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

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  • ROBERT JARROW
  • HAITAO LI
  • FENG ZHAO

Abstract

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.

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  • Robert Jarrow & Haitao Li & Feng Zhao, 2007. "Interest Rate Caps “Smile” Too! But Can the LIBOR Market Models Capture the Smile?," Journal of Finance, American Finance Association, vol. 62(1), pages 345-382, February.
    • Handle: RePEc:bla:jfinan:v:62:y:2007:i:1:p:345-382
    DOI: 10.1111/j.1540-6261.2007.01209.x
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