State Price Density Estimation with an Application to the Recovery Theorem

Abstract

I introduce a model to estimate the risk-neutral density. Current estimation techniques use a single mathematical model to interpolate option prices on two option dimensions: strike price and time-to maturity (TTM). I propose to use B-splines with at-the-money knots for the strike price interpolation and a function that depends on the option expiration horizon for the TTM interpolation. The results of this “hybrid” methodology are significantly better than other risk-neutral density extrapolation methods applied to the Recovery Theorem.

Keywords: Risk Neutral Density, Recovery Theorem, Implied Probabilities, Contingent Pricing, Information and Market Efficiency

JEL Classification: G13, G14, G17