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

Xinyu Song ,

Department of Statistics, University of Wisconsin-Madison, Madison, WI, USA

Yazhen Wang

Department of Statistics, University of Wisconsin-Madison, Madison, WI, USA

Pages 82-91 | Received 07 Mar. 2017, Accepted 17 May. 2017, Published online: 19 Jun. 2017,
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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.

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