April 2000
Joshua Rosenberg
ABSTRACT
This paper derives and implements a nonparametric, arbitrage- free technique for multivariate contingent claims
(MVCC) pricing. This technique is based on nonparametric estimation of a multivariate risk- neutral density function
using data from traded options markets and historical asset returns. “New” multivariate claims are priced using
expectations under this measure. An appealing feature of nonparametric arbitrage- free derivative pricing is that
fitted prices are obtained that are consistent with traded option prices and are not based on specific restrictions
on the underlying asset price process or the functional form of the risk-neutral density.
Nonparametric MVCC pricing utilizes the method of copulas to combine nonparametrically estimated marginal risk- neutral densities (based on options data) into a joint density using a separately estimated nonparametric dependence function (based on historical returns data). This paper provides theory linking objective and risk-neutral dependence functions, and empirically testable conditions that justify the use of historical data for estimation of the risk- neutral dependence function.
The nonparametric MVCC pricing technique is implemented for the valuation of bivariate underperformance and
outperformance options on the S&P500 and DAX index. Price deviations are found to be significant in comparisons
of fitted prices using nonparametric valuation versus standard multivariate diffusion-based valuation. An analysis
of pricing errors indicates that the lognormal marginal density specification poorly approximates the negative
skewness and excess kurtosis implied by market data, and the lognormal copula specification poorly approximates
the asymmetric return dependence implied by market data. These results suggest that correct specification of the
marginal densities and the dependence function that define the multivariate risk- neutral density is essential
for accurate MVCC pricing.
Subject: Investments/Derivatives; Investments/Volatility of Asset Prices; Investments/Econometrics
Classification: Empirical/Theoretical
Joshua Rosenberg
Institution: Department of Finance, Stern School of Business, New York University
Email: jrosenb0@stern.nyu.edu
Telephone: (212) 998-0311
Homepage: www.stern.nyu.edu/~jrosenb0
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