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Nonparametric pricing of multivariate contingent claims

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  • Joshua V. Rosenberg

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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Bibliographic Info

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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References

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  1. 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.
  2. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04.
  3. Boyle, Phelim P & Evnine, Jeremy & Gibbs, Stephen, 1989. "Numerical Evaluation of Multivariate Contingent Claims," Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 241-50.
  4. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  5. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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  7. 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.
  8. 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.
  9. Joshua Rosenberg, 1996. "Pricing Multivariate Contingent Claims Using Estimated Risk-neutral Density Functions," New York University, Leonard N. Stern School Finance Department Working Paper Seires 96-36, New York University, Leonard N. Stern School of Business-.
  10. 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.
  11. 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.
  12. 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, Society for Financial Studies, vol. 8(4), pages 1125-52.
  13. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
  14. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
  15. 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.
  16. 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.
  17. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-50.
  18. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  19. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  20. 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.
  21. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
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Citations

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Cited by:
  1. Hurd, Matthew & Salmon, Mark & Schleicher, Christoph, 2005. "Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index," CEPR Discussion Papers 5114, C.E.P.R. Discussion Papers.
  2. Carluccio Bianchi & Alessandro Carta & Dean Fantazzini & Maria Elena De Giuli & Mario A. Maggi, 2009. "A Copula-VAR-X Approach for Industrial Production Modelling and Forecasting," Quaderni di Dipartimento 105, University of Pavia, Department of Economics and Quantitative Methods.
  3. Mark Salmon & Christoph Schleicher, 2006. "Pricing Multivariate Currency Options with Copulas," Working Papers wpn06-10, Warwick Business School, Finance Group.
  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.
  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.
  6. 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.
  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.
  8. Hulusi Inanoglu & Michael Jacobs, 2009. "Models for Risk Aggregation and Sensitivity Analysis: An Application to Bank Economic Capital," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 2(1), pages 118-189, December.
  9. Patton, Andrew J, 2001. "Estimation of Copula Models for Time Series of Possibly Different Length," University of California at San Diego, Economics Working Paper Series qt3fc1c8hw, Department of Economics, UC San Diego.
  10. Xiaohong Chen & Yanqin Fan & Andrew J. Patton, 2004. "Simple tests for models of dependence between multiple financial time series, with applications to U.S. equity returns and exchange rates," LSE Research Online Documents on Economics 24681, London School of Economics and Political Science, LSE Library.
  11. Joshua V. Rosenberg & Til Schuermann, 2004. "A general approach to integrated risk management with skewed, fat-tailed risks," Staff Reports 185, Federal Reserve Bank of New York.
  12. Bedendo, Mascia & Campolongo, Francesca & Joossens, Elisabeth & Saita, Francesco, 2010. "Pricing multiasset equity options: How relevant is the dependence function?," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 788-801, April.
  13. van den Goorbergh, Rob W.J. & Genest, Christian & Werker, Bas J.M., 2005. "Bivariate option pricing using dynamic copula models," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 101-114, August.

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