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

  • Author(s): Longstaff, Francis A
  • Santa-Clara, Pedro
  • Schwartz, Eduardo S
  • et al.
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 framework, we solve for the correlation matrix implied by the swaptions market and examine the relative valuation of caps and swaptions. The results indicate that swaption prices are generated by four factors and that implied correlations are generally lower than historical correlations. We find evidence that long-dated swaptions are priced inconsistently and that there were major distortions in the swaptions market during the hedge-fund crisis of late 1998. We also find that cap prices periodically deviate significantly from the no-arbitrage values implied by the swaptions market.

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