Valuing and Hedging American Options under Time-Varying Volatility

Abstract

There has been considerable interest in developing stochastic volatility and jump-diffusion option pricing models, e.g. Hull and White (1987, Journal of Finance, 42, 281~300) and Merton (1976, Journal of Financial Economics, 3, 125~144). These models, however, have some undesirable aspects that arise from introducing some non-traded sources of risks to the models. Furthermore, the models require much analytical complications; thus, if they are applied to American options then it is not easy to acquire practical implications for hedging and optimal exercise strategies. This paper examines the American option prices and optimal exercise strategies where the volatility of the underlying asset changes over time in a deterministic way. The paper considers two simple cases: monotonically increasing and decreasing volatilities. The discussion of these two simple cases gives useful implications for the possibility of early-exercise and optimal exercise strategies.