Maximum Likelihood Estimation of the Cox–Ingersoll–Ross Model Using Particle Filters

Rossi, Giuliano

doi:10.1007/s10614-010-9208-0

Cited by 24 publications

(16 citation statements)

References 28 publications

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“…Approaches that derive the probability distributions from the actual model dynamics (as described by SDEs) and then use these distributions to fit parameters. Examples include Kalman filter ( [1]) for the Vasicek model, while for general affine models particle filtering (PF) might be a more natural algorithm (see [10]).…”

Section: Model Calibration/fittingmentioning

confidence: 99%

Consistent Yield Curves via Static Hedging

Rojek¹,

Wilmott²

2013

Wilmott

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Interpolating yield curves between observable points can be done in various ways. In this paper, we show that market making in tradeable instruments with static hedging can be considered as a consistent basis for such interpolation. This approach leads to solutions where parameters match the historical rates while currently quoted prices are also perfectly reconstructed. We also show that the interpolation solution derived from the minimum variance optimization for the static hedge ratios is equivalent to statistical inference with Gaussian Processes Regression (GPR). We offer closed-form solutions for affine interest-rate models for market making as well as for profit-seeking scenarios.

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Section: Model Calibration/fittingmentioning

confidence: 99%

Consistent Yield Curves via Static Hedging

Rojek¹,

Wilmott²

2013

Wilmott

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“…The CIR (Cox, Ingersoll, & Ross, 1985) model has proved to be very popular for achieving that in both the academic literature and among practitioners due to the three features commonly observed in the data; namely: the nonnegativity of interest rates; conditional heteroskedasticity; and the time-varying market prices of risk (De Rossi, 2010). The CIR (Cox, Ingersoll, & Ross, 1985) model has proved to be very popular for achieving that in both the academic literature and among practitioners due to the three features commonly observed in the data; namely: the nonnegativity of interest rates; conditional heteroskedasticity; and the time-varying market prices of risk (De Rossi, 2010).…”

Section: Model and Methodologymentioning

confidence: 99%

“…As an application, we demonstrate that the proposed modification can efficiently capture the extreme quantiles of an instantaneously compounded interest rate-that is, the short rate (and hence the extreme quantiles of the corresponding bond yields), when the short rate is driven by the CIR process (Cox, Ingersoll, & Ross, 1985). In fact, there is extensive literature on the use of filtering frameworks in interest rate modeling (e.g., Chatterjee, 2005;Date & Wang, 2009;De Rossi, 2010;Fileccia, 2012;Geyer & Pichler, 1999). In fact, there is extensive literature on the use of filtering frameworks in interest rate modeling (e.g., Chatterjee, 2005;Date & Wang, 2009;De Rossi, 2010;Fileccia, 2012;Geyer & Pichler, 1999).…”

Section: Introductionmentioning

confidence: 99%

“…The proposed procedure can be adapted to other short-rate processes, such as those proposed by Vasicek (1977), Chan, Karoly, Longstaff, and Sanders (1992), and Longstaff and Schwartz (1993). In fact, there is extensive literature on the use of filtering frameworks in interest rate modeling (e.g., Chatterjee, 2005;Date & Wang, 2009;De Rossi, 2010;Fileccia, 2012;Geyer & Pichler, 1999). Our work may be seen as a generic extension of this existing body of work where the SMC is employed to efficiently extract information about very-low-probability events.…”

Section: Introductionmentioning

confidence: 99%

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A modified sequential Monte Carlo procedure for the efficient recursive estimation of extreme quantiles

Neslihanoğlu

Date

2019

Journal of Forecasting

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Many applications in science involve finding estimates of unobserved variables from observed data, by combining model predictions with observations. The sequential Monte Carlo (SMC) is a well‐established technique for estimating the distribution of unobserved variables that are conditional on current observations. While the SMC is very successful at estimating the first central moments, estimating the extreme quantiles of a distribution via the current SMC methods is computationally very expensive. The purpose of this paper is to develop a new framework using probability distortion. We use an SMC with distorted weights in order to make computationally efficient inferences about tail probabilities of future interest rates using the Cox–Ingersoll–Ross (CIR) model, as well as with an observed yield curve. We show that the proposed method yields acceptable estimates about tail quantiles at a fraction of the computational cost of the full Monte Carlo.

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“…Second, these routines do not rely on the presence of first-order or even second-order derivatives of the likelihood function. This feature is convenient if the likelihood function is evaluated by a particle filter, where the resampling step generates discontinuities in the likelihood function (Fernández-Villaverde and Rubio-Ramírez 2007;Rossi 2004). Thus, a gradient based optimization routine is likely to perform poorly in this case.…”

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confidence: 99%