Pricing Swaptions and Coupon Bond Options in Affine Term Structure Models

Schrager, David; Pelsser, Antoon

doi:10.1111/j.1467-9965.2006.00289.x

Cited by 68 publications

(73 citation statements)

References 29 publications

(106 reference statements)

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“…This is not the case for the exponential affine or quadratic class. Researchers often resort to different dynamics specifications for pricing caps and floors, which are essentially options on zero-coupon bond, than for pricing swaptions; or one must resort to linear approximations to retain tractability (Heidari, Hirsa, and Madan (2007) and Schrager and Pelsser (2006)). By starting with a linearity-generating process, we remove the need for linear approximation on the pricing relation and circumvent the concern on internal consistency when different dynamics or different approximations are used to price different contracts.…”

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confidence: 99%

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing

Carr

Gabaix

2011

SSRN Journal

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We propose to use the linearity-generating framework to accommodate the evidence of unspanned stochastic volatility: Variations in implied volatilities on interest-rate options such as caps and swaptions are independent of the variations on the interest rate term structure. Under this framework, bond valuation depends only on the transition dynamics of interest-rate factors, but not on their volatilities.Thus, interest-rate volatility is truly unspanned. Furthermore, this framework allows tractable pricing of options on any bond portfolios, including both caps and swaptions. This feat is not possible under existing exponential-affine or quadratic frameworks. Finally, the framework allows sequential estimation of the interest-rate term structure and the interest-rate option implied volatility surface, thus facilitating joint empirical analysis. Within this framework, we perform specification analysis on interest-rate factor transition dynamics and its relation to the interest-rate term structure; we also analyze the interest-rate volatility dynamics and its impact on interest-rate option pricing. We estimate several specifications for the transition dynamics to ten years worth of U.S. dollar LIBOR and swap rates across 15 maturities. We also estimate several interest-rate volatility dynamics specifications using ten years of swaption implied volatilities across a matrix of ten option maturities and seven swap tenors. The estimation results show that the volatility dynamics dictate the option implied volatility variation along the option maturity dimension, whereas the interest-rate transition dynamics dictate the implied volatility variation along the underlying swap maturity dimension.JEL Classification: C13; C51; G12; G13.

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confidence: 99%

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing

Carr

Gabaix

2011

SSRN Journal

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“…6 Schrager and Pelsser (2006) and Duffie and Singleton (1997) for the 2-factors C.I.R. model 7 diag(σ) means the diagonalization of the vector σ and chol(ρ) means the Cholesky decomposition of the correlation matrix ρ, where σ and ρ are the volatility vector and the correlation matrix, respectively, of the original paper.…”

Section: Vasicek Model Three-factors Gaussian Model and Cox-ingersolmentioning

confidence: 99%

“…The most important are those of Munk (1999), Collin- Dufresne and Goldstein (2002), Singleton and Umantsev (2002) and Schrager and Pelsser (2006). Munk approximates the price of an option on a coupon bond by a multiple of the price of an option on a zero-coupon bond with time to maturity equal to the stochastic duration of the coupon bond.…”

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Accurate Pricing of Swaptions via Lower Bound

Gambaro

Caldana

Fusai

2017

International Series in Operations Research &Amp; Management Science

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We propose a new lower bound for pricing European-style swaptions for a wide class of interest rate models. This method is applicable whenever the joint characteristic function of the state variables is either known in closed form or can be obtained numerically via some efficient procedure. Our lower bound involves the computation of a one dimensional Fourier transform independently of the underlying swap length. Finally the bound can be used as a control variate to reduce the confidence interval in the Monte Carlo simulation. We test our bound on different affine models, also allowing for jumps. The lower bound is found to be accurate and computationally efficient.

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“…They demonstrated that their approach is accurate compared with Monte Carlo simulation for a three-factor Gaussian model as well as a two-factor square-root model. Schrager and Plesser [2006] investigated the pricing of swaptions within LIBOR market models. They linearized the dynamics of the swap rate under the swap measure ( Jamshidian [1997]) and used the conditional Fourier transform to approximate the swaption price.…”

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confidence: 99%

Pricing Interest-Rate Derivatives with Piecewise Multilinear Interpolations and Transition Parameters

Ben‐Ameur

Karoui

Mnif

2014

JOD

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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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Pricing Swaptions and Coupon Bond Options in Affine Term Structure Models

Cited by 68 publications

References 29 publications

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing

Accurate Pricing of Swaptions via Lower Bound

Pricing Interest-Rate Derivatives with Piecewise Multilinear Interpolations and Transition Parameters

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