The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence

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Abstract
Although traded as distinct products, caps and swaptions are linked by no‐arbitrage relations through the correlation structure of interest rates. Using a string market model, we solve for the correlation matrix implied by swaptions and examine the relative valuation of caps and swaptions. We find that swaption prices are generated by four factors and that implied correlations are lower than historical correlations. Long‐dated swaptions appear mispriced and there were major pricing distortions during the 1998 hedge‐fund crisis. Cap prices periodically deviate significantly from the no‐arbitrage values implied by the swaptions market.