A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation

The purpose of this paper is to bridge two strands of the literature, one pertaining to the objective or physical measure used to model an underlying asset and the other pertaining to the risk-neutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundamental price, St , and a set of option contracts [(pI it )i/1,m] where m*1 and pI it is the Black}Scholes implied volatility. We use Heston's (1993. Review of Financial Studies 6, 327}343) model as an example, and appraise univariate and multivariate estimation of the model in terms of pricing and hedging performance. Our results, based on the S&P 500 index contract, show dominance of univariate approach, which relies solely on options data. A by-product of this "nding is that we uncover a remarkably simple volatility extraction "lter based on a polynomial lag structure of implied volatilities. The bivariate approach, involving both the fundamental security and an option contract, appears useful when the information from the cash market re#ected in the conditional kurtosis provides support to price long term. ( 2000 Elsevier Science S.A. All rights reserved.