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December 2015 Randomisation and recursion methods for mixed-exponential Lévy models, with financial applications
Aleksandar Mijatović, Martijn R. Pistorius, Johannes Stolte
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J. Appl. Probab. 52(4): 1076-1096 (December 2015). DOI: 10.1239/jap/1450802754

Abstract

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 Lévy bridge process that relies in part ona randomisation of the time parameter. We establish this recursion for generalLévy processes and derive its explicit form for mixed-exponentialjump-diffusions, a dense subclass (in the sense of weak approximation) ofLévy processes, which includes Brownian motion with drift, Kou'sdouble-exponential model, and hyper-exponential jump-diffusion models. Wepresent a highly accurate numerical realisation and derive error estimates. Byway of illustration the method is applied to the valuation of range accrualsand barrier options under exponential Lévy models and Bates-typestochastic volatility models with exponential jumps. Compared with standardMonte Carlo methods, we find that the method is significantly more efficient.

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Aleksandar Mijatović. Martijn R. Pistorius. Johannes Stolte. "Randomisation and recursion methods for mixed-exponential Lévy models, with financial applications." J. Appl. Probab. 52 (4) 1076 - 1096, December 2015. https://doi.org/10.1239/jap/1450802754

Information

Published: December 2015
First available in Project Euclid: 22 December 2015

zbMATH: 1334.65008
MathSciNet: MR3439173
Digital Object Identifier: 10.1239/jap/1450802754

Subjects:
Primary: 65C05
Secondary: 91G60

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 4 • December 2015
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