In this article, the authors present a general and flexible numerical procedure for pricing European interest-rate derivatives within multifactor affine term structure models by means of piecewise multilinear interpolations of the option value function. Their procedure relies to the maximum extent on the true density of the state process and solves the pricing problem in quasi-closed form. Then, they show how to generalize their approach for pricing American-style options. As an illustration, they price interest-rate swaptions and Eurodollar futures options, which cannot be analytically evaluated. They use nine affine models and show that their approach converges rapidly and competes well against Monte Carlo simulation. They also demonstrate that their approach remains well-behaved for pricing deeply out-of-the-money interest-rate derivatives.A ff ine term structure models (ATSMs) have rapidly become the standard for modeling the dynamics of the yield curve and, more broadly, valuing fixed-income instruments. The popularity of multifactor affine models among both practitioners and academics is largely ref lective of their tractability, which allows for analytical solutions for government and corporate yields even in the presence of a large number of factors. Another reason for the popularity of these models is their ability to capture several welldocumented empirical, stylized facts. First and foremost, the presence of more than one factor is necessary to adequately model the shape of the yield curve, as shown by Litterman and Scheinkman [1991]. Second, affine models can easily accommodate specifications for the market price of risk, which are able to explain the failure of the expectation hypothesis and the time-varying nature of the term premium (Duffee [2002], Dai and Singleton [2002], and Cheridito et al. [2007]). Finally, affine models can also be constrained in a way that makes volatility uncorrelated with the cross-section of yields, which is consistent with the findings of Collin-Dufresne and Goldstein [2002a]. This phenomenon is referred to as unspanned stochastic volatility (Andersen and Benzoni [2010], Chernov and Bikbov [2009], Collin-Dufresne and Goldstein [2002a], Collin-Dufresne et al. [2008], Jacobs and Karoui [2009], and Li and Zhao [2006]).Despite the tractability of aff ine models and the substantial progress made in improving their empirical performance, the pricing of interest-rate derivatives still poses significant conceptual and computational challenges. We propose a general and f lexible numerical procedure for pricing European interest-rate derivatives within the affine class of term structure models by means of piece-
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