The Mathematical Institute, University of Oxford, Eprints Archive

Computing Greeks using multilevel path simulation

Giles, M. B. and Burgos, Sylvestre (2011) Computing Greeks using multilevel path simulation. Technical Report. .. (Unpublished)

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Abstract

We investigate the extension of the multilevel Monte Carlo method [2, 3] to the calculation of Greeks. The pathwise sensitivity analysis [5] differentiates the path evolution and effectively reduces the smoothness of the payoff. This leads to new challenges: the use of naive algorithms is often impossible because of the inapplicability of pathwise sensitivities to discontinuous payoffs.

These challenges can be addressed in three different ways: payoff smoothing using conditional expectations of the payoff before maturity [5]; an approximation of the above technique using path splitting for the final timestep [1]; the use of a hybrid combination of pathwise sensitivity and the Likelihood Ratio Method [4]. We discuss the strengths and weaknesses of these alternatives in different multilevel Monte Carlo settings.

Item Type:Technical Report (Technical Report)
Subjects:D - G > Game theory, mathematical finance, economics, social and behavioral sciences
Research Groups:Mathematical and Computational Finance Group
ID Code:1046
Deposited By:Eprints Administrator
Deposited On:28 Jan 2011 13:37
Last Modified:28 Jan 2011 13:37

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