Vibrato Monte Carlo and the calculation of greeks

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