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TFM_He_Yuanxi.pdf (1.25 MB)

Tipus de document

Treball de fi de màster

Data de publicació

2026-06-07

Llicència de publicació

cc by-nc-nd (c) He, Yuanxi, 2026
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/230597

Sandwiched Volterra Volatility models: theory and applications

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This thesis begins with an introduction to mathematical finance, reviewing the historical development of asset-price models and several stylised facts observed in financial markets. We then motivate the study of fractional and rough volatility models, which are driven by fractional Brownian motion and provide a more realistic description of volatility dynamics. The necessary definitions and theoretical results concerning fractional Brownian motion are also presented. Building on the work of Di Nunno et al. [15], we study the Sandwiched Volterra Volatility (SVV) model. In particular, we reformulate the general SVV framework in a one-dimensional setting, which allows for a more transparent exposition of the model and more detailed proofs of several key results. We further illustrate the model through a number of examples. In addition, we investigate the Malliavin differentiability of both the volatility and asset-price processes within the SVV framework and provide rigorous proofs of the corresponding results. Finally, we analyse classical rough volatility models in order to characterise those that can be represented within the Sandwiched Volterra Volatility (SVV) framework. We show that most of the models studied fall into this class, with the exception of the Rough Fractional Stochastic Volatility model (for Hurst parameter $H \neq \frac{1}{2}$), the rough Heston model, and the quadratic rough Heston model.

Descripció

Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Any: 2026. Director: Josep Vives i Santa Eulàlia i David Márquez Carreras

Matèries

Càlcul de Malliavin, Matemàtica financera, Anàlisi estocàstica, Treballs de fi de màster

Matèries (anglès)

Malliavin calculus, Business mathematics, Stochastic analysis, Master's thesis

Citació

Col·leccions

Màster Oficial - Matemàtica Avançada

Citació

HE, Yuanxi. Sandwiched Volterra Volatility models: theory and applications. [consulted: 25 of July of 2026]. Available at: https://hdl.handle.net/2445/230597

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