Analytics 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. Similar contracts have been traded on exchanges in Asia. This paper derives an analytic formula for pricing this option with multiple monitoring windows. 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 value can be written as a linear combination of E(e^b.X1_{X∈A}), where X is a multinormal random vector and b is some constant vector. Numerical experiments suggest that the pricing formula approximates the values of arithmetic average trigger reset options accurately. Thus pricing the arithmetic average trigger reset option can benefit from using this formula as the control variate in Monte Carlo simulation. Numerical results also suggest that the geometric average trigger reset option does not have significant delta jump as the standard reset option, and this useful property reduces the hedging risk dramatically.