Term Structure Dynamics and Mortgage Valuation

Cheyette, Oren

doi:10.3905/jfi.1992.408036

Cited by 44 publications

(23 citation statements)

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“…This computational burden can be greatly reduced by using special cases of the HJM models which are Markovian. Notable among these special cases are the 'separable' nfactor models of Cheyette (1992) and Li et al (1995) and Ritchken and Sankarasubramanian (1995). Although the 'separable' n factor models are Markovian, they require n(n ‡ 3)=2 state variables, which still imposes a stiff computational burden.…”

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confidence: 99%

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Markov interest rate models

Hagan¹,

Woodward

1999

Applied Mathematical Finance

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A general procedure for creating Markovian interest rate models is presented. The models created by this procedure automatically fit within the HJM framework and fit the initial term structure exactly. Therefore they are arbitrage free. Because the models created by this procedure have only one state variable per factor, twoand even three-factor models can be computed efficiently, without resorting to Monte Carlo techniques. This computational efficiency makes calibration of the new models to market prices straightforward. Extended Hull- White, extended CIR, Black-Karasinski, Jamshidian's Brownian path independent models, and Flesaker and Hughston's rational log normal models are one-state variable models which fit naturally within this theoretical framework. The 'separable' n-factor models of Cheyette and Li, Ritchken, and Sankarasubramanian - which require n(n + 3)/2 state variables - are degenerate members of the new class of models with n(n + 3)/2 factors. The procedure is used to create a new class of one-factor models, the 'β-η models.' These models can match the implied volatility smiles of swaptions and caplets, and thus enable one to eliminate smile error. The β-η models are also exactly solvable in that their transition densities can be written explicitly. For these models accurate - but not exact - formulas are presented for caplet and swaption prices, and it is indicated how these closed form expressions can be used to efficiently calibrate the models to market prices.

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confidence: 99%

“…The separable models (Li et al, 1995;Ritchken and Sankarasubramanian, 1995;Cheyette, 1992) are derived by presuming that the volatilities have the form…”

Section: E Separable Modelsmentioning

confidence: 99%

Markov interest rate models

Hagan¹,

Woodward

1999

Applied Mathematical Finance

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“…Under special volatility restrictions, the path dependence can be completely removed and closed form solutions are available for bond prices. Here we only discuss a one-dimensional case, which has been considered by Cheyette (1992), Jamshidian (1991), andRitchken andSankarsubramanian (1995). In the one-dimensional case, to remove the path dependence, one can choose …”

Section: The Long Rate In the Duffie-kan Affine Modelsmentioning

confidence: 99%

Term Structure Models: A Perspective from the Long Rate

Yao¹

1999

North American Actuarial Journal

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“…Essentially we extend to the jump diffusion case the approach of the Markovianisation of HJM models developed by a number of authors. Early papers on the Markovianisation of HJM models under Wiener diffusions include Cheyette (1992), Carverhill (1991), Ritchken and Sankarasubramanian (1995) and Bhar and Chiarella (1997), where the conditions on the volatility structure for the spot rate process to be Markovian are examined for the one factor HJM models. Inui and Kijima (1998) and de Jong and Santa-Clara (1999) extend these conditions to multi factor HJM models.…”

Section: Introductionmentioning

confidence: 99%

A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework

Chiarella

Nikitopoulos

2003

Asia-Pacific Finan Markets

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This paper considers a class of term structure models that is a parameterisation of the Shirakawa (1991) extension of the Heath et al. (1992) model to the case of jump-diffusions. We consider specific forward rate volatility structures that incorporate state dependent Wiener volatility functions and time dependent Poisson volatility functions. Within this framework, we discuss the Markovianisation issue, and obtain the corresponding affine term structure of interest rates. As a result we are able to obtain a broad tractable class of jump-diffusion term structure models. We relate our approach to the existing class of jump-diffusion term structure models whose starting point is a jump-diffusion process for the spot rate. In particular we obtain natural jump-diffusion versions of the Hull and White (1990, 1994) one-factor and two-factor models and the Ritchken and Sankarasubramanian (1995) model within the HJM framework. We also give some numerical simulations to gauge the effect of the jump-component on yield curves and the implications of various volatility specifications for the spot rate distribution. Copyright Springer Science + Business Media, Inc. 2003jump-diffusions, Markovian HJM model, state dependent volatility,

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Term Structure Dynamics and Mortgage Valuation

Cited by 44 publications

References 0 publications

Markov interest rate models

Markov interest rate models

Term Structure Models: A Perspective from the Long Rate

A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework

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