Semiparametric Pricing of Multivariate Contingent Claims
August 1999
Joshua Rosenberg
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.
Subject: Investments/Derivatives, Investments/Volatility of Asset Prices, Investments/Econometrics
Rosenberg: (212) 998-0311 jrosenb0@stern.nyu.edu
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