On the role of state variables in interest rates models

Geman, Hélyette; Lacoste, Vincent

doi:10.1002/1526-4025(200007/09)16:3<197::aid-asmb414>3.0.co;2-q

Cited by 12 publications

(6 citation statements)

References 16 publications

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“…Note however that other sources of risk, such as the exchange rate fluctuations for foreign investors, might also be included in the 'effective' volatility of the spot rate used in Eq. (21).…”

Section: Heath-jarrow-mortonmentioning

confidence: 99%

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Phenomenology of the interest rate curve

Bouchaud

Sagna

Cont³

et al. 1999

Applied Mathematical Finance

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This paper contains a phenomenological description of the whole U.S. forward rate curve (frc), based on an data in the period 1990-1996. We find that the average frc (measured from the spot rate) grows as the square-root of the maturity, with a prefactor which is comparable to the spot rate volatility. This suggests that forward rate market prices include a risk premium, comparable to the probable changes of the spot rate between now and maturity, which can 1 be understood as a 'Value-at-Risk' type of pricing. The instantaneous frc however departs form a simple square-root law. The distortion is maximum around one year, and reflects the market anticipation of a local trend on the spot rate. This anticipated trend is shown to be calibrated on the past behaviour of the spot itself. We show that this is consistent with the volatility 'hump' around one year found by several authors (and which we confirm). Finally, the number of independent components needed to interpret most of the frc fluctuations is found to be small. We rationalize this by showing that the dynamical evolution of the frc contains a stabilizing second derivative (line tension) term, which tends to suppress short scale distortions of the frc. This shape dependent term could lead, in principle, to arbitrage. However, this arbitrage cannot be implemented in practice because of transaction costs. We suggest that the presence of transaction costs (or other market 'imperfections') is crucial for model building, for a much wider class of models becomes eligible to represent reality.

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Section: Heath-jarrow-mortonmentioning

confidence: 99%

“…The market seems to price future rates through a Value at Risk procedure (Eqs. 21,22) rather than through an averaging procedure. In a strict sense, Eq.…”

Section: The Average Frc and Value-at-risk Pricingmentioning

confidence: 99%

Phenomenology of the interest rate curve

Bouchaud

Sagna

Cont³

et al. 1999

Applied Mathematical Finance

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“…(23) and (24). Now, by the orthogonality of the principal components we are able to use their variances to identify the most important types of movements in the Brazilian sovereign term structures.…”

Section: Identifying the Main Types Of Movements Of Term Structures Imentioning

confidence: 99%

“…Some of them model the evolution of the short term rates (see for instance [15,42]), while others are multi-factor models, based on the evolution of finite sets of state variables, usually yields or forward rates [22,23]. The empirical versions of these models are usually estimated by a direct application of Maximum Likelihood [13,37].…”

Section: Introductionmentioning

confidence: 99%

A Generalization of Principal Component Analysis for Non-Observable Term Structures in Emerging Markets

Almeida

Duarte

Fernandes

2003

Int. J. Theor. Appl. Finan.

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Principal Component Analysis (PCA) has been traditionally used for identifying the most important factors driving term structures of interest rates movements. Once one maps the term structure dynamics, it can be used in many applications. For instance, portfolio allocation, Asset/Liability models, and risk management, are some of its possible uses. This approach presents very simple implementation algorithm, whenever a time series of the term structure is disposable. Nevertheless, in markets where there is no database for discount bond yields available, this approach cannot be applied. In this article, we exploit properties of an orthogonal decomposition of the term structure to sequentially estimate along time, term structures of interest rates in emerging markets. The methodology, named Legendre Dynamic Model (LDM), consists in building the dynamics of the term structure by using Legendre Polynomials to drive its movements. We propose applying LDM to obtain time series for term structures of interest rates and to study their behavior through the behavior of the Legendre Coefficients levels and first differences properly normalized (Legendre factors). Under the hypothesis of stationarity and serial independence of the Legendre factors, we show that there is asymptotic equivalence between LDM and PCA, concluding that LDM captures PCA as a particular case. As a numerical example, we apply our technique to Brazilian Brady and Global Bond Markets, briefly study the time series characteristics of their term structures, and identify the intensity of the most important basic movements of these term structures.

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“…These compatibility conditions, mentioned in Brennan and Schwartz (1979), thoroughly studied in El Karoui et al (1996) when spot-forward rates are chosen as state variables, can be shortly introduced as follows. Assume that r is one of the state variables (or, equivalently, a linear combination of the state variables).…”

Section: Propositionmentioning

confidence: 99%

Pricing stock and bond derivatives with a multi-factor Gaussian model

Bajeux‐Besnainou¹,

Portait²

1998

Applied Mathematical Finance

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The martingale approach to pricing contingent claims can be applied in a multiple state variable model. The idea is used to derive the prices of derivative securities (futures on stock and bond futures, options on stocks, bonds and futures) given a continuous time Gaussian multi-factor model of the returns of stocks and bonds. The bond market is similar to Langetieg's multi-factor model, which has closed-form solutions. This model is a generalization of Vasicek's model, where the term structure depends on state variables following correlated mean reverting processes. The stock market is affected by systematic and unsystematic risk.Derivative Securities, Multi-factor Model, Continuous-time, Pricing,

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On the role of state variables in interest rates models

Cited by 12 publications

References 16 publications

Phenomenology of the interest rate curve

Phenomenology of the interest rate curve

A Generalization of Principal Component Analysis for Non-Observable Term Structures in Emerging Markets

Pricing stock and bond derivatives with a multi-factor Gaussian model

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