Time Changes, Laplace Transforms and Path-Dependent Options

Path-dependent options have become increasingly popular over the last few years, in particular in FX markets, because of the greater precision with which they allow investors to choose or avoid exposure to well-defined sources of risk. The goal of the paper is to exhibit the power of stochastic time changes and Laplace transform techniques in the evaluation and hedging of path-dependent options in the Black-Scholes-Merton setting. We illustrate these properties in the specific case of Asian options and continuously (de-) activating doublebarrier options and show that in both cases, the pricing and, just as important, the hedging results are more accurate than the ones obtained through Monte Carlo simulations.