Bound on European Option Prices under Stochastic Volatility

In this paper we consider the range of prices consistent with no arbitrage for European options in a
general stochastic volatility model. We give conditions under which the infimum and the supremum
of the possible option prices are equal to the intrinsic value of the option and to the current price of
the stock, respectively, and show that these conditions are satisfied in most of the stochastic volatility
models from the financial literature. We also discuss properties of Black-Scholes hedging strategies
in stochastic volatility models where the volatility is bounded.