2014/10/27 by Aleksandar Mijatović, Mijatovic, Aleksandar, Martijn Pistorius +3
Economics, Econometrics and Finance · Social Sciences · #65C05 #91G60 #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1410.7316
openalex publication_date 2014/10/27 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We develop a new Monte Carlo variance reduction method to estimate the\nexpectation of two commonly encountered path-dependent functionals:\nfirst-passage times and occupation times of sets. The method is based on a\nrecursive approximation of the first-passage time probability and expected\noccupation time of sets of a Levy bridge process that relies in part on a\nrandomisation of the time parameter. We establish this recursion for general\nLevy processes and derive its explicit form for mixed-exponential\njump-diffusions, a dense subclass (in the sense of weak approximation) of Levy\nprocesses, which includes Brownian motion with drift, Kou's double-exponential\nmodel and hyper-exponential jump-diffusion models. We present a highly accurate\nnumerical realisation and derive error estimates. By way of illustration the\nmethod is applied to the valuation of range accruals and barrier options under\nexponential Levy models and Bates-type stochastic volatility models with\nexponential jumps. Compared with standard Monte Carlo methods, we find that the\nmethod is significantly more efficient.\n