SFB 303 Discussion Paper No. B - 435
Author: Frey, Ruediger
Title: Superreplication in Stochastic Volatility Models and Optimal Stopping
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.
As most of the previous work on superheding under stochastic volatility uses a PDE approach
we discuss PDE-characterizations of the value function of our superhedging strategy.
We illustrate our approach by certain examples and simulations.
Keywords: Stochastic volatility, Optimal stopping, Incomplete markets, Superreplication
JEL-Classification-Number: G12, G13
Creation-Date: June 1998
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