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We develop a new Monte Carlo variance reduction method to estimate theexpectation of two commonly encountered path-dependent functionals:first-passage times and occupation times of sets. The method is based on arecursive approximation of the first-passage time probability and expectedoccupation time of sets of a Levy bridge process that relies in part on arandomisation of the time parameter. We establish this recursion for generalLevy processes and derive its explicit form for mixed-exponentialjump-diffusions, a dense subclass (in the sense of weak approximation) of Levyprocesses, which includes Brownian motion with drift, Kou's double-exponentialmodel and hyper-exponential jump-diffusion models. We present a highly accuratenumerical realisation and derive error estimates. By way of illustration themethod is applied to the valuation of range accruals and barrier options underexponential Levy models and Bates-type stochastic volatility models withexponential jumps. Compared with standard Monte Carlo methods, we find that themethod is significantly more efficient.

Randomisation and recursion methods for mixed-exponential Levy models, with financial applications