Pricing multivariate contingent claims using estimated risk–neutral density functions

TLDR

Many asset price series exhibit time‑varying volatility, jumps, and other features that violate the assumptions of standard multivariate contingent‑claim pricing models. The study introduces a flexible NLS pricing method that estimates a multivariate risk‑neutral density from observed asset prices to price MVCCs. The method interpolates the estimated density and applies it to value several bivariate foreign‑exchange contingent claims from 1993–1994. Using the flexible density yields option prices that are more accurate than those from a bivariate log‑normal model and produces substantially different prices, indicating improved pricing accuracy over standard methods.

Abstract

Many asset price series exhibit time-varying volatility, jumps and other features inconsistent with assumptions about the underlying price process made by standard multivariate contingent claims (MVCC) pricing models. This article develops an interpolative technique for pricing MVCCs — flexible NLS pricing — that involves the estimation of a flexible multivariate risk–neutral density function implied by existing asset prices. As an application, the flexible NLS pricing technique is used to value several bivariate contingent claims dependent on foreign exchange rates in 1993 and 1994. The bivariate flexible risk–neutral density function more accurately prices existing options than the bivariate log-normal density implied by a multivariate geometric Brownian motion. In addition, the bivariate contingent claims analyzed have substantially different prices using the two density functions suggesting flexible NLS pricing may improve accuracy over standard methods.