Unspanned Stochastic Volatility: Evidence from Hedging Interest Rate Derivatives




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    • Li is from the Stephen M. Ross School of Business, University of Michigan. Zhao is from Rutgers Business School, Rutgers University. We would like to thank Warren Bailey, Alexander David, Bob Dittmar, Bob Goldstein, Bob Jarrow, Hong Liu, Mark Ready, Robert Stambaugh (the editor), Liuren Wu, Xiaoyan Zhang, Guofu Zhou, an anonymous referee, and seminar participants at Cornell University, Fordham University, Rutgers University, Singapore Management University, SUNY at Binghamton, University of California at Riverside, University of Massachusetts at Amherst, University of Michigan, University of Wisconsin–Madison, and Washington University in St. Louis for helpful comments and discussions. We thank David George for editorial assistance. We are responsible for any remaining errors.


Most existing dynamic term structure models assume that interest rate derivatives are redundant securities and can be perfectly hedged using solely bonds. We find that the quadratic term structure models have serious difficulties in hedging caps and cap straddles, even though they capture bond yields well. Furthermore, at-the-money straddle hedging errors are highly correlated with cap-implied volatilities and can explain a large fraction of hedging errors of all caps and straddles across moneyness and maturities. Our results strongly suggest the existence of systematic unspanned factors related to stochastic volatility in interest rate derivatives markets.