Title: Pricing of simple and path-dependent European options in the Jacobi stochastic volatility model
Other Titles: Bewertung von einfachen und pfadabhängigen Optionen im Jacobi-Stochastische-Volatilitäts-Modell
Language: English
Authors: Götz, Simone 
Qualification level: Diploma
Advisor: Gerhold, Stefan 
Issue Date: 2020
Number of Pages: 97
Qualification level: Diploma
We discuss a stochastic volatility model in which the squared volatility is modeled as anaffine transformed Jacobi process. In this model, which contains the Heston model as limiting case, the log-price density as well as the density of the finite dimensional distributionsof the log-returns admit a closed-form series representation with respect to the generalizedHermite polynomials, known as Gram-Charlier series expansion. We use this to deriveseries representations for option prices and we find explicit formulas for European call,put and binary options. The pricing technique is expanded to path-dependent Europeanoptions whose payoff functions depend on finitely many monitoring dates. Approximationerrors, which occur by truncation of the series at some finite order, are also studied andillustrated by some numerical examples.
Keywords: Stochastische Volatilität; Jacobi-Prozess; Polynomiale Diffusion; Optionsbewertung
Stochastic volatility; Jacobi Process; Polynomial Diffusion; Option pricing
URI: https://doi.org/10.34726/hss.2020.63242
DOI: 10.34726/hss.2020.63242
Library ID: AC15685518
Organisation: E105 - Institut für Stochastik und Wirtschaftsmathematik 
Publication Type: Thesis
Appears in Collections:Thesis

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