Semiparametric pricing of multivariate contingent claims

Abstract

This paper develops and implements a methodology for pricing multivariate contingent claims (MVCC’s) based on semiparametric estimation of the multivariate risk-neutral density function. This methodology generates MVCC prices which are consistent with current market prices of univariate contingent claims. This method allows for completely general marginal risk-neutral densities and is compatible with all univariate risk-neutral density estimation techniques. The univariate risk-neutral densities are related by their risk-neutral correlation, which is estimated using time-series data on asset returns and an empirical pricing kernel (Rosenberg and Engle, 1999). This permits the multivariate risk-neutral density to be identified without requiring observation of multivariate contingent claims prices. The semiparametric MVCC pricing technique is used for valuation of one-month options on the better of two equity index returns. Option contracts with payoffs dependent on are four equity index pairs are considered: S&P500 - CAC40, S&P500 - NK225, S&P500 - FTSE100, and S&P500 - DAX30. Five marginal risk-neutral densities (S&P500, CAC40, NK225, FTSE100, and DAX30) are estimated semiparametrically using a cross-section of contemporaneously measured equity index option prices in each market. A bivariate risk-neutral Plackett (1965) density is constructed using the given marginals and risk-neutral correlation derived using an empirical pricing kernel and the historical joint density of the index returns. Price differences from a lognormal pricing formula using historical and risk-neutral return moments are found to be significant.