The extreme financial markets volatility that the financial crisis unleashed in 2008, continues to challenge researchers on how best to keep track and model such market movements. This book, entitled "Jump Diffusion and Stochastic Volatility Models in Securities Pricing", seeks to add value to the endeavor of modeling volatility and jumps across various asset classes. The aim is to improve risk management efforts and for more accurate pricing of primary and derivative securities. The book presents jump diffusion and stochastic volatility models for the movements of equities, currencies, interest rates, house prices and temperature. All asset classes demonstrate the presence of jumps and stochastic volatility in the movement of their prices.The jumps conform to the Poisson model while stochastic volatility conforms to a normal and a fat-tailed Garch models. Maximum likelihood methods are used to estimate various parameters in the mixture of distributions.