Götz, S. (2020). Pricing of simple and path-dependent European options in the Jacobi stochastic volatility model [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2020.63242
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.
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