEX and analyst's forecasts from Bloomberg and the U.S Energy Information Administration. Weekly estimations for short, medium and long-term risk premiums between 2010 and 2017 are obtained. Results from the model calibration show that risk premiums are clearly stochastic, that short-term risk premiums tend to be higher than long-term ones and that risk premium volatility is much higher for short maturities. An empirical analysis is performed to explore the macroeconomic and oil market variables that may explain the stochastic behavior oil risk-premiums.
Rates and Price Forecasts for Petroleum Valuation
Discussant: Gonzalo Cortazar (Pontificia Universidad Catolica de Chile, Chile)
For their appraisals, most petroleum companies use discount rates that implicitly account for riskiness of projects. They draw this rate from their Weighted Average Cost of Capital (WACC) and then apply it to expected future cash flows. Yet, they forecast cash flows using expected prices that are sometimes at odds with the assumptions in WACC. More specifically, the risk-premiums within the price forecasts and discount rate are of similar nature and should be compatible, but with the multitude of technical and market risks, it is not clear how to estimate these premiums. In this paper, we use the Schwartz and Smith (2000) two-factor price process and implied parameter estimation to discuss a consistent valuation framework. We determine the discount rate together with analysts' long-term prices forecasts. The suggested methodology is particularly useful in valuation of long-term capital investments.
Chairperson: Jacco Thijssen (U of York, UK)
Capitalists' Entry-Exit Investment Decisions
Discussant: Roel Nagy (Norwegian University of Science & Technology, Norway)
In this paper we develop a dynamic model for guiding Venture Capitalists (VC) on their Entry-Exit Investment Decisions. In our setting, a VC is considering an investment in a start-up which is financed along with the entrepreneur. The model accounts both for homogeneous and heterogeneous beliefs about the growth prospects of the firm, and aims to determine the optimal entry timing and the optimal ownership to be required by the VC. The exiting process is also studied. We start by considering no time restrictions about investment period, but the model is then extended to account for the imposed limited duration of the investment for the VC. The determination of the optimal exit multiple is perhaps the most valuable outcome of the model, specifically when the time restriction is in place therefore showing the value destruction that investors are subject to when limiting their investment exposure. Also, some sensitivity analysis performed allows to assess the impact of important variables on the model outcomes.
Abandonment of a Construction Project of Uncertain Duration: UK's High-speed
Discussant: Ricardo M. Ferreira (University of Porto, Portugal)
We consider a new model of optimal investment in projects with stochastic time to build. Both revenues and construction progress are assumed to follow a continuous-time stochastic process. The model is an extension of Thijssen (2015, "A model for irreversible investment with construction and revenue uncertainty", (Journal of Economic Dynamics and Control). Contrary to that model we add additional flexibility. First, the decision maker can postpone exploitation of the project once construction is finished. Secondly, the decision maker has the option to abandon construction before the project is finished. The latter source of flexibility leads to the analysis of a new, genuinely two-dimensional, constrained optimal stopping problem. We prove existence of a solution as well as several of its properties. We introduce a recursive finite difference algorithm to numerically solve this problem. We apply the model to the UK's planned high-speed rail line from London to Birmingham (HS2) and find that it does not currently represent value for money.
Options in Wind Turbines: Life-extension versus Repowering
Discussant: Jacco Thijssen (University of York, United Kingdom)
This paper analyzes the option to repower a wind turbine near the end of its life-time and compares it to the option to extend the life-time by a fixed amount of years and repower the wind turbine afterwards. We analytically derive the condition for which the wind turbine owner exercises the option for a life-time extension and repowering earlier than the option to repower. Our results indicate that lifetime-extension is more valuable than repowering for practical input values. We also found that both end-of-life options will have lower investment thresholds for wind projects with lower interest rates, making them more attractive to wind projects with long-term power contracts relative to most other projects.
Petroleum Models II
Chairperson: Marco AG Dias (PUC-Rio)
of Petroleum Reserves: Comparing Methods
Discussant: Nuran Cihangir Martin (Pontificia Universidade Catolica - PUC Rio de Janeiro, Brazil)
This paper discusses the estimative of oil reserves volume, by comparing the traditional approach based on the discounted cash flow (DCF), the probabilistic approach, and the real options approach that considers the abandonment option. In all cases, we consider both the residual value and the abandonment cost (environmental recovery costs). The traditional DCF uses expected cash flow. The probabilistic approach also uses the DCF rule, but making explicit the probabilistic scenarios and using the DCF rule in each scenario. The real option approach is also probabilistic, but considering the value of waiting before exercising the abandonment option. We use the binomial method considering the oil price uncertainty for both probabilistic and option approaches in order to evaluate both the monetary and the volume values. The option approach gives the higher economic value for the oilfield, followed by the probabilistic approach. I found that, ex-ante, the reserve volume is usually (much more) optimistic with traditional DCF than with the options approach. If we consider the options approach the most rigorous, it means that in most cases the reported reserves are optimistic (without considering future new technologies that could extend the oilfield life). However, ex-post, the use of real option approach will result in higher recoverable volume (reserves) than the DCF rule because the options approach considers the value of waiting for a better oil price before abandoning, whereas the DCF only consider the expected cash flow. For the volume calculus with abandonment option, the paper introduces the technique of pruned Pascal's triangle to access the probability of continuing to produce in any node from the binomial tree. The conclusion is that oil companies using deterministic DCF are ex-ante optimistic regarding oil reserve volume, but ex-post abandon too early the oilfields when using the DCF rule.
Oil Field Rescale: Abandoning Versus Switching to Lower-cost Technology when
Discussant: Marco Antonio Guimaraes Dias (PUC-Rio, Brazil)
A mature oil field rescale describes a switch to a technological alternative more appropriate for the depleted state of an underlying resource. Off-shore oil rigs are an illustration, since their technological scale designed for very large output flows becomes inappropriate as their operational efficiency declines later in life and facing a dwindling output flow, so a more appropriate extraction technology becomes economic. A real option representation is formulated on a stochastic oil price and deteriorating output volume. We view these investment/divestment decisions both separately, and jointly, which have different implications for government policies and also option values. The resulting model yields analytical (or semi-analytical) results indicating that immediate switching to the lower cost technology could sometimes be hastened as the price volatility increases, depending on the current revenue, if divestment and switching are considered jointly. However, greater volatility could also promote hysteresis.
Drilling Rigs and Operating Strategy: Invest, Operate, Lay-up or Scrap in
Discussant: Dean Paxson (Alliance Manchester Business School, United Kingdom)
Offshore drilling rigs are leased to oil and gas companies for the purpose of exploration and production. Independent drilling contractors owning these units often are faced with capacity utilization problems and since the oil price crash in 2014, almost half of the available capacity in the sector has been temporarily idled. Once idled, or "laid up", these assets will only be re-activated in case of a sufficient market uptick, or will be eventually abandoned by way of scrapping otherwise. Such operational decisions as well as asset valuation problem are analyzed under the real options framework in a standard four-stage entry-exit model with stochastic daily revenues. On the basis of the numerical simulations, we conclude that recent bids for asset acquisitions are under-valued. Furthermore, the level of day rates does neither support a fresh investment nor re-activation of mothballed units. Re-activation costs and liquidation value justify maintaining the units in suspension rather than exercising the option to exit.
Blockchain Certificates, Licencing & Patent Litigation
Chairperson: Elizabeth Whalley (U of Warwick, UK)
Energy Certificate Tokens in the Blockchain
Discussant: Elizabeth Whalley (University of Warwick, United Kingdom)
Renewable Energy Certificates (RECs) are instruments that provide incentives for producers to invest in clean and renewable sources of energy. On the other hand, market exchanges based on Distributed Ledger Technology such as the blockchain network protocol have some advantages over traditional exchanges, such as full transparency, low transaction costs and universal access. In this article we analyze three autonomous models for issuing and selling REC based tokens in the blockchain for the renewable energy generator. In all three models, the generator has the option to invest now or in one year for the right to issue RECs and offer them through quarterly sales auctions, considering the energy generated in one year by a single typical 4MW wind turbine. In Model I, we assume that the token price is fixed following a stable coin concept. In Model II, we consider that the price follows an inverse demand function subject to stochastic shocks. Finally, in Model III, the demand for RECs is uncertain and the purpose is to maximize the generator's profit. Through a numerical application, we verify the validity of the models and conclude, considering the parameters adopted, that the generator should invest in Model II, since it was the one with the highest NPV (US$ 60,992.70). However, if the demand volatility is less than 20%, the optimal model for the generator is Model I. The main contribution of this work is to analyze the performance dynamics of digital products under uncertainty.
Licensing and Coopetition Under Imperfect Appropriation Regime
Discussant: Naielly Marques (Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Brazil, Brazil)
We develop a model to examine the behavior of an innovator deciding on whether to license its new process technology to an incumbent rival in the face of an imperfect appropriation regime and uncertain market demand. The innovator must select its innovation effort upfront and later decide whether to license the technology to its rival and whether to propose a fixed fee or a royalty payment scheme. Firms operate in the product market after a delay when market demand uncertainty is resolved. We analyze how the degree of uncertainty and the risk of spillover from imitation impact the innovator's upfront innovation effort and the resulting coopetition strategy among the rivals.
Settlement Options and Strategies in Patent Litigation
Discussant: Benoit Chevalier-Roignant (Cranfield School of Management, United Kingdom)
We use a compound option model to investigate firms' decisions in patent litigation. The model incorporates settlement before and after filing of the lawsuit, the challenger's exit option and the incumbent's option to withdraw from litigation. We find that the challenger's profit relative to the incumbent's loss of profit (gain-to-loss ratio) is a key determinant of whether settlement occurs. The timing of settlement also depends on the relative costs of litigation and settlement. Overall, settlement is less likely for low gain-to-loss ratios, high probability of patent validity, and in more volatile product markets.
Wind & Renewable Energy
Chairperson: Luiz E Brandao (PUC-Rio, Brazil)
Effect of Price and Quantity Correlation on Wind Farm Investments
Discussant: Saul de Santana Mendonca (Universidad ESAN - Graduate Business School, Brazil)
From previous two-factor real options models (e.g., Paxson and Pinto, 2005; Armada et al., 2013), we acknowledge that the output price-quantity correlation coefficient affects significantly the value and timing of the investment (firms invest earlier the lower is the correlation coefficient). We highlight that the opposite result holds for wind energy investments. We study the price-quantity correlation mean of 14 UK wind farms over the time period between January 2003 and December 2014, and conclude that it varies significantly across wind farms (from -0.35 to 0.28). We test the correlation mean differences among the wind farms and find that some are high and statistically significant; thus, we conclude that there are wind farms located on sites which persistently exhibit higher price-quantity correlations and, therefore, ceteris paribus, are more valuable.
Option for Wind Farms: Mining Cryptocurrencies
Discussant: Alcino Azevedo (Aston Business School, United Kingdom)
Rules for long-term energy supply auction in Brazil establish that a power plant, such as wind farms, must supply its contracted energy after a period of years following the winning bid. The constructor can choose to build the energy farm ahead of schedule and sell the produced energy in the open market as an anticipation option. In this work we propose that a wind farm that is bound to supply its energy to the regulated market 5 years after winning the regulator bid, can anticipate the farm construction in up to 4 years and sell its energy produced in the highly volatile free market which might have adverse pricing in regular supply situation since the free market energy should be very low on average. But after anticipating the site construction, the constructor can have a switch option to either sell its energy produced in the free market or, after investing in a cryptocurrency mining facility, mine Bitcoins, yielding another highly volatile income. We modeled these two stochastic variables, energy and Bitcoin prices with two different stochastic processes, and results show that not only the anticipation possibility yields a considerable value to the constructor, but the described switch option from electricity to cryptocurrency significantly increases this value, although simultaneously increasing risk.
in a Renewable Energy Resources Auction in Peru as a Real Option
Discussant: Felipe Araujo (IAG Business School, Pontificia Universidade Catolica of Rio de Janeiro, Brazil)
The structure of a Renewable Energy Resource (RER) auction in Peru is similar to the structure of a composition of financial call options and involves a sequence of similar decisions associated with the aforementioned derivative financial instrument. The perspective of the use of the Real Option Theory to evaluate the strategies of the participants in these auctions is based on their similarities and allows the use of analytical models and mathematical valuation procedures developed and used in financial derivatives markets. The objective of this study was to characterize the structure of RER auctions in Peru as a composition of call options, which involves decisions regarding the payment of premiums for the acquisition of decision rights on established dates. The chosen methodology was the case study and the selected case consists of evaluating the strategy used by ENEL GREEN POWER (EGP) in the fourth RER Auction promoted by the Peruvian Government and consequent adjudication of some of its projects. Since the auction required Bid Bonds, they were characterized as Real Option Auctions, therefore real options could be used as an analogy to understand the rationality of ENEL's strategic decisions in the process. The binomial method was used to estimate the implicit volatility, which was inserted in the Black & Scholes model to calculate the option price (premium). The premium was then compared to the amount of bid bonds presented to determine whether the Real Option on participating on the auctions was above or under the theoretical price of the option.
Day 2 - Friday June 28
Corporate Finance Topics
Chairperson: Arkadiy Sakhartov (U of Illinois at Urbana-Champaigh, USA)
Due Diligence and Economies of Scope in Corporate Acquisitions
Discussant: Carlos Armando Mejia Vega (Universidad Externado de Colombia, Colombia)
This study develops a theory of due diligence in corporate acquisitions. Using a formal model, the study situates due diligence in the context of prospective economies of scope, which are often sought by corporate acquirers but about which acquirers are incompletely informed. Relatedness, the key determinant of economies of scope, and ambiguity, the key determinant of incomplete information, are used to formally derive the optimal due diligence effort and the returns to acquirers that result from that effort. The derived theoretical predictions revisit the conventional wisdom that corporate acquirers cannot be too diligent or implicit assumption that such efforts are exogenous to the transaction. The predictions can be tested in future empirical research on corporate acquisitions, and they may also guide corporate acquirers on the optimal allocation of their research effort in acquisition deals.
of Equity Investment with a Convertible Note in Second Round of Entrepreneurial
Discussant: Arkadiy Sakhartov (University of Illinois at Urbana-Champaign, United States)
Although convertible note is favourably used for the early stage start-up financing, its usage creates a complicated situation among entrepreneur, convertible note holder and new equity investor in the second-round financing negotiation. The main objective of this paper is to build a model dealing with the interactions of these three key parties. This paper aims to figure out the cost for equity investment decision-making by incorporating the real option structure of the conversion of convertible note into equity, as well as the adverse selection problem in the financing negotiation. The results of case simulation suggest that the discount and valuation cap that are accompanied with the convertible note contract have great impacts on the cost for equity investment decision-makings, and entrepreneur should consider it when entering into the financing negotiation in the second financing round.
Risk, Lender Control Rights and Embedded Options in Debt-financed
Discussant: Yasuharu Imai (University of Caen Normandy, France)
This paper presents a dynamic credit risk model for debt financing in infrastructure projects. Specifically, it attempts to combine the structural models and the Monte Carlo simulation techniques by analysing the effects of extensive control rights for lenders through covenants and embedded options, like the option to renegotiate the debt agreement conditions and the option to exit, in the estimation of expected recovery rates and the expected loss along the loan life. Hence, the model proposed by Blanc-Brude and Hasan (2016) is extended to model the dynamics of debt capacity and to estimate the probability of default. Given those conditions, the option to exit and the option to renegotiate the debt conditions are evaluated. In that sense, is shown that the embedded real options can improve the recovery rate and the risk profile.
Incentives, Responses & Switching Models
Chairperson: Stein-Erik Fleten (NTNU, Norway)
Impact of Capacity Payments on the Usage of Flexible Peaking Generators in PJM
Discussant: Lars Sendstad (NTNU, Norway)
This paper aims to study the effects of capacity payments on the operational decisions of plant managers for peaking units in the PJM Interconnection.We achieve this through a structural estimation of maintenance and switching costs between the operational state, the standby state and retirement of generating units. We have focused on the period from 2001 throughout 2016 - a period where we have identified some significant changes in the power market dynamics. We conduct a counterfactual analysis on the level of capacity payments to study the effects of introducing a capacity market in 2007. The reliability of the power system depends crucially on the availability of flexible peaking units to cover load in periods of high demand. Therefore, an understanding of the real costs facing the owners of these units is essential in order to enforce policies that ensure sufficient peak capacity in the power system. Capacity markets are introduced as a means of compensating capacity, and our study aims to analyze the effects of this additional market on switching behavior. The empirical data shows less switching between states after the introduction of capacity remunerations. We find that the role of peaking units has changed, with the units being dispatchedmore often. In the counterfactual analysis, we find a clear connection between the level of capacity payments and switching. We conclude that the current level of capacity payments in PJM incentivizes peaking units to stay in the operational state.
in a Duopoly: Understanding OPEC's Market Response to the Shale Oil Revolution
Discussant: Stein-Erik Fleten (Norwegian University of Science and Technology, Norway)
The combination of horizontal drilling and hydraulic fracturing to produce oil and natural gas has grown dramatically over the last few years taking the market by surprise with the name of "Shale Revolution". The first effects of shale revolution have been an increase of oil and gas supply, especially for US and a drop in crude oil prices in the 2014-2016. One of the remaining open question is why OPEC did not react reducing production to maintain high prices. In the literature the answer falls into three main categories: (1) OPEC tried to defend its market share by flooding the market in an attempt to drive out shale producers; (2) the shale oil revolution changed the market weights leaving the only choice to accept low prices; (3) OPEC was uncertain about the potential of shale oil and needed to test its resilience under low prices. In order to better study and understand the market strategies, we have built a real option model between leader and a follower producers.
Detection of Transition Probabilities for Optimal Investment under Regime
Discussant: Verena Hagspiel (NTNU, Norway)
To capture the dynamic evolution of economic indicators and its impact on option pricing, we develop a regime-switching, real options framework for investment under uncertainty that facilitates time-varying transition probabilities. Considering a private firm with a perpetual option to invest, we use machine-learning techniques to forecast the evolution of transition probabilities and analyse how they affect the value of an investment opportunity. Results indicate that: (a) ignoring the dynamic evolution of transition probabilities can result in severe valuation errors; and (b) when the probability of a regime switch is low, the option value is greater in the good (bad) regime under time-varying than under fixed transition probabilities.
Acquisition, Investment & Financing Strategies
Chairperson: Artur Rodrigues (U of Minho, Portugal)
of Investment and Financing Decisions with Costly Reversibility in Liquidation
Discussant: Artur Rodrigues (University of Minho, Portugal)
We examine the interaction between financing and investment decisions under the condition that debt holders have the option of maximizing the debt-collection amount if a firm is liquidated during financial distress. We add to the literature by incorporating debt holders' optimization considerations related to the debt-collection amount. We show that if the debt-collection amount increases ex post when the firm is liquidated, the firm increases the amounts of debt issuance and investment quantity ex ante, delaying the corporate investment. This relationship is based on the fact that an increase in the debt-collection amount decreases the credit spread of debt holders. These results fit well with those of existing empirical studies.
Timing and Debt Ratio in Leveraged Buyouts
Discussant: Takashi Shibata (Tokyo Metropolitan University, Japan)
We investigate the optimal timing for acquiring a target firm and the optimal capital structure of the new firm in a leveraged buyout (LBO) transaction using a real options model. Furthermore, we examine the case in which the target firm changes its capital structure by issuing bonds by itself. We compare the latter firm's capital structure to the capital structure in the LBO case and show that the leverage ratio of the LBO firm is higher.
Ownership (Toehold) M&A Strategies and Dynamic Games
Discussant: Makoto Goto (Hokkaido University, Japan)
In this paper we show how a toehold held by a bidder can be an effective strategy for inducing a target to accept a hostile bid. We suggest a new explanation for the benefits of using a toehold. By considering both friendly mergers and hostile takeovers as alternative M&A strategies, we show that a toehold enhances the bargaining power of the bidder, inducing the target to be more prone to accept a hostile bid. We show that toehold hostile takeovers require sufficiently large synergies to become preferable over toehold friendly mergers. Uncertainty may have an ambiguous effect on the strategy choice. In general, a higher toehold lowers the required synergies. Larger bidders tend also to be more prone to enter in hostile deals. Accordingly, toeholds can be used to overcome possible size disadvantages of bidders, suggesting that larger firms need less to use toeholds to succeed in hostile takeovers.
Chairperson: Neopytos Lambertides (Cyprus U of Technology)
of Finite Project Life and Option Duration on the Timing and Size of Capacity
Discussant: Julian Kaboth (HHL Graduate School of Management Leipzig, Germany)
The literature on real investment in general departs from two assumptions. First, it is assumed that the project length is infinite, i.e. the firm produces forever after the investment has been undertaken. Second, the option to invest exists forever. This paper relaxes both assumptions. In a monopoly setting we find that, in case the inverse demand function linearly depends on a Geometric Brownian Motion process, a reduction of the project length delays the investment time whereas the investment size is not affected. Having a finite life of the investment option, caused for instance by technological progress making the product obsolete, accelerates investment whereas the investment size is reduced. We also investigate the effect of relaxing these two assumptions on the investment decisions of firms in a duopoly setting.
Effort Allocation and R&D Investment Life-cycle
Discussant: Anne Balter (Tilburg University, Netherlands)
We introduce a two-step model to study the investment dynamics of R&D. Entrepreneurs follow a sequential game: first, they decide how to allocate effort towards short-term assets and a long-term R&D project; second, they decide the optimal timing to invest in the R&D project. Our model endogenously shows that the investment decision, in non-extreme events, is state-dependent so that it provides an additional explanation for the cyclical nature of R&D investment. This life-cycle hypothesis explains why firms tend to invest less in R&D as they mature. We then study which factors govern this hypothesis. We find that uncertainty amplifies the life-cycle hypothesis which corroborates the evidence that the life-span of firms operating in volatile industries is shorter than for firms in less volatile industries. We also retrieve that the effort allocation decision smooths out the positive relationship between the investment trigger and market uncertainty. We conclude that one-dimensional investment real options models exaggerate the influence of uncertainty in the investment trigger, by ignoring the role of the effort allocation decision. We then analyze individually how the quality of the innovation, technical uncertainty and the managing skills of entrepreneurs affect both the effort allocation and the investment decision, as well as its influence on the life-cycle hypothesis. These conclusions spawn important policy implications on how can firms try to counter the life-cycle trap.
Exit Claims and Skewed Returns in Venture Capital Investments
Discussant: Paulo J. Pereira (Faculdade de Economia, Universidade do Porto, Portugal)
Venture capital often involves complex equity contracts, which affect the allocation of cash flows among shareholdings at an exit liquidation. To facilitate economic impact analysis, we structure exit relevant preferential rights by their economic impact in a two-dimensional framework. Based hereon, we provide a model that allows to assess ex-ante value of such shares. We apply our model to a selected sample of ventures and find an average overvaluation on a share class basis of 22.1% (median 23.9%), where overvaluation is particularly severe for common and early-on investments.
Christoph Loch (U of Cambridge)
Investment Characteristics & Processes
Chairperson: Dean Paxson (U of Manchester, UK)
Upfront versus Staged Investment under a Production Cap
Discussant: Fredrik Armerin (KTH, Sweden)
An upper production limit is incorporated as a cap in a real-option formulation for investigating the conditions favouring a lumpy single-stage investment versus a flexible consecutive two-stage variant. Although having no effect on the investment threshold and timing decision unless the cap is breached, the production cap deflates the investment option value evaluated in the absence of any cap and consequently influences the lumpy-flexible choice. Also, the cap disengages the accepted positive link between volatility and option value, since for volatilities above a certain level, the option value declines with increasing volatility in the presence of a cap. We demonstrate that a flexible as opposed to a lumpy investment policy can be more attractive and sometimes significantly so.
with Decreasing Cost due to Technological Innovation Improvements
Discussant: Roger Adkins (University of Bradford, United Kingdom)
In this paper we address, in the context of real options, an investment problem with two sources of uncertainty: the price (reflected in the revenue of the firm) and the level of technology. The level of technology impacts in the investment cost, that decreases when there is a technology innovation. The price follows a geometric Brownian motion, whereas the technology innovations are driven by a Poisson process. As a consequence, the investment region may be attained in a continuous way (due to an increase of the price) or in a discontinuous way (due to a sudden decrease of the investment cost). For this optimal stopping problem no analytical solution is known, and therefore we propose a quasi-analytical method to find an approximated solution that preserves the qualitative features of the exact solution. This method is based on a truncation procedure and we prove that the truncated solution converges to the solution of the original problem. We provide results for the comparative statics for the investment thresholds. These results show interesting behaviors, particularly, the investment may be postponed or anticipated with the intensity of the technology innovations and with their impact on the investment cost.
Investment with Varying Risk Premia
Discussant: Claudia Nunes (IST and CEMAT, Portugal)
We consider a model where the risk premium is varying. The risk premium is driven by a continuous time Markov chain, representing the state in the economy, and the stochastic process generating the cash flows is a Markov-modulated geometric Brownian motion. An existing firm is facing the possibility of competitors entering the market, and due to this, cash flows are limited at levels which are dependent on the state of the economy. This results in a regulated Markov-modulated geometric Brownian motion, and the resulting accumulated supply can have jumps, something that is not possible in a model with only one regime.
Capacity Investment & Competition
Chairperson: Richard Ruble (EMLYON, France)
Capital Divisibility and Competitive Preemption with Endogenous Sunk Cost
Discussant: Xingang Wen (Universitat Bielefeld, Germany)
Greater divisibility allows a firm to maintain a rival on the brink of entry by accumulating capital gradually so as to enter the product market at a time which is both a myopic optimum and a preemptive equilibrium. This conduct is both the optimal policy of a firm that regulates its rival's entry threat through incremental capital accumulation and the limit of equilibrium outcomes of asymmetric preemption as investment steps become arbitrarily small. If the price of capital follows a stochastic process greater volatility delays the firm's jump to completion so option value overrides the strategic investment motive. An emblematic historical example of strategic commitment is discussed in light of this analysis.
Timing and Capacity Decisions with Time-to-Build in a Duopoly Market
Discussant: Richard Ruble (emlyon business school and GATE-LSE (CNRS), France)
We investigate firms' optimal decisions of investment timing and capacity in the presence of time-to-build and competition. Because of uncertainty in time-to-build, the product of the leader which makes the investment first might enter the market later than the follower's one. We show that a firm dominated in terms of investment lags can become a leader and that the leader's optimal capacity increases in the size of the dominated firm's lags, even when the dominated one becomes the leader. This result is consistent with electric vehicles market in which a relatively new firm lacking in the experience of mass production makes aggressive investment, while the biggest car makers capable of mass production with shorter lags are timing their investment. With welfare-maximizing policy, however, the dominant firm always becomes the leader. Comparing with investments chosen by welfare-maximizing policy, those of the leader and the follower chosen in the market are made inefficiently late and early, respectively. The welfare-maximizing capacities of both the leader and the follower are much higher than those determined in the market but the difference is more pronounced in the leader's capacity. There is a significant loss of social welfare resulting from the dominated firm becoming the leader, and the loss increases as the dominated firm's time-to-build gets longer.
Capacity Investment with Output Flexibility
Discussant: Haejun Jeon (Osaka University, Japan)
This article considers investment decisions in an uncertain and competitive framework, with a first investor, the leader, always producing up to full capacity (dedicated) and a second investor, the follower, being able to adjust output levels within constraint of the installed capacity (flexible). Both firms need to decide on the investment timing and investment capacity size. The main findings are as follows. Compared to a situation where the follower always produces up to full capacity, the leader has a larger incentive to accommodate a flexible follower. This is because the leader also benefits from the follower's volume flexibility. Due to the first mover advantage, the leader's value is higher than the follower's value, despite the follower's technological advantage in flexibility. Moreover, this paper also tries to analyze the preemption between the flexible and the dedicated firm in a competitive framework.
Investment, Debt, Credit & Financial Constraints
Chairperson: Lenos Trigeorgis (King's College London & U of Cyprus)
Investment Timing, Capacity and Debt Policy for a Financially Constrained
Discussant: Nicos Koussis (Frederick University, Cyprus)
This paper considers the investment strategy of an entrant that is financially constrained, i.e. it requires to issue debt. We find the optimal investment moment for the firm in an environment with market uncertainty and bankruptcy risk as well as the optimal production capacity. In addition, the optimal debtholder policy is determined. The effect of debt financing on the investment strategy, total welfare, and the debtholder policy is studied.
Flexibility under Financial Constraints
Discussant: Nick Huberts (University of York, United Kingdom)
We develop the notion of outsourcing as providing flexibility overcoming financial constraints and provide empirical evidence concerning the role of flexibility on the likelihood and value of outsourcing. The results show that the likelihood of outsourcing is higher, the greater the firm's financial constraints before outsourcing (or the less its financial flexibility). The effect of financial flexibility on the probability of outsourcing is greater, the lower the ex-ante operational flexibility, implying substitutability between financial and operational flexibility. We also find that the market valuation of outsourcing announcements is positive due to net flexibility gains and that such ex post valuation is positively related to ex ante financial constraints. Our findings are consistent with the notion that outsourcing is a vehicle for flexibility acquisition and that financial constraints play a prominent role in such acquisition.
Bank Credit Line under Heterogeneous Risk Beliefs
Discussant: Ming Ju (Louisiana Tech University, United States)
We study a firm with multistage investment options and a bank providing a commitment for financing using a credit line. We consider possible differences in beliefs between equity holders and the bank about the risk of assets before agreeing on the provided credit line and show that unfavorable beliefs by the bank reduce credit line capacity and lead to underinvestment. Constraints on alternative sources of financing cause firms to rely more heavily on bank credit lines even when facing unfavorable beliefs by the bank about the risk of assets. Higher loan commitment fees charged by the bank on the unused portion of the credit line accelerate initial investment but may reduce follow-on investment and use of the credit line. Our analysis examines the optimal choice between accelerated versus sequential investment and provides predictions on the optimal credit line drawdown activity used to finance these investments.
Human Capital, Signaling & Preemption Games
Chairperson: Hamed Ghoddusi (Stevens Institute of Technology, USA)
Investment in Human Capital and Brain Drain under Migration Uncertainty
Discussant: Oana Ionescu (GAEL, G2ELab, Grenoble INP CNRS, INRA, Univ. Grenoble-Alpes, France)
This paper develops a model of optimal education investment of an agent who has an option to emigrate. We distinguish between local and global human capital in a stochastic dynamic framework of optimal human capital investment. We analyze the time evolution of human capital in the source country and investigate the role of migration opportunities in the accumulation of different types of human capital. The analysis shows that the accumulation of human capital depends crucially on the level of uncertainty and the transferability of human capital across countries. Government subsidies are an important determinant of the composition of different types of human capital and can be crucial in alleviating the brain drain problem.
Signaling Game of Equity Financing under Information Asymmetry
Discussant: Hamed Ghoddusi (Stevens Institute of Technology, United States)
We develop the real option signaling game models of equity financing of a risky project under asymmetric information, where the firm quality is known to the firm management but not outside investors. Unlike the usual assumption of perpetuity of investment, we assume that the time window of the investment opportunity has a finite time horizon. The firm chooses the optimal time to issue equity to raise capital for the investment project. The number of shares of equity issued to fund the project depends on the outside investors' belief on the firm quality. The low-type firm has the incentive to sell overpriced securities through mimicking the investment strategy of the high-type firm in terms of investment timing and number of equity shares. On the other hand, the high-type firm may adopt the separating strategy by imposing mimicking costs on the low-type firm. We examine the incentive compatibility constraints faced by the firm under different quality types and discuss characterization of separating and pooling equilibriums. We also explore how the separating and pooling equilibriums evolve over the time span of the investment opportunity. The information costs and abnormal returns exhibit interesting time dependent behaviors, in particular, at time close to expiry of the investment opportunity.
Strategy: Gazprom and the Threat of US LNG Mass Entry in Europe
Discussant: Qiuqi Wang (Hong Kong University of Science and Technology, Hong Kong)
This article examines the extent to which Russia could delay a massive entry of US LNG into Europe by using its spare capacity on the European spot gas market. With a real option-game model with one-sided incomplete information and characterized by the presence of an historical gas supplier and a potential entrant, we show that the flexibility offered by the spare capacity may delay the entry of a new competitor.
Day 3, Saturday June 29
Chairperson: Tarik Driouchi (King's College London, UK)
Role of Correlation in Choosing Output Price and Production Cost Combination
for Optimal Investment
Discussant: Mingyu (Chandler) Chen (Lancaster University, United Kingdom)
Often, firms can choose among different combinations of price and cost processes. For example, they can choose between different production locations or technologies, between different products to produce, or between different locations to sell them. To study the choice of the optimal combination, we return to the Dixit and Pindyck (1994) model where both output price and production cost are stochastic processes, and add a novel focus on how the correlation between these processes affects the firm's decision. We find that, ceteris paribus, the firm prefers the combination with the lowest correlation between the processes, as it seeks a greater profitability variance which maximizes its value.
Project Upgrade and Product Switching under Uncertainty: Balancing Risk and
Discussant: Yishay Maoz (The Open University of Israel, Israel)
We consider a firm that is currently producing an established product subject to a stochastic environment. The firm has the one-time opportunity to undertake an irreversible investment to switch to a new product, which changes the drift and volatility of the firm's underlying stochastic profit flow. We show that it is optimal to invest in the new product if an increase in the expected growth outweighs the increase in risk from switching. We find that the effect of uncertainty on the optimal investment strategy is not straightforward. The overall effect of uncertainty is determined by the interplay between the value of waiting and the effect of Jensen's inequality. Contrary to the standard real options result, that higher uncertainty delays investment, we show that an increase in volatility in the old market can both accelerate or delay the investment. We perform an analysis of the antecedents of this non-monotonic effect of uncertainty, and provide extensive economical reasoning for the results. Further, we show that an investment opportunity with changing characteristics of the stochastic environment and constant profit function, can be transformed to a case of changing profit function and constant parameters of the stochastic process.
Accuracy and Explainability of Accounting-based (Non)Linear Equity Valuation
Discussant: Tord Olsen (Norwegian University of Science and Technology, Norway)
We examine the forecast accuracy and explainability of landmark linear accounting-based equity valuation models (Ohlson, 1995; Feltham and Ohlson, 1995, 1996) and non-linear accounting-based valuation models with real options components (Hwang and Sohn, 2010; Ashton et al. 2003; Zhang, 2000) using historical data for the UK. Empirical results show that non-linear equity valuation models with real options characteristics provide higher forecast accuracy and stronger explainability than linear equity valuation counterparts. More specifically, we utilize the Hwang and Sohn (2010) real option adjustment in the Ohlson and Feltham framework and find the adjusted models perform better in terms of accuracy and explainability than the underlying linear models. We also find superior performance for the valuation models of Ashton et al. (2003) and Zhang (2000) and further demonstrate that this improvement in performance is due to their option characteristics. Our conclusions hold in an alternative dataset of U.S-listed firms.
Chairperson: Motoh Tsujimura (Doshisha U, Japan)
Credit Contract Design and Regulation
Discussant: Hidekazu Yoshioka (Shimane University, Japan)
This paper provides a theoretical analysis of trade credit within a real options framework. We show that under trade credit the buyer delays the decision to stop, getting closer to the supply chain optimal stopping threshold. Therefore, trade credit serves as a coordination device. Moreover, we show that the supplier can optimally choose to offer trade credit for free, since this will guarantee her business for a longer period of time. Optimal trade credit design is analyzed for an integrated supply chain (cooperative solution) and for external procurement (Nash bargaining and Stackelberg solutions). When regulation imposes a limit on trade credit maturity, we show that the two parties, buyer and supplier, might have difficulties in undoing regulation, despite the complementarity between price discount and trade credit. The model's predictions are in line with recent empirical evidence on the effects of regulation in the retail and trucking industry.
Boundary Fitting in Real Option Valuation of Complex Mining Investments
Discussant: Franck Moraux (Univ Rennes, CNRS, CREM – UMR6211, France)
Real option analysis is recognized as a superior method to quantify the value of real-world investment opportunities where managerial flexibility can influence their worth, as compared to standard discounted cash-flow methods typically used in industry. However, realistic models that try to account for a number of risk factors can be mathematically complex, and in situations where many future outcomes are possible, many layers of analysis may be required. The focus of this research is the development of a real options valuation methodology geared towards practical use with mining valuation as a context. A key innovation of the methodology to be presented is the idea of fitting optimal decision making boundaries to optimize the expected value, based on Monte Carlo simulated stochastic processes that represent important uncertain factors. Our specific emphasis in this work will be to explore theoretical / numerical aspects associated with the simulation methodology as they pertain to 1) a Bermudan put option, 2) a Bermudan-like option with variable strike price, 3) an American put option and 4) a build / abandon real option example.
Optimal Control Subject to Ambiguous Jump Intensity
Discussant: Yuri Lawryshyn (Univeristy of Toronto, Canada)
A model problem on optimal control of stochastic jump-driven systems subject to an ambiguous jump intensity is considered. The problem is formulated on the basis of the multiplier-robust control whose resolution reduces to solving a Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation with a term that is nonlinear and nonlocal. Mathematical analysis focusing on this term is carried out in this paper. We show that the equation admits a unique continuous viscosity solution: the value function. Furthermore, we present a convergent finite difference scheme that can numerically handle the equation, generating numerical solutions consistent with the mathematical analysis results.
Best Student Papers Session
Chairperson: Stein-Erik Fleten (NTNU, Norway)
Capital Structure with Illiquidity and Over-indebtedness: Theory and Evidence
Discussant: Zhou Zhang (Warwick Business School, University of Warwick, United Kingdom)
Existing dynamic capital structure models are based on single triggers determining bankruptcy, mainly over-indebtedness or illiquidity. The latter one tends to underestimate optimal capital structures by ignoring capital providers' flexibility to inject fresh money. The former one leans towards overestimation as it neglects agency conflicts between equity investors and debt holders while implying infinitely "deep pockets" of equity investors. This article incorporates both constraints, over-indebtedness and illiquidity, examining corporate debt value and optimal capital structure in a double barrier world with knock-in and knock-out options. We are first to derive closed-form solutions for all value components of a levered firm and for the optimal capital structure in such a setting. By testing our model for firms publicly listed in the US, we gain evidence that incorporating both triggers allows for capital structure estimations that are in accordance with empirical findings.
Policies and Internal Governance with Heterogeneous Risk Preferences
Discussant: Tim Kutzker (University of Cologne, Germany)
We consider a group of investors with heterogeneous risk preferences that determines a firm's investment policy, and each investor's compensation function. The optimal investment policy is a time-varying weighted average of investors' optimal policies and converges to the policy of the least (most) risk averse investor in booms (busts), reconciling the diversification of opinions hypothesis and the group shift hypothesis. The most (least) risk averse investor has a strictly concave (convex) claim on the firm's net worth. For intermediate risk preferences investors' claim is S-shaped, resembling preferred stock. We derive investors' utility weights absent wealth distribution and under social optimization.
Order and Timing of Entry in Duopoly
Discussant: Shiqi Chen (University of Cambridge, United Kingdom)
We incorporate optimism about future growth prospects into a real-options duopolistic setting and show that an optimistic firm will enter earlier than an otherwise identical non-optimistic competitor but at a higher threshold than if neither firm were optimistic. More generally, optimism can change entry order: a more optimistic firm may enter first even if its competitor has higher monopoly and duopoly revenues and lower costs (as long as the difference is not too great). Optimism can thus compensate for competitive advantage in costs and revenues in determining entry order. Furthermore, in contrast to the impact of optimism in non-competitive settings where investment thresholds decrease with optimism, an optimistic firm's entry thresholds as a leader in duopolistic competition when it needs to enter pre-emptively increase with the firm's optimism.
Business Planning Models
Chairperson: Makoto Goto (Hokkaido U, Japan)
Business Planning with Optimal Portfolio, Consumption and Exit Decisions
Discussant: Makoto Goto (Hokkaido U, Japan)
This paper presents an entrepreneurial optimal business plan in which optimal consumption and portfolio rules, and optimal exit strategy for an entrepreneur are jointly determined in the presence of undiversifiable idiosyncratic risk. We find that the entrepreneur is more likely to exit from her risky business as investment opportunity worsens or as her risk aversion coefficient increases or as the idiosyncratic risk increases. When the entrepreneur decumulates wealth, she can achieve a partial hedging effect of a risky portfolio against the business risk by optimally increasing her risky portfolio as the idiosyncratic risk increases. Accordingly, stock market participation is of importance to the entrepreneur for the purpose of risk diversification and a smooth continuation of her risky business.
Demand Forecast and Real Options Valuation: The Case of Crude Oil Production
Discussant Seyoung Park (Loughborough University, United Kingdom)
In this paper, we propose a risk-neutral multi-factors stochastic model for commodity demand. The model estimation is able to incorporate information from demand historical time series as well as market prices of commodity financial derivatives. Then, the risk-neutral model is applied to the case study of crude oil commodity. Inspired from the empirical literature, we consider a two factors model for the demand dynamic. The factors are the commodity spot price and the real per capita gross domestic product. The factors coefficients are estimated using historical series. Furthermore, the risk-neutral model of crude oil spot price is calibrated on derivatives prices quoted in the market (Futures and options on crude oil). Finally, we apply the risk-neutral demand dynamic to a real project valuation, e.g. a crude oil production plant. We assess the optimal operating capacity and the maximally expected profit of the production plant. Moreover, we evaluate the expected profit of the plant, considering an option of expansion and its optimal timing. In the real option valuation, we assess the impact of adopting average type options and we compare different risk neutral price/demand dynamics (e.g. diffusive and jump-diffusive processes) and different plausible values of the factors coefficients.
Impact of Volatility on Option Prices: Case of Managerial Compensation with
Discussant: Anna Maria Gambaro (Universita del Piemonte Orientale, Italy)
We provide general results regarding the impact of volatility on option prices (i.e., Vega). Contrary to what is widely believed and taught, we show that the price of a large class of options is non-monotonic with respect to volatility: the value first increases but eventually decreases with the volatility. This seemingly counter-intuitive proposition is driven by a particular feature of Martingale processes bounded from below (including the Geometric Brownian Motion (GBM) and the CIR processes). We show that in such processes a higher variance parameter may reduce the probably mass of realizations above the expected value. When the volatility approaches infinity, the probability of hitting a barrier above the mean goes to zero. As a real-world case, we apply the results to managerial compensation in the presence of risk shifting. We show that risk-shifting can be mitigated by concavifying option-like components of managers' compensation scheme.
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