Optimal exercise frontier of Bermudan options by simulation methods

Dejun Xie, David A. Edwards and Xiaoxia Wu
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Dejun Xie: Financial and Actuarial Mathematics, Xi’an Jiaotong Liverpool University, Suzhou, China
David A. Edwards: ��Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
Xiaoxia Wu: ��Department of Mathematics, The University of Texas at Austin, Austin, USA

International Journal of Financial Engineering (IJFE), 2022, vol. 09, issue 03, 1-20

Abstract: In this paper, a novel algorithm for determining the free exercise boundary for high-dimensional Bermudan option problems is presented. First, a rough estimate of the boundary is constructed on a fine (daily) time grid. This rough estimate is used to generate a more accurate estimate on a coarse time grid (exercise opportunities). Antithetic branching is used to reduce the computational workload. The method is validated by comparing it with other methods of solving the standard Black–Scholes problem. Finally, the method is applied to two cases of Bermudan options with a second stochastic variable: a stochastic interest rate and a stochastic volatility.

Keywords: Simulation; Bermudan options; exercise boundary; antithetic branching; stochastic interest rate; Heston model (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S242478632250013X

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