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Volatility Misspecification, Option Pricing and Superreplication via Coupling
David G. Hobson
The Annals of Applied Probability
Vol. 8, No. 1 (Feb., 1998), pp. 193-205
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2667242
Page Count: 13
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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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The Annals of Applied Probability © 1998 Institute of Mathematical Statistics