Vibrato Monte Carlo and the calculation of greeks

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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.

Available Versions of this Item

• Vibrato Monte Carlo and the calculation of greeks. (deposited 02 Jul 2008)
  • Vibrato Monte Carlo and the calculation of greeks. (deposited 09 Jul 2008) [Currently Displayed]