Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation

Heath, David; Jarrow, Robert A.; Morton, Anthony

doi:10.2307/2951677

Cited by 2,625 publications

(1,073 citation statements)

References 14 publications

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“…Such volatility structures can be combined to form two-factor models. For instance, a two-factor model where the first factor is given by the Ho-Lee structure and the second by the Hull-White structure was introduced by Heath et al (1992). It will be denoted by HL-HW and analogous notation will be used for the other models considered.…”

Section: The Modelsmentioning

confidence: 99%

Consistent calibration of HJM models to cap implied volatilities

Angelini

Herzel

2005

J. Fut. Mark.

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This paper proposes a calibration algorithm that fits multi-factor Gaussian models to the implied volatilities of caps using the respective minimal consistent family to infer the forward rate curve. The algorithm is applied to three forward rate volatility structures and their combination to form two-factor models. The efficiency of the consistent calibration is evaluated through comparisons with non-consistent methods. The selection of the number of factors and of the volatility functions is supported by a Principal Component Analysis. Models are evaluated in terms of in-sample and out-of-sample data fitting as well as stability of parameter estimates. The results are analyzed mainly focusing on the capability of fitting the market implied volatility curve and, in particular, of reproducing its characteristic humped shape.

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Section: The Modelsmentioning

confidence: 99%

Consistent calibration of HJM models to cap implied volatilities

Angelini

Herzel

2005

J. Fut. Mark.

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“…The resulting term structure estimated from the statistical techniques can be directly put into the interest rate models such as the Hull [9], and Heath [10] models, for pricing interest rate contingent claims. Since a coupon bond can be considered as a portfolio of discount bonds with maturities dates consistent with the coupon dates, the discount bond prices can thus be extracted from the actual coupon bond prices by statistical techniques.…”

Section: Literature Surveymentioning

confidence: 99%

In Search of the Best Zero Coupon Yield Curve for Nairobi Securities Exchange: Interpolation Methods vs. Parametric Models

Muthoni¹

2015

JMF

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We seek to determine which yield curve construction method produces the best zero coupon yield curve (ZCYC) for Nairobi Securities Exchange (NSE). The ZCYC should be differentiable at all points and at the same time, should produce a continuous and positive forward curve at all knot points. A decreasing discount curve is also expected from the resulting ZCYC, as an indication of monotonicity. For the interpolation method, we will use an improvement of monotone preserving interpolation method on ( ) r t t , while the Nelson and Siegel [1] model is the parametric model of choice. This is because compared to other interpolation methods, the improvement of monotone preserving interpolation method on ( ) r t t produces curves with the desirable trait of differentiability, while the Nelson-Siegel [1] model is shown to produce the best-fit results for Kenyan bond data. We compare the models' performance in terms of accuracy in pricing back the fixed-income securities. For this study, we use bond data from Central Bank of Kenya (CBK). The better of the two methods will be used for the Kenyan securities market and, consequently, the East African Securities markets.

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“…As regards the demographic scenario, the Poisson Lee Carter model is considered according to the three different approaches for forecasting mortality rates: the Iterative Procedure (IP) proposed by Renshaw & Haberman (2003c) The dataset that we refer to for estimating the survival probabilities is the Italian male population death rates collected in the period 1950-2006. For the financial markets assumptions, we adopt the interest rate structure based on the Heath, Jarrow and Morton model (HJM, from here on - Heath et al 1992). The HJM model describes the dynamics of instantaneous forward-rates which are wholly specified through their instantaneous volatility structures modelled as follows:…”

Section: The Case Of a Pension Annuity Portfoliomentioning

confidence: 99%

The Poisson Log-Bilinear Lee-Carter Model

D’Amato

Lorenzo

Haberman

et al. 2011

North American Actuarial Journal

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractLife insurance companies deal with two fundamental types of risks when issuing annuity contracts: financial risk and demographic risk. As regards the latter, recent work has focused on modelling the trend in mortality as a stochastic process. A popular method for modelling death rates is the Lee-Carter model. This methodology has become widely used and there have been various extensions and modifications proposed to obtain a broader interpretation and to capture the main features of the dynamics of mortality rates. In order to improve the measurement of uncertainty in survival probability estimates, in particular for older ages, the paper proposes an extension based on simulation procedures and on the bootstrap methodology. It aims to obtain more reliable and accurate mortality projections, based on the idea of obtaining an acceptable accuracy of the estimate by means of variance reducing techniques. In this way, the forecasting procedure becomes more efficient. The longevity question constitutes a critical element in the solvency appraisal of pension annuities. The demographic models used for the cash flow distributions in a portfolio impact on the mathematical reserve and surplus calculations and affect the risk management choices for a pension plan. The paper extends the investigation of the impact of survival uncertainty for life annuity portfolios and for a guaranteed annuity option in the case where interest rates are stochastic. In a framework in which insurance companies need to use internal models for risk management purposes and for determining their Solvency Capital Requirement, the authors consider the surplus value, calculated as the ratio between the market value of the projected assets to that of the liabilities, as a meaningful measure of the company's financial position, expressing the degree to which the liabilities are covered by the assets.

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Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation

Cited by 2,625 publications

References 14 publications

Consistent calibration of HJM models to cap implied volatilities

Consistent calibration of HJM models to cap implied volatilities

In Search of the Best Zero Coupon Yield Curve for Nairobi Securities Exchange: Interpolation Methods vs. Parametric Models

The Poisson Log-Bilinear Lee-Carter Model

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