Burgos, Sylvestre (2009) *Investigation into Vibrato Monte Carlo for the Computation of Greeks of Discontinuous Payoffs.* Masters thesis, Mathematical Institute.

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## Abstract

Monte Carlo simulation is a popular method in computational finance. Its basic theory is relatively simple, it is also quite easy to implement and allows nevertheless an efficient pricing of financial options, even in high-dimensional problems (basket options, interest rates products...).

The pricing of options is just one use of Monte Carlo in finance. More important than the prices themselves are their sensitivities to input parameters (underlying asset value, interest rates, market volatility...). Indeed we need those sensitivities (also known as "Greeks") to hedge against market risk.

In this paper, we will first recall classical approaches to the computation of Greeks through Monte Carlo simulation: finite differences, Likelihood Ratio method (LRM) and Pathwise Sensitivities (PwS). Each of those approaches has particular limitations in the case of options with discontinuous payoffs. We will expound those limitations and introduce a new hybrid method proposed by Prof. Mike Giles, the Vibrato Monte Carlo, which combines both Pathwise Sensitivity and Likelihood Ratio methods to get around their shortcomings.

We will discuss the possible use of Vibrato Monte Carlo ideas for options with discontinuous payoffs. My personal contribution is an improvement to the standard Vibrato Monte Carlo yielding both computational savings and an improved accuracy. I will call it Allargando Vibrato Monte Carlo (AVMC). I then also extend the Vibrato Monte Carlo technique to discretely sampled path dependent options (digital option with discretely sampled barrier, lookback option with discretely sampled maximum).

Item Type: | Thesis (Masters) |
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Subjects: | H - N > Mathematics education |

Research Groups: | Mathematical and Computational Finance Group |

ID Code: | 785 |

Deposited By: | Laura Auger |

Deposited On: | 23 Jul 2009 08:26 |

Last Modified: | 03 Aug 2009 10:28 |

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