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Nonparametric pricing of multivariate contingent claims

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Author Info
Joshua V. Rosenberg

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Abstract

In this paper, I derive and implement a nonparametric, arbitrage-free technique for multivariate contingent claim (MVCC) pricing. Using results from the method of copulas, I show that the multivariate risk-neutral density can be written as a product of marginal risk-neutral densities and a risk-neutral dependence function. I then develop a pricing technique using nonparametrically estimated marginal risk-neutral densities (based on options data) and a nonparametric dependence function (based on historical return data). By using nonparametric estimation, I avoid the pricing biases that result from incorrect parametric assumptions such as lognormality. ; I apply this technique to estimate the joint risk-neutral density of euro-dollar and yen-dollar returns. I compare the nonparametric risk-neutral density with density based on a lognormal dependence function and nonparametric marginals. The nonparametric euro-yen risk-neutral density has greater volatility, skewness, and kurtosis than the density based on a lognormal dependence function. In a comparison of pricing accuracy for euro-yen futures options, I find that the nonparametric model is superior to the lognormal model.

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Paper provided by Federal Reserve Bank of New York in its series Staff Reports with number 162.

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Date of creation: 2003
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Handle: RePEc:fip:fednsr:162

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Related research
Keywords: Asset pricing ; Estimation theory ; Euro-dollar market ; Yen; Japanese;

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
    Other versions:
  2. Boyle, Phelim P & Evnine, Jeremy & Gibbs, Stephen, 1989. "Numerical Evaluation of Multivariate Contingent Claims," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 2(2), pages 241-50. [Downloadable!] (restricted)
  3. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July. [Downloadable!] (restricted)
  4. Christian Walter & Jose A. Lopez, 2000. "Is implied correlation worth calculating? Evidence from foreign exchange options and historical data," Working Papers in Applied Economic Theory 2000-02, Federal Reserve Bank of San Francisco. [Downloadable!]
    Other versions:
  5. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September. [Downloadable!] (restricted)
  6. Stapleton, Richard C & Subrahmanyam, Marti G, 1984. " The Valuation of Multivariate Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 39(1), pages 207-28, March. [Downloadable!] (restricted)
  7. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March. [Downloadable!]
  8. Andrew J. Patton, 2001. "Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula," University of California at San Diego, Economics Working Paper Series 2001-09, Department of Economics, UC San Diego. [Downloadable!]
  9. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February. [Downloadable!]
    Other versions:
  10. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(4), pages 1211-50. [Downloadable!] (restricted)
  11. Jean-David FERMANIAN & Olivier SCAILLET, 2003. "Nonparametric Estimation of Copulas for Time Series," FAME Research Paper Series rp57, International Center for Financial Asset Management and Engineering. [Downloadable!]
  12. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  13. Johnson, Herb, 1987. "Options on the Maximum or the Minimum of Several Assets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 277-283, September. [Downloadable!]
  14. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  15. Stapleton, Richard C & Subrahmanyam, Marti G, 1984. " The Valuation of Options When Asset Returns Are Generated by a Binomial Process," Journal of Finance, American Finance Association, vol. 39(5), pages 1525-39, December. [Downloadable!] (restricted)
  16. Ho, Teng-Suan & Stapleton, Richard C & Subrahmanyam, Marti G, 1995. "Multivariate Binomial Approximations for Asset Prices with Nonstationary Variance and Covariance Characteristics," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 8(4), pages 1125-52. [Downloadable!] (restricted)
  17. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley. [Downloadable!]
  18. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 8(4), pages 1091-1124. [Downloadable!] (restricted)
  19. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December. [Downloadable!] (restricted)
  20. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-86, March. [Downloadable!] (restricted)
  21. Stulz, ReneM., 1982. "Options on the minimum or the maximum of two risky assets : Analysis and applications," Journal of Financial Economics, Elsevier, vol. 10(2), pages 161-185, July. [Downloadable!] (restricted)
  22. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 247-64, April. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Andrew Patton, 2001. "Estimation of Copula Models for Time Series of Possibly Different Length," University of California at San Diego, Economics Working Paper Series 2001-17, Department of Economics, UC San Diego. [Downloadable!]
  2. Andrew J. Patton, 2001. "Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula," University of California at San Diego, Economics Working Paper Series 2001-09, Department of Economics, UC San Diego. [Downloadable!]
  3. Yacine Aït-Sahalia & Michael W. Brandt, 2008. "Consumption and Portfolio Choice with Option-Implied State Prices," NBER Working Papers 13854, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  4. Rob van den Goorbergh, 2004. "A Copula-Based Autoregressive Conditional Dependence Model of International Stock Markets," DNB Working Papers 022, Netherlands Central Bank, Research Department. [Downloadable!]
  5. Ozun, Alper & Cifter, Atilla, 2007. "Portfolio Value-at-Risk with Time-Varying Copula: Evidence from the Americas," MPRA Paper 2711, University Library of Munich, Germany. [Downloadable!]
  6. Goorbergh, R.W.J. van den & Genest, C. & Werker, B.J.M., 2003. "Multivariate option pricing using dynamic copula models," Discussion Paper 122, Tilburg University, Center for Economic Research. [Downloadable!]
  7. Elisa Luciano, 2007. "Copula-Based Default Dependence Modelling: Where Do We Stand?," ICER Working Papers - Applied Mathematics Series 21-2007, ICER - International Centre for Economic Research. [Downloadable!]
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