We first develop a unifying Malliavin calculus in a jump-diffusion context, by taking into account all the randomness involved (Brownian motion, jump times and jump amplitudes) and by stating an integration by parts formula which gives the starting point of our work. The results are then applied to study representation formulas both for sensitivities (delta) and conditional expectations (in terms of non conditional Z_t=(X_t,Y_t), in which X stands for a jump diffusion and Y_t=\int_0^t X_r dr. Therefore, the link with problems arising from Finance (price/delta of Asian options) is studied. Several examples are analyzed in details and equipped with numerical studies.

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A.A. 2007/2008
Matematica
20.
We first develop a unifying Malliavin calculus in a jump-diffusion context, by taking into account all the randomness involved (Brownian motion, jump times and jump amplitudes) and by stating an integration by parts formula which gives the starting point of our work. The results are then applied to study representation formulas both for sensitivities (delta) and conditional expectations (in terms of non conditional Z_t=(X_t,Y_t), in which X stands for a jump diffusion and Y_t=\int_0^t X_r dr. Therefore, the link with problems arising from Finance (price/delta of Asian options) is studied. Several examples are analyzed in details and equipped with numerical studies.
Malliavin calculus; Asian options; Monte Carlo methods
Settore MAT/06 - Probabilita' e Statistica Matematica
English
Tesi di dottorato
Marchisio, V. (2009). Malliavin representation formulas for Asian options in a jump-diffusion model.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/1001