American Options Exercise Boundary When the Volatility Changes Randomly |
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Authors: | N Touzi |
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Institution: | (1) CEREMADE, Université Paris IX Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France touzi@ceremade.dauphine.fr and CREST, 15 bd Gabriel Péri, 92240 Malakoff cedex, France , FR |
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Abstract: | The American put option exercise boundary has been studied extensively as a function of time and the underlying asset price.
In this paper we analyze its dependence on the volatility, since the Black and Scholes model is used in practice via the (varying)
implied volatility parameter. We consider a stochastic volatility model for the underlying asset price. We provide an extension
of the regularity results of the American put option price function and we prove that the optimal exercise boundary is a decreasing
function of the current volatility process realization.
Accepted 13 January 1998 |
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Keywords: | , Incomplete markets, Optimal stopping, Viscosity solutions, AMS Classification, 60G40, 90A09, 93E20, |
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