Filip Andersson: Forward start option pricing with four different stochastic volatility models

Ever since the famous Black-Scholes model (1973), a vast amount of research has aimed at relaxing the assumptions and also allow for non-constant volatility and non-normal return distributions. In this thesis, we study four stochastic volatility models, from the Heston's single factor volatility model (1993) to extensions of it with two-factor stochastic volatility model allowing for log-normal distributed jumps in the underlying process. Instead of pursuing the classical route to find "true" model parameters using a multiple cross-sectional estimation, we assume that the models are all to some degree mis-specified and estimate the models at 22 different days in October 2008. The results show that the more extensive models seemingly suffer from over-parameterisation as the parameter values are varying both over time and across the different loss functions used for the estimations. The estimated parameters are used for pricing forward-start call options, and we carry out a simple sensitivity analysis on the option prices to highlight the importance of the specific parameters. The results show that small changes in the long-run mean of the volatility together with the jump frequency have the greatest impact on the option price.