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Interest Rate Caps “Smile” Too! But Can the LIBOR Market Models Capture the Smile?





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    • Jarrow is from the Johnson Graduate School of Management, Cornell University. Li is from the Stephen M. Ross School of Business, University of Michigan. Zhao is from the Rutgers Business School, Rutgers University. We thank Warren Bailey, Peter Carr, Fousseni Chabi-Yo, Jefferson Duarte, Richard Green (the editor), Pierre Grellet Aumont, Anurag Gupta, Bing Han, Paul Kupiec, Francis Longstaff, Kenneth Singleton, Marti Subrahmanyam, Siegfried Trautmann, an anonymous referee, and seminar participants at the Federal Deposit Insurance Corporation, Rutgers University, the 2003 European Finance Association Meeting, the 2004 Econometric Society Winter Meeting, the 2004 Western Finance Association Meeting, Bank of Canada Fixed-Income Conference, the 15th Annual Derivatives Conference, and the Financial/Actuarial Mathematics Seminar at the University of Michigan for helpful comments. We are responsible for any remaining errors.


Using 3 years of interest rate caps price data, we provide a comprehensive documentation of volatility smiles in the caps market. To capture the volatility smiles, we develop a multifactor term structure model with stochastic volatility and jumps that yields a closed-form formula for cap prices. 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.