Real Option Games with R&D and Learning Spillovers

We model pre-investment R&D decisions in the presence of spillover effects in an option pricing framework with analytic tractability. Two firms face two decisions that are solved for interdependently in a two-stage game. The first-stage decision is: what is the optimal level of coordination (optimal policy/technology choice)? The second-stage decision is: what is the optimal effort for a given level of the spillover effects and the cost of information acquisition? The framework is extended to a two-period stochastic game with (path-dependency inducing) switching costs that make strategy revisions harder. Strategy shifts are easier to observe in more volatile environments.Benefit Analysis; Real Options; Coordination Games; R&D

Assessing the performance of symmetric and assymetric implied volatility functions

This study examines several alternative symmetric and asymmetric model specifications of regression-based deterministic volatility models to identify the one that best characterizes the implied volatility functions of S&P 500 Index options in the period 1996–2009. We find that estimating the models with nonlinear least squares, instead of ordinary least squares, always results in lower pricing errors in both in- and out-of-sample comparisons. In-sample, asymmetric models of the moneyness ratio estimated separately on calls and puts provide the overall best performance. However, separating calls from puts violates the put-call-parity and leads to severe model mis-specification problems. Out-of-sample, symmetric models that use the logarithmic transformation of the strike price are the overall best ones. The lowest out-of-sample pricing errors are observed when implied volatility models are estimated consistently to the put-call-parity using the joint data set of out-of-the-money options. The out-of-sample pricing performance of the overall best model is shown to be resilient to extreme market conditions and compares quite favorably with continuous-time option pricing models that admit stochastic volatility and random jump risk factors

Artificial Neural Network Enhanced Parametric Option Pricing

In this paper we explore ways that alleviate problems of nonparametric (artificial neural networks) and parametric option pricing models by combining the two. The resulting enhanced network model is compared to standard artificial neural networks and to parametric models with several historical and implied parameters. Empirical results using S\&P 500 index call options strongly support our approach.Option pricing, implied volatilities, implied parameters, artificial neural networks, optimization

Real Option Games with R&D and Learning Spillovers

We model pre-investment R&D decisions in the presence of spillover effects in an option pricing framework with analytic tractability. Two firms face two decisions that are solved for interdependently in a two-stage game. The first-stage decision is: what is the optimal level of coordination (optimal policy/technology choice)? The second-stage decision is: what is the optimal effort for a given level of the spillover effects and the cost of information acquisition? The framework is extended to a two-period stochastic game with (path-dependency inducing) switching costs that make strategy revisions harder. Strategy shifts are easier to observe in more volatile environments

Real Option Games with R&D and Learning Spillovers

We model pre-investment R&D decisions in the presence of spillover effects in an option pricing framework with analytic tractability. Two firms face two decisions that are solved for interdependently in a two-stage game. The first-stage decision is: what is the optimal level of coordination (optimal policy/technology choice)? The second-stage decision is: what is the optimal effort for a given level of the spillover effects and the cost of information acquisition? The framework is extended to a two-period stochastic game with (path-dependency inducing) switching costs that make strategy revisions harder. Strategy shifts are easier to observe in more volatile environments

Subsidies for Renewable Energy Facilities under Uncertainty

YesWe derive the optimal investment timing and real option value for a facility with price and quantity uncertainty, where there might be a government subsidy proportional to production quantity. Where the subsidy is proportional to the multiplication of the price and quantity, dimensionality can be reduced. Alternatively, we provide quasi-analytical solutions for different quantity subsidy arrangements: permanent (policy is certain); retractable; suddenly permanent; and suddenly retractable. Whether policy uncertainty acts as a disincentive for early investment depends on the type of subsidy arrangement. The greatest incentive for early investment is an actual retractable subsidy, a ‘flighty bird in hand’

Numerical valuation of two-asset options under jump diffusion models using Gauss-Hermite quadrature

In this work a finite difference approach together with a bivariate Gauss-Hermite quadrature technique is developed for partial-integro differential equations related to option pricing problems on two underlying asset driven by jump-diffusion models. Firstly, the mixed derivative term is removed using a suitable transformation avoiding numerical drawbacks such as slow convergence and inaccuracy due to the appearance of spurious oscillations. Unlike the more traditional truncation approach we use 2D Gauss-Hermite quadrature with the additional advantage of saving computational cost. The explicit finite difference scheme becomes consistent, conditionally stable and positive. European and American option cases are treated. Numerical results are illustrated and analyzed with experiments and comparisons with other well recognized methods.This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economía y Competitividad Spanish grant MTM2013-41765-P

Rivalry and uncertainty in complementary investments with dynamic market sharing

We study the effects of revenue and investment cost uncertainty, as well non- preemption duopoly competition, on the timing of investments in two complementary inputs, where either spillover-knowledge is allowed or proprietary-knowledge holds. We find that the ex-ante and ex-post revenue market shares play a very important role in firms’ behavior. When competition is considered, the leader’s behavior departs from that of the monopolist firm of Smith (Ind Corp Change 14:639–650, 2005). The leader is justified in following the conventional wisdom (i.e., synchronous investments are more likely), whereas, the follower’s behavior departs from that of the conventional wisdom (i.e., asynchronous investments are more likely)