The Mathematical Institute, University of Oxford, Eprints Archive

Vibrato Monte Carlo and the calculation of greeks

Keegan, Sinead (2008) Vibrato Monte Carlo and the calculation of greeks. Masters thesis, University of Oxford.

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Abstract

In computational ¯nance Monte Carlo simulation can be used to calculate
the correct prices of ¯nancial options, and to compute the values of the as-
sociated Greeks (the derivatives of the option price with respect to certain
input parameters). The main methods used for the calculation of Greeks
are finite difference, likelihood ratio, and pathwise sensitivity. Each of these
has its limitations and in particular the pathwise sensitivity approach may
not be used for an option whose payoff function is discontinuous. Vibrato
Monte Carlo is a new idea that addresses the limitations of previous methods;
it combines the pathwise sensitivity approach for the SDE path calculation
with the likelihood ratio method for payoff evaluation. This thesis discusses
Vibrato Monte Carlo approximations for a digital option on an asset follow-
ing one-dimensional geometric Brownian motion.

Item Type:Thesis (Masters)
Subjects:H - N > Mathematics education
Research Groups:Mathematical and Computational Finance Group
ID Code:716
Deposited By:Laura Auger
Deposited On:09 Jul 2008
Last Modified:20 Jul 2009 14:23

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