Determining and benchmarking risk neutral distributions implied from option prices

Abstract

a b s t r a c tRisk neutral probability density functions (RNDs) play a central role in assessing models for stock market behavior. However, it remains challenging to distill a realistic estimate for the RND from empirical data. In this work we introduce a novel method to infer a RND estimate from observed option prices. Our method efficiently yields a realistic rational function approximation to the RND, it is flexible w.r.t. the shape of the underlying distribution and robust in the presence of noise. To show this, we first investigate how well a method can actually retrieve a known distribution from noisy option prices. Then we consider real market data and show how our method can be used to derive a single continuously differentiable RND estimate from empirical call and put option price data.

Risk Neutral Measure Determination from Price Ranges: Single Period Market Models

“…However, they deal with the price ranges differently. Other approaches include the use of a different entropy functional, as in [21], as well as work on the determination of risk neutral densities using approximations by rational functions, as in [22].…”