Is It Possible to Reconcile the Caplet and Swaption Markets? Evidence from the U.S.-Dollar Market

Abstract

One of the persistent and annoying puzzles in the area of interest rate derivatives is that models that can price interest rate caps consistently relative to their prices in the market fail to price swaptions properly, and vice versa, even though the payoffs to both types of derivative depend on the same spot and forward interest rates. Is reconciling the two markets just a matter of finding the right interest rate process? In this article, Rebonato and Pogudin take the very general class of models that falls within the LIBOR market model-stochastic alpha, beta, rho (LMM-SABR) family to explore whether a common valuation model can be obtained. Calibrating to caplet prices, they find overall reasonable fits but have difficulty matching swaption market prices; in particular, those with long underlying swapmaturities seem overpriced in the market. Exploring alternative assumptions on the term structure of forward rate volatilities and volatility of volatility brings them to a strategy that super-replicates a swaption payoff with an early-stopping cap contract. The model can price the two reasonably well, but in the market, the swaptions are regularly priced very close to the model-free noarbitrage bound. Moreover, the assumptions needed to get to that result entail highly unrealistic expectations about future cap prices. So, after careful exploration that illuminates the nature of the puzzle, the puzzle remains puzzling. <b>TOPICS:</b>Interest-rate and currency swaps, factor-based models