Spilda, Juraj (2010) *Adjoint methods for computing sensitivities in local volatility surfaces.* Masters thesis, Mathematical Institute.

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## Abstract

In this paper we present the adjoint method of computing sensitivities of option prices with respect to nodes in the local volatility surface. We first introduce the concept of algorithmic differentiation and how it relates to

path-wise sensitivity computations within a Monte Carlo framework. We explain the two approaches available: forward mode and adjoint mode. We illustrate these concepts on the simple example of a model with a geometric Brownian motion driving the underlying price process, for which

we compute the Delta and Vega in forward and adjoint mode. We then go on to explain in full detail how to apply these ideas to a model where the underlying has a volatility term defined by a local volatility surface. We provide source codes for both the simple and the more complex case and

analyze numerical results to show the strengths of the adjoint approach.

Item Type: | Thesis (Masters) |
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Subjects: | H - N > Mathematics education |

Research Groups: | Mathematical and Computational Finance Group |

ID Code: | 931 |

Deposited By: | Laura Auger |

Deposited On: | 21 Jul 2010 07:37 |

Last Modified: | 21 Jul 2010 07:37 |

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