Analytics and algorithms for geometric average trigger reset options

The geometric average trigger reset option resets the strike price based on the geometric average of the underlying asset's prices over a monitoring window. This paper derives an analytic formula and two numerical methods for pricing this option with multiple resets. The analytic formula in fact is a corollary of a general formula that holds for a large class of path-dependent options: It prices any option whose payoff function can be written as e/sup b/spl middot/X/1/sub {X/spl isin/A}/. For general American-style reset options, an O(n/sup 4/h/sup 2/)-time algorithm on n-period binomial lattice is presented. A much more efficient O(n/sup 3/ hm)-time algorithm prices European-style reset options. Monte Carlo simulation suggests that the European-style geometric average trigger reset option and the arithmetic version have similar option values. This implies that results in this paper give tight prices for the difficult arithmetic version.