Monte Carlo applied to exotic digital options

Victor Vaugirard

Applied Mathematical Finance, 2001, vol. 8, issue 3, 183-196

Abstract: This paper tailors Monte Carlo simulations to the scope of binary options whose underlying dynamics obey jump-diffusion or jump-mean-reverting processes and may not be traded. In the process, the existence of well-defined arbitrage prices is justified notwithstanding a framework of incomplete markets. The all-or-nothing feature of digital options makes simulations unstable in the vicinity of their threshold, which entails the implementation of variance reduction techniques. An extension to stochastic interest rates highlights the fact that probabilistic techniques and simulations can be married to further improve the accuracy of the estimations.

Keywords: Mean-REVERTING Process; Jump-DIFFUSION Process; Control Variate Method; Antithetic Technique; Change Of Numeraire (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1080/13504860110115194

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