×

Bivariate option pricing using dynamic copula models. (English) Zbl 1102.91059

Summary: This paper examines the behavior of bivariate option prices in the presence of association between the underlying assets. Parametric families of copulas offering various alternatives to the Gaussian dependence structure are used to model this association, which is explicitly assumed to vary over time as a function of the volatilities of the assets. These dynamic copula models are applied to better-of-two-markets and worse-of-two-markets options on the Standard and Poor’s 500 and Nasdaq indexes. Results show that option prices implied by dynamic copula models can differ substantially from prices implied by models that fix the dependence between the underlyings, particularly in times of high volatilities. In the study, the Gaussian copula also produced option prices that differed significantly from those induced by non-Gaussian copulas, irrespective of initial volatility levels. Within the class of alternatives considered, option prices were robust with respect to the choice of copula.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91B84 Economic time series analysis
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ait-Sahalia, Y.; Lo, A.W., Nonparametric estimation of state-price densities implicit in financial asset prices, J. finan., 53, 499-547, (1998)
[2] Black, F.; Scholes, M.S., The pricing of options and corporate liabilities, J. Pol. econ., 81, 637-654, (1973) · Zbl 1092.91524
[3] Bollerslev, T., Generalized autoregressive conditional heteroskedasticity, J. econ., 31, 307-327, (1986) · Zbl 0616.62119
[4] Boyer, B.H., Gibson, M.S., Loretan, M., 1999. Pitfalls in tests for changes in correlations. International Finance Discussion Papers, No 597, Board of Governors of the Federal Reserve System, Washington, DC.
[5] Cherubini, U.; Luciano, E., Bivariate option pricing with copulas, Appl. math. finan., 9, 69-86, (2002) · Zbl 1013.91050
[6] Comte, F.; Lieberman, O., Asymptotic theory for multivariate GARCH processes, J. multivariate anal., 84, 61-84, (2003) · Zbl 1038.62077
[7] Cox, J.C.; Ross, S.A.; Rubinstein, M., Option pricing: a simplified approach, J. finan. econ., 7, 229-263, (1979) · Zbl 1131.91333
[8] Duan, J.-C., The GARCH option pricing model, Math. finan., 5, 13-32, (1995) · Zbl 0866.90031
[9] Embrechts, P.; McNeil, A.J.; Straumann, D., Correlation and dependence in risk management: properties and pitfalls, (), 176-223
[10] Engle, R.F.; Kroner, K.F., Multivariate simultaneous generalized ARCH, Econ. theory, 11, 122-150, (1995)
[11] Fermanian, J.-D., Wegkamp, M.J., 2004. Time-dependent copulas. Working Paper, Centre de recherche en économie et en statistique, Paris, France.
[12] Gänssler, P.; Stute, W., ()
[13] Genest, C., Frank’s family of bivariate distributions, Biometrika, 74, 549-555, (1987) · Zbl 0635.62038
[14] Genest, C.; Ghoudi, K.; Rivest, L.-P., A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, 82, 543-552, (1995) · Zbl 0831.62030
[15] Genest, C.; MacKay, R.J., Copules archimédiennes et familles de lois bidimensionnelles dont LES marges sont données, Can. J. stat., 14, 145-159, (1986) · Zbl 0605.62049
[16] Genest, C.; Rivest, L.-P., Statistical inference procedures for bivariate Archimedean copulas, J. am. stat. assoc., 88, 1034-1043, (1993) · Zbl 0785.62032
[17] Genest, C.; Werker, B.J.M., Conditions for the asymptotic semiparametric efficiency of an omnibus estimator of dependence parameters in copula models, (), 103-112 · Zbl 1142.62330
[18] Ghoudi, K.; Khoudraji, A.; Rivest, L.-P., Propriétés statistiques des copules de valeurs extrêmes bidimensionnelles, Can. J. stat., 26, 187-197, (1998) · Zbl 0899.62071
[19] Johnson, H., Options on the maximum or the minimum of several assets, J. finan. quant. analysis, 22, 277-283, (1987)
[20] Margrabe, W., The value of an option to exchange one asset for another, J. finan., 33, 177-186, (1978)
[21] Nelsen, R.B., An introduction to copulas, lecture notes in statistics no. 139, (1999), Springer New York
[22] Patton, A.J., 2003. Modeling asymmetric exchange rate dependence. Discussion Paper 01-09, University of California, San Diego, CA.
[23] Patton, A.J., On the out-of-sample importance of skewness and asymmetric dependence for asset allocation, J. finan. econ., 2, 130-168, (2004)
[24] Reiner, E., Quanto mechanics, from black – scholes to black holes: new frontiers in options, (), 147-154
[25] Rosenberg, J.V., Pricing multivariate contingent claims using estimated risk-neutral density functions, J. int. money finan., 17, 229-247, (1998)
[26] Rosenberg, J.V., 1999. Semiparametric pricing of multivariate contingent claims. Working Paper S-99-35, Stern School of Business, New York University, New York.
[27] Rosenberg, J.V., Nonparametric pricing of multivariate contingent claims, J. derivatives, 10, 9-26, (2003)
[28] Shih, J.H.; Louis, T.A., Inferences on the association parameter in copula models for bivariate survival data, Biometrics, 51, 1384-1399, (1995) · Zbl 0869.62083
[29] Shimko, D.C., Options on futures spreads: hedging, speculation, and valuation, J. futures markets, 14, 183-213, (1994)
[30] Sklar, A., Fonctions de répartition à n dimensions et leurs marges, Publ. inst. statist. univ. Paris, 8, 229-231, (1959) · Zbl 0100.14202
[31] Stulz, R.M., Options on the minimum or the maximum of two risky assets: analysis and applications, J. finan. econ., 10, 161-185, (1982)
[32] van der Vaart, A.W.; Wellner, J.A., Weak convergence and empirical processes, (1996), Springer New York · Zbl 0862.60002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.