Implied Bivariate State Price Density

Abstract

In this paper, we extend the research on state price density (SPD) to a bivariate setting. This extention allows us to price derivative securities whose value depends on several state variables. As an example, we examine a bivariate SPD of stock price and discount rate. We propose a semi-nonparametric (SNP) method of estimating the bivariate SPD implicit in prices of the long- term S&P 500 index options (LEAPS) and treasury bills and notes. The bivariate SPD approach can be potentially extended to account for multiple state variables.