An Option Pricing Model with Probability Measure Ambiguity

Abstract

This paper develops an option pricing model that admits probability measure ambiguity. It formulates a piecewise risk-ambiguity-neutral probability density function and derives analytical pricing formula. Options and their underlying assets are exposed to different scopes of ambiguity that cannot be hedged, implying that options are generically non-redundant assets and have different Sharpe ratios than the underlying assets. Introduction of probability measure ambiguity reduces the in-sample and 1-day (5-day) out-of-sample pricing errors of the Black-Scholes-Merton model by 80% and 66% (61%) in pricing S&P 500 index options, and remarkably alleviates volatility smile. Option-implied market ambiguity premium is counter-cyclical and contains distinct information compared to VIX.