One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities

Hull, John C.; White, Alan

doi:10.2307/2331288

Cited by 373 publications

(195 citation statements)

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“…4 There is an analogous class of so-called no-arbitrage term-structure models that are calibrated to fit exactly the observed cross-section of bond yields. See, for example, Black et al (1990), Brandt and Yaron (2002), Heath et al (1992), Ho and Lee (1986), and Hull and White (1993). 5 Other references on deterministic volatility function models include Aït-Sahalia and Lo (1998), Barle and Cakici (1995), Breeden and Litzenberger (1978), Burashi and Jackwerth (2001), Chriss (1997), and Jackwerth and Rubinstein (1996a,b).…”

Section: Introductionmentioning

confidence: 99%

Cross-sectional tests of deterministic volatility functions

Brandt

2002

Journal of Empirical Finance

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We study the cross-sectional performance of option pricing models in which the volatility of the underlying stock is a deterministic function of the stock price and time. For each date in our sample of FTSE 100 index option prices, we fit an implied binomial tree to the panel of all European style options with different strike prices and maturities and then examine how well this model prices a corresponding panel of American style options. We find that the implied binomial tree model performs no better than an ad-hoc procedure of smoothing Black -Scholes implied volatilities across strike prices and maturities. Our cross-sectional results complement the time-series findings of

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Section: Introductionmentioning

confidence: 99%

Cross-sectional tests of deterministic volatility functions

Brandt

2002

Journal of Empirical Finance

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Section: Discussionmentioning

confidence: 99%

“…The lattice produces an array of interest rates that result in prices of bonds that are the same as those observed in the market and follow the behavioral characteristics of the SDEs. Some of the most well-known models that use this approach are Ho and Lee [1986], Black, Derman, and Toy [1990], Hull andWhite [1990, 1993], Black and Karasinski [1991], and Heath, Jarrow, and Morton [1992].…”

Section: T H I S a R T I C L E I N A N Y F O R M A T December 2001mentioning

confidence: 99%

“…The models are: Ho and Lee; Kalotay, Williams, and Fabozzi; Black, Derman, and Toy; Hull and White; and Black and Karasinski. In the trinomial framework, we use the implementation technique of Hull and White [1990White [ , 1993White [ , 1994.We show that these interest rate models produce substantially different effective duration, effective convexity, and option-adjusted spread estimates for different bond structures, namely, regular callable and putable bonds and callable and putable range notes. This is true for regular callable and putable bonds, but the differences are even more pronounced for more complex bond structures such as range notes.…”

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confidence: 99%

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Impact of Different Interest Rate Models on Bond Value Measures

Buetow¹,

Hanke²,

Fabozzi³

2001

JFI

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he readily notes that the empirical evidence is far from conclusive.We examine differences in the effective duration, effective convexity, and the option-adjusted spread resulting from different one-factor no-arbitrage interest rate models. The models considered are: the Ho and Lee (HL) [1986] model; the Kalotay, Williams, and Fabozzi (KWF) [1993] model; the Black, Derman, and Toy (BDT) [1990] model; the Hull and White (HW) [1994] I. NO-ARBITRAGE INTEREST RATE MODELSThe interest rate models we examine assume that the short-term interest rate follows a certain process that can be represented by a stochastic differential equation. All the interest rate models are special cases of the general form of changes in the short-term rate:( 1) where f and g are suitably chosen functions of the short-term rate and are the same for most models presented here, θ will be shown to be the drift of the short-term rate, and ρ is the mean reversion term to an equilibrium short-term rate. The term σ is the local volatility of the short-term rate, and z is a normally distributed Wiener process that captures the randomness of future changes in the short-term rate.Equation (1) is a one-factor model that gives only the short-term rate (one factor).2 Its first component (the dt term) is the expected or average change in the short-term rate over a short period of time. The second component is the risk term, as it includes the random component dz. All the interest rate models we consider are special cases of Equation (1). The Ho-Lee ModelThe Ho-Lee model assumes that changes in the shortterm rate can be modeled using Equation (1) by setting f(r) = r and ρ = 0, so that the process for the short-term rate is:Since dz is a normally distributed Wiener process, the HL process is a normal process for the short-term gu @ +w,gw . +w,g} gi+u+w,, @ ++w, . +w,j+u+w,,,gw . +u+w,> w,g} rate. As can be seen from Equation (2), the short-term rate may become negative if the random term is large enough to dominate the drift term (dt). This is a serious shortcoming of the HL model, although it is argued that as long as the HL model provides good prices for bonds with embedded options, it does not matter if some of its assumptions are unrealistic. Another possible drawback of the model, however, is that the volatility of the short-term rate does not depend on the level of the rate, and the short-term rate does not meanrevert to a long-term equilibrium rate, as many practitioners believe would hold in reality.Some of these restrictive assumptions are relaxed in the other models. Note that the distributional properties will have a tendency to bias the values of the embedded contingent claim.The simplicity of the HL model combined with the fact that it provides reasonable prices under many circumstances makes it a very popular interest rate model. The Kalotay-Williams-Fabozzi ModelThe Kalotay-Williams-Fabozzi model assumes that changes in the short-term rate can be modeled using Equation (1) by setting f(r) = ln (r) (where ln is the natural logarithm) and...

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“…Por su parte, Bjork, Myhrman Persson (1987) y Björk (2004 imponen un tiempo de paro para no generar soluciones de control degeneradas. Dos de los temas distintivos, en el marco de los modelos anteriores, son la obtención de precios de activos financieros y la valuación de productos derivados, cuya literatura es muy vasta y variada; considérense al respecto los artícu-los, algunos seminales y otros de referencia, de Black y Scholes (1973); Merton (1973); Cox y Ross (1976) ;Cox, Ingersoll y Ross (1985a;1985b); Geske y Shastri (1985); Ho y Lee (1986) ;Hull y White (1987;; Detemple y Tian (2002); Venegas-Martínez (2006; ;Sierra (2007); 2 Ángeles-Castro y Venegas-Martínez (2010), y Venegas-Martínez y Cruz-Ake (2010), entre otros. Una característica común, tal vez una limitación, que guardan estas investigaciones es que consideran una temporalidad, infinita o finita, determinista para la valuación de derivados.…”

Section: Introductionunclassified

Un modelo macroeconómico con agentes de vida finita y estocástica: cobertura de riesgo de mercado con derivados americanos

Palacios

Martínez

2014

ETYP

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ResumenEn esta investigación se desarrolló un modelo de economía estocástica, pequeña y abierta, poblada por consumidores racionales idénticos que tienen vida finita, pero estocásti-ca; además, son adversos al riesgo y disponen de una riqueza inicial. Estos agentes enfrentan la decisión de distribuir su riqueza entre consumo e inversión en un portafolio de activos en un ambiente de riesgo de mercado y de política fiscal incierta. La cobertura se lleva a cabo mediante una opción americana de venta y su valuación se realiza en térmi-nos de cuánto está dispuesto a pagar el consumidor representativo por mantener dicho contrato a fin de cubrir un activo riesgoso contra caídas en su precio. El precio del contrato se determina en términos del premio al riesgo, el cual se caracteriza mediante la solución de una ecuación diferencial parcial lineal de segundo orden. Por último, se obtiene una formula de aproximación para el precio de la opción americana y se realiza un análisis de sensibilidad de dicho precio con respecto de sus parámetros.Palabras clave: decisiones de consumo y portafolio, valuación de productos derivados, política fiscal, riesgo de mercado, modelos de equilibrio. Clasificación jel: D91, G13, E62, D50, D81. AbstractThis paper develops a stochastic model of a small and open economy populated by identical rational consumers having finite life but stochastic, who are risk averse and have an initial wealth. These agents face the decision to allocate his wealth between consumption and investment in a portfolio of assets under an environment of risk market and uncertain fiscal policy. Hedging is performed via an American put option and its pricing is carried out in terms of how much the representative consumer is willing to pay to keep that contract to hedge a fall in the risky asset price. The option price is determined in terms of the risk premium, which is characterized by the solution of a second-order, linear partial differential equation. Finally, an approximated formula for the American option price is obtained, and a sensitive analysis of such a price with respect to its parameters is carried out.

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One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities

Cited by 373 publications

References 16 publications

Cross-sectional tests of deterministic volatility functions

Cross-sectional tests of deterministic volatility functions

Impact of Different Interest Rate Models on Bond Value Measures

Un modelo macroeconómico con agentes de vida finita y estocástica: cobertura de riesgo de mercado con derivados americanos

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