Valuation of Arithmetic Average Reset Options

Abstract

Options whose payoffs are based on an arithmetic average of the price of the underlying can have some useful advantages over standard options. The payoff is less susceptible to manipulation of the price at expiration, and in many cases a hedger is more interested in locking in the average value of some cost or price over a period of time than in fixing it as of a specific date. For reset options, whose strike prices may be reset at fixed dates depending on the value of the underlying, arithmetic averaging substantially reduces the problem that the option's delta can jump on the reset date. However, arithmetic averaging of lognormally distributed random variables produces a substantial problem for valuation, because the underlying average is not lognormal. In this article, Kim, Chang, and Byun provide an effective valuation methodology for arithmetic average reset options.