Superreplication in Stochastic Volatility Models and Optimal Stopping

Publikation: Wissenschaftliche FachzeitschriftOriginalbeitrag in FachzeitschriftBegutachtung

Abstract

In this paper we discuss the superreplication of derivatives in a stochastic volatility model under the additional assumption that the volatility follows a bounded process. We characterize the value process of our superhedging strategy by an optimal-stopping problem in the context of the Black-Scholes model which is similar to the optimal stopping problem that arises in the pricing of American-type derivatives. Our proof is based on probabilistic arguments. We study the minimality of these superhedging strategies and discuss PDE-characterizations of the value function of our superhedging strategy. We illustrate our approach by examples and simulations.
OriginalspracheEnglisch
Seiten (von - bis)161 - 188
FachzeitschriftFinance and Stochastics
Ausgabenummer4
PublikationsstatusVeröffentlicht - 1 Mai 2000

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