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Interest Rate Caps “Smile” Too! But Can the LIBOR Market Models Capture the Smile?
Author(s) -
JARROW ROBERT,
LI HAITAO,
ZHAO FENG
Publication year - 2007
Publication title -
the journal of finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 18.151
H-Index - 299
eISSN - 1540-6261
pISSN - 0022-1082
DOI - 10.1111/j.1540-6261.2007.01209.x
Subject(s) - implied volatility , volatility smile , econometrics , volatility (finance) , economics , stochastic volatility , libor , forward volatility , interest rate , sabr volatility model , moneyness , libor market model , interest rate derivative , financial economics , monetary economics
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.