Pricing a bivariate option with copulas Online publication date: Mon, 21-Jan-2019
by Christian Bucio-Pacheco; Francisco López-Herrera; Roberto J. Santillán-Salgado
International Journal of Bonds and Derivatives (IJBD), Vol. 4, No. 1, 2018
Abstract: The diversity of exotic-option contracts available in the market has increased significantly in recent years, and has aroused the interest to develop alternative valuation methodological approaches. Among the most interesting innovations, copulas analysis represents a major contribution to improve valuation methodologies. This paper explores the pricing of a bivariate call option on the better-of-two-markets: Mexico's Stock Exchange index, and the Standard & Poor's 500. The approach consists of a GARCH process that combines with copulas analysis and the Black and Scholes classical European call option valuation model. Copulas from the elliptical and Archimedean families provide the dependence structure among the underlying assets, and the estimated prices prove significantly different from those obtained using a static dependence assumption. The study concludes that dynamic copulas produce more robust prices than static dependence models.
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