ABSTRACT
In this paper we suggest a new nonparametric approach of estimating the risk neutral density (RND) of asset prices or log-returns. Our approach exploits a relationship between the call and put prices and the conditional characteristic function of the asset price and the log-return. The latter is used to nonparametrically estimate the risk neutral moments of the underlying asset price or its log-return. These moments’ estimates can be employed to estimate the RND using the generalized Edgeworth series expansion of a density. We then evaluate the performance of our approach by estimating the RND for the asset price and/or its associated log-return for three popular option pricing models: the Black-Scholes model, the stochastic volatility and the stochastic volatility jump diffusion model. Using S&P 500 option prices and implied volatilities we estimate the implied RND.
