Analytics and algorithms for geometric average trigger reset options

Abstract

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 f o r pricing this option with multiple resets. The analytic formula in fact i s a corollary of a general formula that holds f o r a large class of pathdependent options: It prices any option whose payoff function can be written as e b ' X 1 i x E A i . For general American-style reset options, a n O(n h )-tame algorithm on n-period binomial lattice i s presented. A much more eficient 0(n3 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 f o r the dificult arithmetic version.