Closed-form approximations for option prices in stochastic volatility models via the mixing solution
thesisposted on 03.12.2019 by KAUSTAV DAS
In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.
We consider the classical European option pricing problem in a general stochastic volatility framework with time-dependent parameters. It is possible to express the price of a European option as the expectation of a functional of the integrated variance process. In particular, this functional itself is similar to that of a Black-Scholes formula, which possesses many well studied properties. From there, it is possible to utilise expansion techniques to approximate the option price in a closed-form manner. We achieve this using two different types of approaches, one contingent on change of measure techniques, the other on Malliavin calculus machinery.