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

Feng Zhao, Robert Jarrow () and Haitao Li

No 431, Econometric Society 2004 North American Winter Meetings from Econometric Society

Abstract: Using more than two years of daily interest rate cap price data, this paper provides a systematic documentation of a volatility smile in cap prices. We find that Black (1976) implied volatilities exhibit an asymmetric smile (sometimes called a sneer) with a stronger skew for in-the-money caps than out-of-the-money caps. The volatility smile is time varying and is more pronounced after September 11, 2001. We also study the ability of generalized LIBOR market models to capture this smile. We show that the best performing model has constant elasticity of variance combined with uncorrelated stochastic volatility or upward jumps. However, this model still has a bias for short- and medium-term caps. In addition, it appears that large negative jumps are needed after September 11, 2001. We conclude that the existing class of LIBOR market models can not fully capture the volatility smile

Keywords: LIBOR market models; volatility smile; interest rate caps (search for similar items in EconPapers)
JEL-codes: C4 C5 G1 (search for similar items in EconPapers)
Date: 2004-08-11
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Citations: View citations in EconPapers (11)

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