Financial/Actuarial Mathematics Seminar

Using three years of interest rate caps price data, we provide one of the first comprehensive documentations of volatility smiles in the caps market. Using a multifactor term structure model with stochastic volatility and jumps, we develop a closed-form solution for cap prices and test the performance of our new models in capturing the volatility smile. We show that although a three-factor stochastic volatility model can price at-the-money caps well, significant negative jumps in interest rates are needed to capture the smile. The volatility smile contains information that is not available using only at-the-money caps, and this information is important for understanding term structure models.