TY - JOUR T1 - Non-Parametric Pricing of Multivariate Contingent Claims JF - The Journal of Derivatives SP - 9 LP - 26 DO - 10.3905/jod.2003.319198 VL - 10 IS - 3 AU - Joshua V. Rosenberg Y1 - 2003/02/28 UR - https://pm-research.com/content/10/3/9.abstract N2 - The Black-Scholes (BS) framework is based on the assumption that an option’s underlying asset follows a lognormal diffusion. From the beginning, however, we have known that actual returns are not lognormal. Density functions estimated from realized returns invariably exhibit fat tails and other departures from lognormality. This has led to use of more flexible parametric returns distributions, and to non-parametric estimation techniques. Pervasive smile and skew patterns in the implied volatilities from option prices indicate that the market clearly anticipates departures from lognormality. An increasing number of derivative instruments, as well as procedures for assessing risk exposure more generally, require consideration of correlations among multiple risk factors. Here, again, real world returns data show correlation behavior that is inconsistent with standard models, particularly multivariate (log)normality. The method of copulas offers a general approach to more flexible and realistic modeling of correlations. In this article, Rosenberg first explains the fundamentals of this important new technology. He then illustrates its application in pricing euro-yen options using data on euro-dollar and yen-dollar exchange rates. The individual exchange rate volatilities are obtained non-parametrically from options prices, and the empirical copula function is estimated from historical returns data. The resulting estimate of the joint density function produces a better fit than standard models to prices of traded euro-yen options, and also reveals the effects of known specific events, such as the period of market disruption in October 1998. ER -