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February 1998 Volatility misspecification, option pricing and superreplication via coupling
David G. Hobson
Ann. Appl. Probab. 8(1): 193-205 (February 1998). DOI: 10.1214/aoap/1027961040

Abstract

Consider the performance of an options writer who misspecifies the dynamics of the price process of the underlying asset by overestimating asset price volatility. When does he overprice the option? If he follows the hedging strategy suggested by his model, when does the terminal value of his strategy dominate the option payout?

We show that both these events happen if the option payoff is a convex function of the price of the underlying at maturity. The proofs involve the simple, powerful and intuitive techniques of coupling.

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David G. Hobson. "Volatility misspecification, option pricing and superreplication via coupling." Ann. Appl. Probab. 8 (1) 193 - 205, February 1998. https://doi.org/10.1214/aoap/1027961040

Information

Published: February 1998
First available in Project Euclid: 29 July 2002

zbMATH: 0933.91012
MathSciNet: MR1620358
Digital Object Identifier: 10.1214/aoap/1027961040

Subjects:
Primary: 60G44 , 60J30 , 90A09

Keywords: coupling , Diffusions , Options , robust hedging , super-replication , Volatility

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 1 • February 1998
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