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Pricing Multivariate Contingent Claims Using Estimated Risk-neutral Density Functions

  • Joshua Rosenberg

Many asset price series exhibit time-varying volatility, jumps, and other features inconsistent with assumptions about the underlying price process made by standard multivariate contingent claims (MVCC) pricing models. This paper develops an interpolative technique for pricing MVCCs ' flexible NLS pricing ' that involves the estimation of a flexible multivariate risk-neutral density function implied by existing asset prices. As an application, the flexible NLS pricing technique is used to value several bivariate contingent claims dependent on foreign exchange rates in 1993 and 1994. The bivariate flexible risk-neutral density function more accurately prices existing options than the bivariate lognormal density implied by a multivariate geometric brownian motion. In addition, the bivariate contingent claims analyzed have substantially different prices using the two density functions suggesting flexible NLS pricing may improve accuracy over standard methods.

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Paper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 96-36.

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Date of creation: Jan 1996
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Handle: RePEc:fth:nystfi:96-36
Contact details of provider: Postal: U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126
Phone: (212) 998-0100
Web page: http://w4.stern.nyu.edu/finance/
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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. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
  3. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  4. 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.
  5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  6. 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.
  7. 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.
  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. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
  10. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  11. 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.
  12. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
  13. 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.
  14. 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.
  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. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  17. Boyle, Phelim P. & Tse, Y. K., 1990. "An Algorithm for Computing Values of Options on the Maximum or Minimum of Several Assets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(02), pages 215-227, June.
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