Option Price Decomposition for Local and Stochastic Volatility Jump Diffusion Models
[eng] In this thesis, an option price decomposition for local and stochastic volatility jump diffusion models is studied. On the one hand, we generalise and extend the Alòs decomposition to be used in a wide variety of models such as a general stochastic volatility model, a stochastic volatility jum...
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| Formato: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/177349 |
| Acesso em linha: | https://hdl.handle.net/2445/177349 http://hdl.handle.net/10803/671682 |
| Access Level: | acceso abierto |
| Palavra-chave: | Processos estocàstics Descomposició (Matemàtica) Opcions (Finances) Stochastic processes Decomposition (Mathematics) Options (Finance) |
| Resumo: | [eng] In this thesis, an option price decomposition for local and stochastic volatility jump diffusion models is studied. On the one hand, we generalise and extend the Alòs decomposition to be used in a wide variety of models such as a general stochastic volatility model, a stochastic volatility jump dffusion model with finite activity or a rough volatility model. Furthermore, we note that in the case of local volatility models, speci_cally, spot-dependent models, a new decomposition formula must be used to obtain good numerical results. In particular, we study the CEV model. On the other hand, we observe that the approximation formula can be improved by using the decomposition formula recursively. Using this decomposition method, the call price can be transformed into a Taylor type formula containing an infinite series with stochastic terms. New approximation formulae are obtained in the Heston model case, finding better approximations. |
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