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 [(σitI)i=1,m] where m⩾1 and σitI 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 finding is that we uncover a remarkably simple volatility extraction filter 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 reflected in the conditional kurtosis provides support to price long term.