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Multivariate Binomial Approximations for Asset Prices with Nonstationary Variance and Covariance Characteristics

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  • Ho, Teng-Suan
  • Stapleton, Richard C
  • Subrahmanyam, Marti G

Abstract

In this article, we suggest an efficient method of approximating a general, multivariate log-normal distribution by a multivariate binomial process. There are two important features of such multivariate distributions. First, the state variables may have volatilities that change over time. Second, the two or more relevant state variables involved may covary with each other in a specified manner, with a time-varying covariance structure. We discuss the asymptotic properties of the resulting processes and show how the methodology can be used to value a complex, multiple exercisable option whose payoff depends on the prices of two assets. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Suggested Citation

  • Ho, Teng-Suan & Stapleton, Richard C & Subrahmanyam, Marti G, 1995. "Multivariate Binomial Approximations for Asset Prices with Nonstationary Variance and Covariance Characteristics," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1125-1152.
    • Handle: RePEc:oup:rfinst:v:8:y:1995:i:4:p:1125-52
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    Cited by:

    1. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York.
    2. Rosenberg, Joshua V., 1998. "Pricing multivariate contingent claims using estimated risk-neutral density functions," Journal of International Money and Finance, Elsevier, vol. 17(2), pages 229-247, April.
    3. Peterson, Sandra & Stapleton, Richard C. & Subrahmanyam, Marti G., 2003. "A Multifactor Spot Rate Model for the Pricing of Interest Rate Derivatives," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(4), pages 847-880, December.
    4. Viral V. Acharya & Jennifer N. Carpenter, 2002. "Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy," The Review of Financial Studies, Society for Financial Studies, vol. 15(5), pages 1355-1383.
    5. Chuang-Chang Chang & Jun-Biao Lin & Wei-Che Tsai & Yaw-Huei Wang, 2012. "Using Richardson extrapolation techniques to price American options with alternative stochastic processes," Review of Quantitative Finance and Accounting, Springer, vol. 39(3), pages 383-406, October.
    6. Warren J. Hahn & James S. Dyer, 2011. "A Discrete Time Approach for Modeling Two-Factor Mean-Reverting Stochastic Processes," Decision Analysis, INFORMS, vol. 8(3), pages 220-232, September.
    7. R.C. Stapleton & Marti G. Subrahmanyam, 1999. "The Term Structure of Interest Rate-Futures Prices," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-045, New York University, Leonard N. Stern School of Business-.
    8. Hahn, Warren J. & Dyer, James S., 2008. "Discrete time modeling of mean-reverting stochastic processes for real option valuation," European Journal of Operational Research, Elsevier, vol. 184(2), pages 534-548, January.
    9. Hennessy, David A., 2011. "Modeling Stochastic Crop Yield Expectations with a Limiting Beta Distribution," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 36(1), pages 1-15, April.
    10. Dirk Sierag & Bernard Hanzon, 2018. "Pricing derivatives on multiple assets: recombining multinomial trees based on Pascal’s simplex," Annals of Operations Research, Springer, vol. 266(1), pages 101-127, July.
    11. Yoram Landskroner & Alon Raviv, 2008. "The valuation of inflation‐indexed and FX convertible bonds," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(7), pages 634-655, July.
    12. Sandra Peterson & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "The Valuation of American-Style Swaptions in a Two-factor Spot-Futures Model," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-078, New York University, Leonard N. Stern School of Business-.
    13. Andrea Gamba & Lenos Trigeorgis, 2007. "An Improved Binomial Lattice Method for Multi-Dimensional Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 453-475.
    14. Dong Zou & Pu Gong, 2017. "A Lattice Framework with Smooth Convergence for Pricing Real Estate Derivatives with Stochastic Interest Rate," The Journal of Real Estate Finance and Economics, Springer, vol. 55(2), pages 242-263, August.
    15. Ho, T. S. & Stapleton, Richard C. & Subrahmanyam, Marti G., 1997. "The valuation of American options on bonds1," Journal of Banking & Finance, Elsevier, vol. 21(11-12), pages 1487-1513, December.
    16. Peter W. Duck & Chao Yang & David P. Newton & Martin Widdicks, 2009. "Singular Perturbation Techniques Applied To Multiasset Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 457-486, July.
    17. Sandra Peterson & Richard Stapleton, 2002. "The pricing of Bermudan-style options on correlated assets," Review of Derivatives Research, Springer, vol. 5(2), pages 127-151, May.
    18. Nicolas P. B. Bollen & Berk A. Sensoy, 2022. "How much for a haircut? Illiquidity, secondary markets, and the value of private equity," Financial Management, Financial Management Association International, vol. 51(2), pages 501-538, June.
    19. Niffikeer, Cindy I. & Hewins, Robin D. & Flavell, Richard B., 2000. "A synthetic factor approach to the estimation of value-at-risk of a portfolio of interest rate swaps," Journal of Banking & Finance, Elsevier, vol. 24(12), pages 1903-1932, December.
    20. San-Lin Chung, 2000. "American option valuation under stochastic interest rates," Review of Derivatives Research, Springer, vol. 3(3), pages 283-307, October.
    21. Christian Gourieroux & Razvan Sufana, 2004. "Derivative Pricing with Multivariate Stochastic Volatility : Application to Credit Risk," Working Papers 2004-31, Center for Research in Economics and Statistics.
    22. Katarzyna Toporek, 2012. "Simple is better. Empirical comparison of American option valuation methods," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 29.
    23. Joshua Rosenberg, 1999. "Semiparametric Pricing of Multivariate Contingent Claims," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-028, New York University, Leonard N. Stern School of Business-.

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