Stochastic Correlation and the Relative Pricing of Caps and Swaptions in a Generalized-Affine Framework

Several recent papers document significant relative mis-pricings between caps and swaptions using traditional multi-factor models of the term structure. Below we argue that these mis-pricings are due to the severe restrictions that traditional models place on the joint evolution of the i) term structure, ii) volatility structure, and iii) correlation structure. We first provide additional empirical evidence for the existence of each of these types of risk. We then introduce a 'generalized-affine' class of models with regime shifts in correlation to model these empirical findings. We show that this class of models remains very tractable, permitting closed-form solutions for caps, and an efficient and accurate method for pricing swaptions. Contrary to intuition, we demonstrate that a cap, which is effectively a portfolio-of-options, is much more sensitive to changes in correlation than is a swaption, which is effectively an option-on-a-portfolio.

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