Characterization of Optimal Stopping Regions of American Path Dependent Options

Abstract

A general framework is developed to analyze the optimal stopping (exercise) regions of American path dependent options with either Asian feature or lookback feature. We examine the monotone properties of the option values and stopping regions with respect to the interest rate, dividend yield and time. From the ordering properties of the values of American lookback options and American Asian options, we deduce the corresponding nesting relations between the exercise regions of these American options. We illustrate how some properties of the exercise regions of the American Asian options can be inferred from those of the American lookback options.

Keywords: American options, optimal stopping, Asian feature, lookback feature, monotone properties

JEL Classification: G13