An Option Pricing Model with Probability Measure Ambiguity

48 Pages Posted: 12 Feb 2020 Last revised: 23 Feb 2020

See all articles by Yu Liu

Yu Liu

Tsinghua University

Hao Wang

Tsinghua University

Lihong Zhang

Tsinghua University - School of Economics & Management

Date Written: January 17, 2020

Abstract

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

Liu, Yu and Wang, Hao and Zhang, Lihong, An Option Pricing Model with Probability Measure Ambiguity (January 17, 2020). Available at SSRN: https://ssrn.com/abstract=3521604 or http://dx.doi.org/10.2139/ssrn.3521604

Yu Liu

Tsinghua University ( email )

Beijing, 100084
China
86 15210589482 (Phone)

Hao Wang (Contact Author)

Tsinghua University ( email )

318 Weilun Building
Tsinghua University
Beijing, 100084
China
86 10 62797482 (Phone)
86 10 62794554 (Fax)

Lihong Zhang

Tsinghua University - School of Economics & Management ( email )

Beijing, 100084
China

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