Todeschi, Tiziano
(2021)
Calibration of local-stochastic volatility models with neural networks.
[Laurea magistrale], Università di Bologna, Corso di Studio in
Matematica [LM-DM270]
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Abstract
During the last twenty years several models have been proposed to improve the classic Black-Scholes framework for equity derivatives pricing. Recently a new model has been proposed: Local-Stochastic Volatility Model (LSV). This model considers volatility as the product between a deterministic and a stochastic term. So far, the model choice was not only driven by the capacity of capturing empirically observed market features well, but also by the computational tractability of the calibration process. This is now undergoing a big change since machine learning technologies offer new perspectives on model calibration. In this thesis we consider the calibration problem to be the search for a model which generates given market prices and where additionally technology from generative adversarial networks can be used. This means parametrizing the model pool in a way which is accessible for machine learning techniques and interpreting the inverse problems a training task of a generative network, whose quality is assessed by an adversary. The calibration algorithm proposed for LSV models use as generative models so-called neural stochastic differential equations (SDE), which just means to parameterize the drift and volatility of an Ito-SDE by neural networks.
Abstract
During the last twenty years several models have been proposed to improve the classic Black-Scholes framework for equity derivatives pricing. Recently a new model has been proposed: Local-Stochastic Volatility Model (LSV). This model considers volatility as the product between a deterministic and a stochastic term. So far, the model choice was not only driven by the capacity of capturing empirically observed market features well, but also by the computational tractability of the calibration process. This is now undergoing a big change since machine learning technologies offer new perspectives on model calibration. In this thesis we consider the calibration problem to be the search for a model which generates given market prices and where additionally technology from generative adversarial networks can be used. This means parametrizing the model pool in a way which is accessible for machine learning techniques and interpreting the inverse problems a training task of a generative network, whose quality is assessed by an adversary. The calibration algorithm proposed for LSV models use as generative models so-called neural stochastic differential equations (SDE), which just means to parameterize the drift and volatility of an Ito-SDE by neural networks.
Tipologia del documento
Tesi di laurea
(Laurea magistrale)
Autore della tesi
Todeschi, Tiziano
Relatore della tesi
Scuola
Corso di studio
Indirizzo
Curriculum A: Generale e applicativo
Ordinamento Cds
DM270
Parole chiave
neural networks stochastic differential equations SDE calibration local-stochastic volatility black-scholes pricing machine deep learning
Data di discussione della Tesi
26 Marzo 2021
URI
Altri metadati
Tipologia del documento
Tesi di laurea
(NON SPECIFICATO)
Autore della tesi
Todeschi, Tiziano
Relatore della tesi
Scuola
Corso di studio
Indirizzo
Curriculum A: Generale e applicativo
Ordinamento Cds
DM270
Parole chiave
neural networks stochastic differential equations SDE calibration local-stochastic volatility black-scholes pricing machine deep learning
Data di discussione della Tesi
26 Marzo 2021
URI
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