A Discrete Time Approach for Modeling Two-Factor Mean-Reverting Stochastic Processes

Two-factor stochastic processes have been developed to more accurately describe the intertemporal dynamics of variables such as commodity prices. In this paper we develop an approach for modeling these types of stochastic processes in discrete time as two-dimensional binomial sequences. This approach facilitates the numerical solution of dynamic optimization problems such as investment decision making under uncertainty and option valuation related to commodities. We implement this approach in a two-dimensional lattice format, apply it to two hypothetical valuation problems discussed by Schwartz and Smith, and compare the results to those from simulation-and dynamic-programming-based methods.

[1]  R. C. Merton,et al.  Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[2]  W. J. Hahn,et al.  Flexibility as a source of value in the production of alternative fuels: The ethanol case , 2009 .

[3]  James S. Dyer,et al.  Using Binomial Decision Trees to Solve Real-Option Valuation Problems , 2005, Decis. Anal..

[4]  Hua He,et al.  Convergence from Discrete to Continuous Time Contingent Claims Prices , 1990 .

[5]  Sebastian Jaimungal,et al.  Levy Based Cross-Commodity Models and Derivative Valuation , 2011, SIAM J. Financial Math..

[6]  Evis Këllezi,et al.  Valuing Bermudan options when asset returns are Lévy processes , 2004 .

[7]  San-Lin Chung,et al.  Generalized Cox-Ross-Rubinstein Binomial Models , 2007, Manag. Sci..

[8]  Kumar Muthuraman,et al.  American Options Under Stochastic Volatility , 2007, Oper. Res..

[9]  John C. Hull,et al.  Numerical Procedures for Implementing Term Structure Models II , 1994 .

[10]  Les Clewlow,et al.  Implementing derivatives models , 1998 .

[11]  R. Raz,et al.  Response to Comments on , 2012, Journal of child neurology.

[12]  Chung-Li Tseng,et al.  A Framework Using Two-Factor Price Lattices for Generation Asset Valuation , 2007, Oper. Res..

[13]  R. Maller,et al.  A MULTINOMIAL APPROXIMATION FOR AMERICAN OPTION PRICES IN LÉVY PROCESS MODELS , 2006 .

[14]  P. Boyle.  A Lattice Framework for Option Pricing with Two State Variables , 1988, Journal of Financial and Quantitative Analysis.

[15]  Patrick Jaillet,et al.  Valuation of Commodity-Based Swing Options , 2004, Manag. Sci..

[16]  James E. Smith,et al.  Alternative Approaches for Solving Real-Options Problems: (Comment on Brandão et al. 2005) , 2005, Decis. Anal..

[17]  H. Jacoby,et al.  Reversion, Timing Options, and Long-Term Decision-Making , 1993 .

[18]  S. Ross,et al.  Option pricing: A simplified approach☆ , 1979 .

[19]  Francis A. Longstaff,et al.  Valuing American Options by Simulation: A Simple Least-Squares Approach , 2001 .

[20]  Eduardo S. Schwartz.  The stochastic behavior of commodity prices: Implications for valuation and hedging , 1997 .

[21]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[22]  Eduardo S. Schwartz,et al.  Short-Term Variations and Long-Term Dynamics in Commodity Prices , 2000 .

[23]  James E. Smith,et al.  Valuing Risky Projects: Option Pricing Theory and Decision Analysis , 1995 .

[24]  Sebastian Jaimungal,et al.  Asymptotic Pricing of Commodity Derivatives using Stochastic Volatility Spot Models , 2008 .

[25]  Alan G. White,et al.  One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities , 1993, Journal of Financial and Quantitative Analysis.

[26]  H. Bessembinder,et al.  Mean Reversion in Equilibrium Asset Prices: Evidence from the Futures Term Structure , 1995 .

[27]  M. Subrahmanyam,et al.  Multivariate Binomial Approximations for Asset Prices with Non-Stationary Variance and Covariance Characteristics , 1995 .

[28]  Eduardo S. Schwartz.  Valuing Long-Term Commodity Assets , 1998 .

[29]  A. Robert,et al.  HAUGEN, . The New Finance: The Case against Efficient Markets (Englewood Prentice Hall. , 1995 .

[30]  Daniel B. Nelson,et al.  Simple Binomial Processes as Diffusion Approximations in Financial Models , 1990 .

[31]  Eduardo S. Schwartz,et al.  Stochastic Convenience Yield and the Pricing of Oil Contingent Claims , 1990 .

[32]  James S. Dyer,et al.  Discrete time modeling of mean-reverting stochastic processes for real option valuation , 2008, Eur. J. Oper. Res..

[33]  James S. Dyer,et al.  Response to Comments on Brandão et al. (2005) , 2005, Decis. Anal..

[34]  Michael Reiter.  Solving higher-dimensional continuous-time stochastic control problems by value function regression , 1999 .

[35]  D. W. Stroock,et al.  Multidimensional Diffusion Processes , 1979 .