A model of discontinuous interest rate behavior, yield curves, and volatility

Heston, Steven L.

doi:10.1007/s11147-008-9020-3

Cited by 8 publications

(5 citation statements)

References 26 publications

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“…The interest rate has been assumed to follow a gamma distribution in some traditional researches (Heston 2007;Fabozzi et al 2009). Some studies show that the CIR process (Cox et al 1985) yields a non-central chi-square transitional distribution, while the marginal density is a gamma distribution (Feller 1951;Ait-Sahalia 1996).…”

Section: The Modelmentioning

confidence: 99%

The Valuation Model for a Risky Asset When Its Risky Factors Follow Gamma Distributions

Tsai

Chiang

2016

Int Rev Finance

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This paper constructed a pricing model for the asset with multi‐risks by specifying the risky factors (i.e., interest rate and termination hazard rates) to follow gamma distributions. The model not only avoids the possibility of the termination hazard rate taking an irrational (i.e., negative) value, but it also makes it easier to derive a valuation formula for a risky asset. Our model can also effortless apply because the parameters of the gamma distribution can easily be estimated from market data. An example using Taiwanese bond data illustrates how the model can be utilized for practical applications. To facilitate understanding of how accurately the different models price risky bonds, we compare their out‐of‐sample pricing errors for different hazard rate specifications assuming normal and gamma distributions. The results show that our pricing formula is realistic and accurate in its applications. Therefore, it should help market participants to accurately price risky assets and to effectively manage complicated portfolios.

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Section: The Modelmentioning

confidence: 99%

The Valuation Model for a Risky Asset When Its Risky Factors Follow Gamma Distributions

Tsai

Chiang

2016

Int Rev Finance

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“…valid for |α| < 1 and h ≥ 0 (Erdélyi 1953), which gives us the required series expansion of the exponential gamma martingale in powers of α. In particular, by setting h = mt and z = γ t in equation (12), we are able to deduce that for each value of n the process {L Schoutens 2000). For example, we have…”

Section: Gamma Processes and Associated Martingalesmentioning

confidence: 99%

“…We note that the change-of-measure density martingale arising in this example is obtained by taking the standard gamma exponential martingale (10) defined above, and setting α = (1 − κ)/κ. The gamma process has been used as the basis of a number of different asset pricing models; see, for example, Madan & Seneta (1990), Madan and Milne (1991), Heston (1995)…”

Section: Gamma Processes and Associated Martingalesmentioning

confidence: 99%

Dam rain and cumulative gain

2008

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We consider a financial contract that delivers a single cash flow given by the terminal value of a cumulative gains process. The problem of modelling such an asset and associated derivatives is important, for example, in the determination of optimal insurance claims reserve policies, and in the pricing of reinsurance contracts. In the insurance setting, aggregate claims play the role of cumulative gains, and the terminal cash flow represents the totality of the claims payable for the given accounting period. A similar example arises when we consider the accumulation of losses in a credit portfolio, and value a contract that pays an amount equal to the totality of the losses over a given time interval. An expression for the value process of such an asset is derived as follows. We fix a probability space, together with a pricing measure, and model the terminal cash flow by a random variable; next, we model the cumulative gains process by the product of the terminal cash flow and an independent gamma bridge; finally, we take the filtration to be that generated by the cumulative gains process. An explicit expression for the value process is obtained by taking the discounted expectation of the future cash flow, conditional on the relevant market information. The price of an Arrow-Debreu security on the cumulative gains process is determined, and is used to obtain a closedform expression for the price of a European-style option on the value of the asset at the given intermediate time. The results obtained make use of remarkable properties of the gamma bridge process, and are applicable to a wide variety of financial products based on cumulative gains processes such as aggregate claims, credit portfolio losses, defined benefit pension schemes, emissions and rainfall.

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“…Debe establecerse que las estructuras de información modeladas de esta manera no permiten la existencia de eventos que sean sorpresivos; la evolución de la variable aleatoria relevante mantendrá un comportamiento relativamente suave, sin grandes cambios y sin saltos en su evolución temporal. No obstante, las investigaciones empíricas contemporáneas desarrollada por Chan, Karolyi, Longstaff y Sanders(1992), Brenner, Harjes y Corner(1994), Das(1994), Heston (1995) y Ait-Sahalia (1995) apuntan a que en algunas ocasiones ello es insuficiente para capturar correctamente la dinámica de variables financieras como los rendimientos, por lo que se debe recurrir a la incorporación de discontinuidades en los procesos estocásticos que describan mejor la trayectoria de las variables. Una forma de capturar el exceso de curtosis de las series financieras es mediante la aplicación de modelos que permitan incorporar explícitamente los saltos en la evolución estocástica de las variables.…”

Section: Introductionunclassified

Procesos Poisson-Gaussianos para el análisis de rendimientos en el mercado accionarial en México

Mora¹,

Valdés

Gallegos³

2021

EEA

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En la investigación de finanzas y economía es ampliamente reconocido que variables como los rendimientos pueden presentar comportamientos discontinuos. En este sentido, el presente artículo realiza la estimación de los rendimientos para un grupo de acciones pertenecientes a la Bolsa Mexicana de Valores, utilizando para ello procesos de saltos Poisson-Gaussianos y de tipo ARCH, y empleando la aproximación de Das (1998 y 2002) para generar una función de verosimilitud que asegure una estimación robusta. Con base a la metodología planteada, se encuentra que los procesos con saltos capturan características de los datos mexicanos que no siempre son obtenidos mediante la aplicación de los modelos de difusión.

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A model of discontinuous interest rate behavior, yield curves, and volatility

Abstract: Interest rates, Yield curve, Levy process,

Cited by 8 publications

References 26 publications

The Valuation Model for a Risky Asset When Its Risky Factors Follow Gamma Distributions

The Valuation Model for a Risky Asset When Its Risky Factors Follow Gamma Distributions

Dam rain and cumulative gain

Procesos Poisson-Gaussianos para el análisis de rendimientos en el mercado accionarial en México

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