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 (Unpublished)

| PDF 252Kb |

## 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 |

Repository Staff Only: item control page