A Glimpse at the Mathematics of Stochastic Volatility

This book is a thought process that begins with a basic understanding of Financial Mathematics that graduates towards an understanding of Stochastic Volatility and in particular a variation of the popular Cox-Ingersoll-Ross Model (CIR). Due to the nature of the research, the beginning chapter outlines key ideas and techniques that need to be understood in order to define what stochastic volatility is, why it came into use, and how to tie theory to practical application. Once done, a question is posed. Does stock price affect the volatility driving process in the CIR Model? By utilizing the information presented, the groundwork for this hypothesis is presented in detail. Later parts of the book follow closely along with the work of Jean-Pierre Fouque's analysis of the Ornstein-Uhlenbeck (OU) process, by utilizing asymptotic estimation to calculate the pricing process of our CIR Model variation. The final result will then utilize real-time bond prices in order to give an estimate to the equation presented and a conclusion will be drawn.