Estimating Option-Implied Risk-Neutral Densities: A Novel Parametric Approach

Abstract

“Practitioner Black–Scholes”—the BS equation with a different implied volatility (IV) for each option—is in conflict with the underlying theory from which the model is derived. Figlewski (JOD, Fall 2002) asked whether this ad hoc approach is any better than just using some equation that satisfies the static no-arbitrage conditions of option pricing but has no valuation theory behind it at all. The basic answer was that, in fact, such a “model-free” pricing model works very well for most options. Subsequent research extended the original simple equation to fit better in the tails. In this article, Orosi develops further extensions that produce a full valuation surface covering all strikes and maturities from the same equation and even a variant that allows nonzero bankruptcy risk. Simulation shows that the model can be very flexible in fitting options priced under complex shapes for the risk-neutral density, and empirical analysis with S&P 500 Index options shows that the non-model model performs about as well as Gatheral’s SVI model.