Valuation of Arithmetic Average Reset Options

Abstract

A reset option is a path-dependent contingent claim whose strike price can be adjusted in favor of its holders at predetermined reset dates. A standard reset option uses the underlying stock prices at the reset dates as trigger prices, and an arithmetic average reset option uses the arithmetic averages of the stock prices. Arithmetic average reset options have the advantages of greatly reducing the potential for price manipulation and of mitigating the hedging problem caused by sudden changes in option delta near the reset dates. This article develops a lattice method to numerically compute the value of arithmetic average reset options. Two augmented state variables are used at each standard lattice node, and a method is introduced to calculate the minimum necessary range of these variables.