Swishchuk, AnatoliyWang, Zijia2017-08-102017-08-1020172017http://hdl.handle.net/11023/4004In this thesis, we consider volatility swap, variance swap and VIX future pricing under different asset models. Specifically, we obtain the new results of swaps and futures pricing for the geometric Markov renewal processes (GMRP) models under different schemes and approximation approaches. We also consider four different stochastic volatility models and jump diffusion models which are commonly used in financial market, and use convexity correction approximation technique and Laplace transform method to evaluate the variance and volatility strikes and estimate the VIX future prices. In empirical study, we use Markov chain Monte Carlo algorithm for model calibration based on S&P 500 market data, evaluate the effect of adding jumps into the asset price processes on volatility derivatives pricing, and compare the performance of different pricing approaches.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Education--FinanceMathematicsvariance and volatility swapsgeometric Markov renewal processVIX futuresmaster thesis10.11575/PRISM/28632