An Option Pricing Model with Probability Measure Ambiguity

50 Pages Posted: 12 Feb 2020 Last revised: 23 Jul 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 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.

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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