Swishchuk, AnatoliyDevauld, Wesley2013-05-302013-11-122013-05-302013http://hdl.handle.net/11023/745We model asset prices with stochastic volatilities driven by fractional Brownian motion. Price paths and their endpoints are used to obtain a Monte Carlo value estimate of vanilla european options, lookback options as well as variance swaps. Underlying models for price movements are driven by stochastic volatility models driven by fractional Brownian motion with H > 1/2 . These models exhibit a strong autocorrelation in volatility evolution. The models considered are fractional Ornstein Uhlenbeck, fractional Cox-Ingersoll-Ross, fractional Continuous GARCH(1,1) and fractional Heston.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.MathematicsMathematicsStochastic VolatilityMonte CarloEuropean OptionsLookback OptionsVariance Swapsfractional Brownian MotionStochastic Variancemaster thesis10.11575/PRISM/27003