An Option Pricing Model with Probability Measure Ambiguity
48 Pages Posted: 12 Feb 2020 Last revised: 23 Feb 2020
Date Written: January 17, 2020
This paper develops an option pricing model that admits probability measure ambiguity. It formulates the pricing kernel that transforms the reference probability measure of the Black-Scholes-Merton (BSM) model into the risk-ambiguity-neutral measure (equivalent martingale measure), and derives analytical pricing formula for European options. Introduction of probability measure ambiguity significantly improves model internal consistency, and remarkably alleviates volatility smile. In pricing the S&P 500 index options, it helps reduce the in-sample and 1-day (5-day) out-of-sample pricing errors of the BSM model by 80% and 66% (61%), respectively. The option-implied market ambiguity premium is counter-cyclical, and moderately correlated to the VIX and other market indices.
Keywords: probability measure ambiguity, pricing kernel, equivalent martingale measure, call-put parity, ambiguity premium, volatility smile
JEL Classification: G12, G13
Suggested Citation: Suggested Citation