Pricing Options with Geometric Average Reset Feature

Abstract

A geometric average trigger reset option resets the strike price based on the geometric average of the underlying asset's prices over a monitoring window. There can be multiple monitoring windows, thus multiple resets. Similar contracts have been traded on exchanges in Asia. Cheng and Zhang [2000] give an analytic formula for a more limited case which permits only a single reset; unfortunately, their formula is incorrect. Our paper gives the correct analytic formula that can handle an arbitrary number of monitoring windows. A reset call will not be exercised early if the underlying asset does not pay dividends; hence our formula applies to American-style reset calls in this case. Some properties of reset options are analyzed rigorously in the paper: like the relationship between the option prices and the number of samples in a monitoring window, the relationship between the option prices and the length of a monitoring window, and the relationship between the geometric and the arithmetic average trigger reset options. Monte Carlo simulation suggests that the European-style geometric average trigger reset option and the arithmetic version have similar option values. Thus our formula give close prices for the difficult arithmetic version. Besides, unlike the standard reset option, the geometric average trigger reset option does not have significant delta jumps. This useful property reduces the hedging risk dramatically.