In this thesis, the research focuses on the development and implementation of two hybrid models for pricing variance swaps and variance options. Some variance derivatives (i.e., variance swap) are priced using portfolios of put and call options. However, longer-term options price not only stock...

In this dissertation we propose a new model which captures observed features of asset prices. The model reproduces the skewness and fat tails of asset returns by introducing a discretized variance gamma process as the driving innovation process, in addition to a double gamma process to reflect...

In this thesis two contributions are made to the area of mathematical finance. First, in order to explain the non-trivial skewness and kurtosis that is observed in the time series data of constant maturity swap (CMS) rates, we employ the pure jump Levy processes, i.e. in particular Variance...

Studies of asset returns time-series provide strong evidence that at least two stochastic factors drive volatility. The first essay investigates whether two volatility risks are priced in the stock option market and estimates volatility risk prices in a cross-section of stock option returns. The...

Levy processes have gained great success in pricing single asset options. In this thesis, we introduce a methodology enabling us to extend the single asset pricing technique based on Levyprocesses to multiasset cases.In our method, we assume the log-return of each asset as a linear sum of...

In this thesis, stochastic volatility models with Levy processes are treatedin parameter calibration by the Carr-Madan fast Fourier transform (FFT) method and pricingthrough the partial integro-differential equation (PIDE) approach. First, different models where the underlying log stock price or...