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The Valuation of Caps, Floors and Swaptions in a Multi-Factor Spot-Rate Model. We build a multi-factor, no-arbitrage model of the term structure of interest rates. The stochastic factors are the short-term interest rate and the premia of the futures rates over the short-term interest rate. In the three-factor version of the model, for example, the rst factor is the threemonth LIBOR, the second factor is the premium of the rst futures LIBOR over spot LIBOR, and the third factor is the incremental premium of the second futures over the rst. The model provides an extension of the lognormal interest rate model of Black and Karasinski (1991) to multiple factors, each of which can exhibit mean-reversion. The method is computationally eÆcient for several reasons. First, since our model is based on LIBOR futures prices, we can satisfy the noarbitrage condition without resorting to iterative methods. Second, we modify and implement the binomial approximation methodology of Nelson and Ramaswamy (1990) and Ho, Stapleton and Subrahmanyam (1995) to compute a multi-period tree of rates with the no-arbitrage property. The method uses a recombining two or three-dimensional binomial lattice of interest rates that minimizes the number of states and term structures over time. In addition to these computational advantages, a key feature of the model is that it is consistent with the observed term structure of futures rates as well as the term structure of volatilities implied by the prices of interest rate caps and oors. We use the model to price European-style, Bermudan-style, and American-style swaptions. These prices are shown to be sensitive to the number of factors and their volatility and correlation characteristics. In an empirical illustration we rst calibrate a two-factor version of the model to the caplet impliedvolatility curve and use the model to price European-style swaptions. We nd that the model overprices the swaptions relative to market quotations. However, when we extend the model to three factors we nd the mispricing is considerably reduced. In line with previous work by Cooper and Rebonato (1995), we conclude that at least three factors are required to explain market cap, oor and swaption prices. The calibrated three-factor model is then used to price American-style and Bermudan-style swaptions as well as other yield-curve dependent options such as yield-spread options. The Valuation of Caps, Floors and Swaptions 1