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Quasi-Monte Carlo simulation of Brownian sheet with application to option pricing

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  • Xinyu Song
  • Yazhen Wang

Abstract

Monte Carlo and quasi-Monte Carlo methods are widely used in scientific studies. As quasi-Monte Carlo simulations have advantage over ordinary Monte Carlo methods, this paper proposes a new quasi-Monte Carlo method to simulate Brownian sheet via its Karhunen–Loéve expansion. The proposed new approach allocates quasi-random sequences for the simulation of random components of the Karhunen–Loéve expansion by maximum reducing its variability. We apply the quasi-Monte Carlo approach to an option pricing problem for a class of interest rate models whose instantaneous forward rate driven by a different stochastic shock through Brownian sheet and we demonstrate the application with an empirical problem.

Suggested Citation

  • Xinyu Song & Yazhen Wang, 2017. "Quasi-Monte Carlo simulation of Brownian sheet with application to option pricing," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 1(1), pages 82-91, January.
    • Handle: RePEc:taf:tstfxx:v:1:y:2017:i:1:p:82-91
    DOI: 10.1080/24754269.2017.1332965
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