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Journal articles on the topic 'Vasicek short rate model'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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1

FERGUSSON, K. "ASYMPTOTICS OF BOND YIELDS AND VOLATILITIES FOR EXTENDED VASICEK MODELS UNDER THE REAL-WORLD MEASURE." Annals of Financial Economics 12, no. 01 (March 2017): 1750005. http://dx.doi.org/10.1142/s2010495217500051.

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Vasicek's short rate model is a mean reverting model of the short rate which permits closed-form pricing formulae of zero coupon bonds and options on zero coupon bonds. This paper supplies proofs which are valid for any single factor mean reverting Gaussian short rate model having time-inhomogeneous parameters. The formulae are for the expected present value of payoffs under the real-world probability measure, known as actuarial pricing. Importantly, we give formulae for asymptotic levels of bond yields and volatilities for extended Vasicek models when suitable conditions are imposed on the model parameters.

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2

Inoue, Akihiko, Shingo Moriuchi, and Yusuke Nakamura. "A Vasicek-Type Short Rate Model With Memory Effect." Stochastic Analysis and Applications 33, no. 6 (October 23, 2015): 1068–82. http://dx.doi.org/10.1080/07362994.2015.1087864.

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3

Zhang, Xili. "Modeling the Dynamics of Shanghai Interbank Offered Rate Based on Single-Factor Short Rate Processes." Mathematical Problems in Engineering 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/540803.

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Using the Shanghai Interbank Offered Rate data of overnight, 1 week, 2 week and 1 month, this paper provides a comparative analysis of some popular one-factor short rate models, including the Merton model, the geometric Brownian model, the Vasicek model, the Cox-Ingersoll-Ross model, and the mean-reversion jump-diffusion model. The parameter estimation and the model selection of these single-factor short interest rate models are investigated. We document that the most successful model in capturing the Shanghai Interbank Offered Rate is the mean-reversion jump-diffusion model.

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4

Halgašová, Jana, Beáta Stehlíková, and Zuzana Bučková. "Estimating the Short Rate from the Term Structures in the Vasicek Model." Tatra Mountains Mathematical Publications 61, no. 1 (December 1, 2014): 87–103. http://dx.doi.org/10.2478/tmmp-2014-0029.

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Abstract In short rate models, bond prices and term structures of interest rates are determined by the parameters of the model and the current level of the instantaneous interest rate (so called short rate). The instantaneous interest rate can be approximated by the market overnight, which, however, can be influenced by speculations on the market. The aim of this paper is to propose a calibration method, where we consider the short rate to be a variable unobservable on the market and estimate it together with the model parameters for the case of the Vasicek model

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5

BRODY, DORJE C., LANE P. HUGHSTON, and DAVID M. MEIER. "LÉVY–VASICEK MODELS AND THE LONG-BOND RETURN PROCESS." International Journal of Theoretical and Applied Finance 21, no. 03 (May 2018): 1850026. http://dx.doi.org/10.1142/s0219024918500267.

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The classical derivation of the well-known Vasicek model for interest rates is reformulated in terms of the associated pricing kernel. An advantage of the pricing kernel method is that it allows one to generalize the construction to the Lévy–Vasicek case, avoiding issues of market incompleteness. In the Lévy–Vasicek model the short rate is taken in the real-world measure to be a mean-reverting process with a general one-dimensional Lévy driver admitting exponential moments. Expressions are obtained for the Lévy–Vasicek bond prices and interest rates, along with a formula for the return on a unit investment in the long bond, defined by [Formula: see text], where [Formula: see text] is the price at time [Formula: see text] of a [Formula: see text]-maturity discount bond. We show that the pricing kernel of a Lévy–Vasicek model is uniformly integrable if and only if the long rate of interest is strictly positive.

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6

Mamon, Rogemar S. "Three ways to solve for bond prices in the Vasicek model." Journal of Applied Mathematics and Decision Sciences 8, no. 1 (January 1, 2004): 1–14. http://dx.doi.org/10.1155/s117391260400001x.

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Three approaches in obtaining the closed-form solution of the Vasicek bond pricing problem are discussed in this exposition. A derivation based solely on the distribution of the short rate process is reviewed. Solving the bond price partial differential equation (PDE) is another method. In this paper, this PDE is derived via a martingale approach and the bond price is determined by integrating ordinary differential equations. The bond pricing problem is further considered within the Heath-Jarrow-Morton (HJM) framework in which the analytic solution follows directly from the short rate dynamics under the forward measure.

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7

FERGUSSON, K., and E. PLATEN. "APPLICATION OF MAXIMUM LIKELIHOOD ESTIMATION TO STOCHASTIC SHORT RATE MODELS." Annals of Financial Economics 10, no. 02 (December 2015): 1550009. http://dx.doi.org/10.1142/s2010495215500098.

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The application of maximum likelihood estimation is not well studied for stochastic short rate models because of the cumbersome detail of this approach. We investigate the applicability of maximum likelihood estimation to stochastic short rate models. We restrict our consideration to three important short rate models, namely the Vasicek, Cox–Ingersoll–Ross (CIR) and 3/2 short rate models, each having a closed-form formula for the transition density function. The parameters of the three interest rate models are fitted to US cash rates and are found to be consistent with market assessments.

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8

Huang, Guoan, Guohe Deng, and Lihong Huang. "Valuation for an American Continuous-Installment Put Option on Bond under Vasicek Interest Rate Model." Journal of Applied Mathematics and Decision Sciences 2009 (June 7, 2009): 1–11. http://dx.doi.org/10.1155/2009/215163.

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The valuation for an American continuous-installment put option on zero-coupon bond is considered by Kim's equations under a single factor model of the short-term interest rate, which follows the famous Vasicek model. In term of the price of this option, integral representations of both the optimal stopping and exercise boundaries are derived. A numerical method is used to approximate the optimal stopping and exercise boundaries by quadrature formulas. Numerical results and discussions are provided.

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9

BALLESTRA, LUCA VINCENZO, GRAZIELLA PACELLI, and DAVIDE RADI. "A NOTE ON FERGUSSON AND PLATEN: “APPLICATION OF MAXIMUM LIKELIHOOD ESTIMATION TO STOCHASTIC SHORT RATE MODELS”." Annals of Financial Economics 11, no. 04 (December 2016): 1650018. http://dx.doi.org/10.1142/s2010495216500184.

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In a very recent and interesting paper, Fergusson and Platen (2015) investigate the applicability of the maximum likelihood (ML) method for estimating the parameters of some of the most popular stochastic models for the short interest rate. One of the main results of this paper is the analytical expression of the so-called observed Fisher information matrix for the Vasicek model at the ML point. However, in such a matrix some entries are not derived correctly and one entry is left unspecified. In the following, we provide the correct analytical expression of that matrix.

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10

Kaplun, A. "The Continuous-Time Ehrenfest Process in Term Structure Modelling." Journal of Applied Probability 47, no. 03 (September 2010): 693–712. http://dx.doi.org/10.1017/s0021900200007014.

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In this paper, a finite-state mean-reverting model for the short rate, based on the continuous-time Ehrenfest process, will be examined. Two explicit pricing formulae for zero-coupon bonds will be derived in the general and special symmetric cases. Its limiting relationship to the Vasicek model will be examined with some numerical results.

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11

Kaplun, A. "The Continuous-Time Ehrenfest Process in Term Structure Modelling." Journal of Applied Probability 47, no. 3 (September 2010): 693–712. http://dx.doi.org/10.1239/jap/1285335404.

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In this paper, a finite-state mean-reverting model for the short rate, based on the continuous-time Ehrenfest process, will be examined. Two explicit pricing formulae for zero-coupon bonds will be derived in the general and special symmetric cases. Its limiting relationship to the Vasicek model will be examined with some numerical results.

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12

Sari, Meylita, Sndah R. M. Putri, and Nuri Wahyuningsih. "Modelling of Short Rate (β 2) Parameter Diebold-Li Model Using Vasicek Stochastic Differential Equations." Journal of Physics: Conference Series 1218 (May 2019): 012059. http://dx.doi.org/10.1088/1742-6596/1218/1/012059.

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13

Bučková, Zuzana, Zuzana Girová, and Beáta Stehlíková. "Estimating the Domestic Short Rate in a Convergence Model of Interest Rates." Tatra Mountains Mathematical Publications 75, no. 1 (April 1, 2020): 33–48. http://dx.doi.org/10.2478/tmmp-2020-0003.

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AbstractIn this paper we study the convergence model of interest rates by Corzo and Schwartz. It models the situation when a country is going to enter a monetary union, for example the eurozone. We are interested in estimating the underlying short rate, which is a theoretical variable, not observed on the market. We use the procedure already employed for the Vasicek model to the eurozone data and for the case of a zero correlation we show that a similar procedure can be used also for the estimation of the domestic parameters and the short rate values. The assumption of the zero correlation allows us to simplify the optimization problem, but using simulations we show that our algorithm is robust to the specification of the correlation. It estimates the short rate with a high precision also in the original case of a nonzero correlation, as well as in the case of a dynamic correlation, when the correlation is modelled as a function of time. Finally, we use the algorithm to real market data and estimate the short rate before adoption of the euro currency in Slovakia, Estonia, Latvia and Lithuania.

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14

LEUNG, TIM, and HYUNGBIN PARK. "LONG-TERM GROWTH RATE OF EXPECTED UTILITY FOR LEVERAGED ETFs: MARTINGALE EXTRACTION APPROACH." International Journal of Theoretical and Applied Finance 20, no. 06 (September 2017): 1750037. http://dx.doi.org/10.1142/s0219024917500376.

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This paper studies the long-term growth rate of expected utility or expected return from holding a leveraged exchanged-traded fund (LETF), which is a constant proportion portfolio of the reference asset. We develop a martingale extraction approach to tackle the path-dependence in the expectation and determine the long-term growth rate through the eigenpair associated with the infinitesimal generator of a time-homogeneous Markovian diffusion. The long-term growth rates are derived explicitly under a number of models for the reference asset, including the geometric Brownian motion model, GARCH model, inverse GARCH model, extended CIR model, 3/2 model, quadratic model, as well as the Heston and [Formula: see text] stochastic volatility models. We also investigate the impact of stochastic interest rate such as the Vasicek model and the inverse GARCH short rate model. Additionally, we determine the optimal leverage ratio that maximizes the long-term growth rate, and examine the effects of model parameters.

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15

ZHUO, XIAOYANG, and OLIVIER MENOUKEU-PAMEN. "EFFICIENT PIECEWISE TREES FOR THE GENERALIZED SKEW VASICEK MODEL WITH DISCONTINUOUS DRIFT." International Journal of Theoretical and Applied Finance 20, no. 04 (May 24, 2017): 1750028. http://dx.doi.org/10.1142/s0219024917500285.

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In this paper, we explore two new tree lattice methods, the piecewise binomial tree and the piecewise trinomial tree for both the bond prices and European/American bond option prices assuming that the short rate is given by a generalized skew Vasicek model with discontinuous drift coefficient. These methods build nonuniform jump size piecewise binomial/trinomial tree based on a tractable piecewise process, which is derived from the original process according to a transform. Numerical experiments of bonds and European/American bond options show that our approaches are efficient as well as reveal several price features of our model.

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16

XIE, DEJUN, XINFU CHEN, and JOHN CHADAM. "Optimal payment of mortgages." European Journal of Applied Mathematics 18, no. 3 (June 2007): 363–88. http://dx.doi.org/10.1017/s0956792507006997.

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This article provides a borrower's optimal strategies to terminate a mortgage with a fixed interest rate by paying the outstanding balance all at once. The problem is modelled as a free boundary problem for the appropriate analogue of the Black-Scholes pricing equation under the assumption of the Vasicek model for the short-term rate of investment. Here the free boundary provides the optimal time at which the mortgage contract is to be terminated. A number of integral identities are derived and then used to design efficient numerical codes for computing the free boundary. For numerical simulation, parameters for the Vasicek model are estimated via the method of maximum likelihood estimation using 40 years of data from US government bonds. The asymptotic behaviour of the free boundary for the infinite horizon is fully analysed. Interpolating this infinite horizon behaviour and a known near-expiry behaviour, two simple analytical approximation formulas for the optimal exercise boundary are proposed. Numerical evidence shows that the enhanced version of the approximation formula is amazingly accurate; in general, its relative error is less than 1%, for all time before expiry.

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17

Deng, Guohe. "Pricing Catastrophe Equity Put Options in a Mixed Fractional Brownian Motion Environment." Mathematical Problems in Engineering 2020 (May 11, 2020): 1–15. http://dx.doi.org/10.1155/2020/6197506.

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This paper considers the pricing of the CatEPut option (catastrophe equity put option) in a mixed fractional model in which the stock price is governed by a mixed fractional Brownian motion (mfBM model), which manifests long-range correlation and fluctuations from the financial market. Using the conditional expectation and the change of measure technique, we obtain an analytical pricing formula for the CatEPut option when the short interest rate is a deterministic and time-dependent function. Furthermore, we also derive analytical pricing formulas for the catastrophe put option and the influence of the Hurst index when the short interest rate follows an extended Vasicek model governed by another mixed fractional Brownian motion so that the environment captures the long-range dependence of the short interest rate. Based on the numerical experiments, we analyze quantitatively the impacts of different parameters from the mfBM model on the option price and hedging parameters. Numerical results show that the mfBM model is more close to the realistic market environment, and the CatEPut option price is evaluated accurately.

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18

Paseka, Alex, and Aerambamoorthy Thavaneswaran. "Bond valuation for generalized Langevin processes with integrated Lévy noise." Journal of Risk Finance 18, no. 5 (November 20, 2017): 541–63. http://dx.doi.org/10.1108/jrf-09-2016-0125.

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Purpose Recently, Stein et al. (2016) studied theoretical properties and parameter estimation of continuous time processes derived as solutions of a generalized Langevin equation (GLE). In this paper, the authors extend the model to a wider class of memory kernels and then propose a bond and bond option valuation model based on the extension of the generalized Langevin process of Stein et al. (2016). Design/methodology/approach Bond and bond option pricing based on the proposed interest rate models presents new difficulties as the standard partial differential equation method of stochastic calculus for bond pricing cannot be used directly. The authors obtain bond and bond option prices by finding the closed form expression of the conditional characteristic function of the integrated short rate process driven by a general Lévy noise. Findings The authors obtain zero-coupon default-free bond and bond option prices for short rate models driven by a variety of Lévy processes, which include Vasicek model and the short rate model obtained by solving a second-order Langevin stochastic differential equation (SDE) as special cases. Originality/value Bond and bond option pricing plays an important role in capital markets and risk management. In this paper, the authors derive closed form expressions for bond and bond option prices for a wider class of interest rate models including second-order SDE models. Closed form expressions may be especially instrumental in facilitating parameter estimation in these models.

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Gao, Jianwei, and Huicheng Liu. "Pricing Longevity Bonds Under the Uncertainty Theory Framework." International Journal of Pattern Recognition and Artificial Intelligence 33, no. 06 (April 21, 2019): 1959020. http://dx.doi.org/10.1142/s0218001419590201.

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This paper aims to develop a new pricing approach for longevity bonds under the uncertainty theory framework. First, we describe the life expectancy by a canonical uncertain process and illustrate the dynamic of short interest rate via an uncertain Vasicek interest rate model. Then, based on these descriptions, we construct an uncertain survival index model and present its procedure for parameter estimation. By applying the chain rule, we derive a pricing formula of the uncertain zero-coupon bond. Considering that the financial market is incomplete, we put forward an uncertain distortion operator. Furthermore, based on the uncertain survival index, the uncertain zero-coupon bond pricing formula and the uncertain distortion operator, we develop a pricing formula of the uncertain longevity bond and its calculation algorithm. Finally, a numerical example is shown to illustrate the influence of parameters on the price of the uncertain longevity bond.

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20

Lee, Jaesung, and Youngrok Lee. "THE PRICING OF QUANTO OPTIONS UNDER THE VASICEK'S SHORT RATE MODEL." Communications of the Korean Mathematical Society 31, no. 2 (April 30, 2016): 415–22. http://dx.doi.org/10.4134/ckms.2016.31.2.415.

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21

CRÉPEY, STÉPHANE, RÉMI GERBOUD, ZORANA GRBAC, and NATHALIE NGOR. "COUNTERPARTY RISK AND FUNDING: THE FOUR WINGS OF THE TVA." International Journal of Theoretical and Applied Finance 16, no. 02 (March 2013): 1350006. http://dx.doi.org/10.1142/s0219024913500064.

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The credit crisis and the ongoing European sovereign debt crisis have highlighted the native form of credit risk, namely the counterparty risk. The related credit valuation adjustment (CVA), debt valuation adjustment (DVA), liquidity valuation adjustment (LVA) and replacement cost (RC) issues, jointly referred to in this paper as total valuation adjustment (TVA), have been thoroughly investigated in the theoretical papers [8, 9]. The present work provides an executive summary and numerical companion to these papers, through which the TVA pricing problem can be reduced to Markovian pre-default TVA BSDEs. The first step consists in the counterparty clean valuation of a portfolio of contracts, which is the valuation in a hypothetical situation where the two parties would be risk-free and funded at a risk-free rate. In the second step, the TVA is obtained as the value of an option on the counterparty clean value process called contingent credit default swap (CCDS). Numerical results are presented for interest rate swaps in the Vasicek, as well as in the inverse Gaussian Hull-White short rate model, which allows also to assess the related model risk issue.

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22

Orlando, Giuseppe, Rosa Maria Mininni, and Michele Bufalo. "Interest rates calibration with a CIR model." Journal of Risk Finance 20, no. 4 (August 19, 2019): 370–87. http://dx.doi.org/10.1108/jrf-05-2019-0080.

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Purpose The purpose of this paper is to model interest rates from observed financial market data through a new approach to the Cox–Ingersoll–Ross (CIR) model. This model is popular among financial institutions mainly because it is a rather simple (uni-factorial) and better model than the former Vasicek framework. However, there are a number of issues in describing interest rate dynamics within the CIR framework on which focus should be placed. Therefore, a new methodology has been proposed that allows forecasting future expected interest rates from observed financial market data by preserving the structure of the original CIR model, even with negative interest rates. The performance of the new approach, tested on monthly-recorded interest rates data, provides a good fit to current data for different term structures. Design/methodology/approach To ensure a fitting close to current interest rates, the innovative step in the proposed procedure consists in partitioning the entire available market data sample, usually showing a mixture of probability distributions of the same type, in a suitable number of sub-sample having a normal/gamma distribution. An appropriate translation of market interest rates to positive values has been introduced to overcome the issue of negative/near-to-zero values. Then, the CIR model parameters have been calibrated to the shifted market interest rates and simulated the expected values of interest rates by a Monte Carlo discretization scheme. We have analysed the empirical performance of the proposed methodology for two different monthly-recorded EUR data samples in a money market and a long-term data set, respectively. Findings Better results are shown in terms of the root mean square error when a segmentation of the data sample in normally distributed sub-samples is considered. After assessing the accuracy of the proposed procedure, the implemented algorithm was applied to forecast next-month expected interest rates over a historical period of 12 months (fixed window). Through an error analysis, it was observed that our algorithm provides a better fitting of the predicted expected interest rates to market data than the exponentially weighted moving average model. A further confirmation of the efficiency of the proposed algorithm and of the quality of the calibration of the CIR parameters to the observed market interest rates is given by applying the proposed forecasting technique. Originality/value This paper has the objective of modelling interest rates from observed financial market data through a new approach to the CIR model. This model is popular among financial institutions mainly because it is a rather simple (uni-factorial) and better model than the former Vasicek model (Section 2). However, there are a number of issues in describing short-term interest rate dynamics within the CIR framework on which focus should be placed. A new methodology has been proposed that allows us to forecast future expected short-term interest rates from observed financial market data by preserving the structure of the original CIR model. The performance of the new approach, tested on monthly data, provides a good fit for different term structures. It is shown how the proposed methodology overcomes both the usual challenges (e.g. simulating regime switching, clustered volatility and skewed tails), as well as the new ones added by the current market environment (particularly the need to model a downward trend to negative interest rates).

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Teichmann, Josef, and Mario V. Wüthrich. "CONSISTENT YIELD CURVE PREDICTION." ASTIN Bulletin 46, no. 2 (February 5, 2016): 191–224. http://dx.doi.org/10.1017/asb.2015.30.

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AbstractWe present an arbitrage-free non-parametric yield curve prediction model which takes the full discretized yield curve data as input state variable. Absence of arbitrage is a particularly important model feature for prediction models in case of highly correlated data as, for instance, interest rates. Furthermore, the model structure allows to separate constructing the daily yield curve from estimating its volatility structure and from calibrating the market prices of risk. The empirical part includes tests on modeling assumptions, out-of-sample back-testing and a comparison with the Vasiček (1977) short-rate model.

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24

Rajabzadeh, Yalda, Amir Hossein Rezaie, and Hamidreza Amindavar. "Short-term traffic flow prediction using time-varying Vasicek model." Transportation Research Part C: Emerging Technologies 74 (January 2017): 168–81. http://dx.doi.org/10.1016/j.trc.2016.11.001.

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25

SUKANASIH, NI KOMANG, I. NYOMAN WIDANA, and KETUT JAYANEGARA. "CADANGAN PREMI ASURANSI JOINT-LIFE DENGAN SUKU BUNGA TETAP DAN BERUBAH SECARA STOKASTIK." E-Jurnal Matematika 7, no. 2 (May 13, 2018): 79. http://dx.doi.org/10.24843/mtk.2018.v07.i02.p188.

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Joint life is an insurance that covered two or more individuals in one policy. This research aims to determine the value and comparison of fixed deposit rate premium and stochastic rate with Vasicek model. It used prospective calculation method. The mortality table in the research used TMI-2011, for participant were couple age 40 and 35 years old with 10 year premium payment. Under this condition the value of constant rate premium and Vasicek rate premium is and . Besed of this research showed the value of the Vasicek rate premium is smaller than constant rate premium.

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Choi, Youngsoo, Se Jin O, and Jae Yeong Seo. "Korean Treasury Bond Futures Pricing Model." Journal of Derivatives and Quantitative Studies 12, no. 1 (May 30, 2004): 1–22. http://dx.doi.org/10.1108/jdqs-01-2004-b0001.

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This paper proposes two alternative methods which are used for pricing the theoretical value of the KTB futures on the non-traded underlying asset; first method is to use the CKLS model, under which the volatility of interest rate changes is highly sensitive to the level of the interest rate, and then employ binomial trees to compute the theoretical value of futures, second one is to use the multifactor Vasicek model considering correlations between yields-to-maturity and then employ the Monte Carlo simulation to compute it. In the empirical study on KTB303 and KTB306, an CKLS methodology is superior to the conventional KORFX method based on the cost-of-carry model in terms of the size of difference between market price and theoretical price. However, the phenomena, the price discrepancy using the KOFEX methodology is very small for all test perlod, implies that the KOFEX one is being used for the most market participants. The reasons that an multifactor Vasicek methodlogy is performed poorly in comparison to another methods are 1) the Vasicek model might be not a good model for explaining the level of interest rates, or 2) the important point considered by the most market participants may be on the volatility or interest rate, not on the correlations between yields-to-maturity.

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Widana, I. Nyoman, and Ni Made Asih. "Perhitungan Iuran Normal Program Pensiun dengan Asumsi Suku Bunga Mengikuti Model Vasicek." Jurnal Matematika 7, no. 2 (December 30, 2017): 85. http://dx.doi.org/10.24843/jmat.2017.v07.i02.p85.

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Labor has a very important role for national development. One way to optimize their productivity is to guarantee a certainty to earn income after retirement. Therefore the government and the private sector must have a program that can ensure the sustainability of this financial support. One option is a pension plan. The purpose of this study is to calculate the normal cost with the interest rate assumed to follow the Vasicek model and analyze the normal contribution of the pension program participants. Vasicek model is used to match with the actual conditions. The method used in this research is the Projected Unit Credit Method and the Entry Age Normal method. The data source of this research is lecturers of FMIPA Unud. In addition, secondary data is also used in the form of the interest rate of Bank Indonesia for the period of January 2006-December 2015. The results of this study indicate that the older the age of the participants, when starting the pension program, the greater the first year normal cost and the smaller the benefit which he or she will get. Then, normal cost with constant interest rate greater than normal cost with Vasicek interest rate. This occurs because the Vasicek model predicts interest between 4.8879%, up to 6.8384%. While constant interest is only 4.25%. In addition, using normal cost that proportional to salary, it is found that the older the age of the participants the greater the proportion of the salary for normal cost.

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Yanishevskyi, V. S., and L. S. Nodzhak. "The path integral method in interest rate models." Mathematical Modeling and Computing 8, no. 1 (2020): 125–36. http://dx.doi.org/10.23939/mmc2021.01.125.

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An application of path integral method to Merton and Vasicek stochastic models of interest rate is considered. Two approaches to a path integral construction are shown. The first approach consists in using Wieners measure with the following substitution of solutions of stochastic equations into the models. The second approach is realised by using transformation from Wieners measure to the integral measure related to the stochastic variables of Merton and Vasicek equations. The introduction of boundary conditions is considered in the second approach in order to remove incorrect time asymptotes from the classic Merton and Vasicek models of interest rates. By the example of Merton model with zero drift, a Dirichlet boundary condition is considered. A path integral representation of term structure of interest rate is obtained. The estimate of the obtained path integrals is performed, where it is shown that the time asymptote is limited.

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29

Deakin, A. S., and Matt Davison. "An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model." Journal of Applied Mathematics 2010 (2010): 1–5. http://dx.doi.org/10.1155/2010/263451.

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This paper provides the analytic solution to the partial differential equation for the value of a convertible bond. The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms.

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Ma, Chaoqun, Jian Liu, and Qiujun Lan. "Studying Term Structure of SHIBOR with the Two-Factor Vasicek Model." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/539230.

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With the development of the Chinese interest rate market, SHIBOR is playing an increasingly important role. Based on principal component analysing SHIBOR, a two-factor Vasicek model is established to portray the change in SHIBOR with different terms. And parameters are estimated by using the Kalman filter. The model is also used to fit and forecast SHIBOR with different terms. The results show that two-factor Vasicek model fits SHIBOR well, especially for SHIBOR in terms of three months or more.

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31

Udoye, Adaobi, Lukman Akinola, and Eka Ogbaji. "EXTENSION OF VASICEK MODEL TO THE MODELLING OF INTEREST RATE." FUDMA JOURNAL OF SCIENCES 4, no. 2 (July 2, 2020): 151–55. http://dx.doi.org/10.33003/fjs-2020-0402-94.

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Interest rate modelling is an interesting aspect of stochastic processes. It has been observed that interest rates fluctuates at random times, hence the need for its modelling as a stochastic process. In this paper, we apply the existing Vasicek model, Itô’s lemma and least-square regression method in the modelling and providing dynamics for a given interest rate.

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Hao, Ruili, Yonghui Liu, and Shoubai Wang. "Pricing Credit Default Swap under Fractional Vasicek Interest Rate Model." Journal of Mathematical Finance 04, no. 01 (2014): 10–20. http://dx.doi.org/10.4236/jmf.2014.41002.

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Chen, Homing, and Cheng-Feng Hu. "On the resolution of the Vasicek-type interest rate model." Optimization 58, no. 7 (October 2009): 809–22. http://dx.doi.org/10.1080/02331930902944101.

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Dang-Nguyen, S., and Y. Rakotondratsimba. "Control of price acceptability under the univariate Vasicek model." International Journal of Financial Engineering 03, no. 03 (September 2016): 1650014. http://dx.doi.org/10.1142/s2424786316500146.

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The valuation of the probability of a financial contract to be lower or higher than a given price under the univariate Vasicek model is discussed in this paper. This price restriction can be justified by consistency reasons, since some prices may not be coherent on a financial point of view, e.g. they imply negative yields, or thought as unreachable by the asset manager. At first, assuming that the pricing functions is monotone, the price constraints are formulated in terms of a threshold on the value of the spot rate process. Since this process is Gaussian, these limits are reformulated in terms of a barrier of the Gaussian increments. Next, once the thresholds are identified, the probability to satisfy the price restriction after the generation of the spot rate at one future date can be computed. Then, assuming that the bounds on the spot rate are constant during a Monte-Carlo simulation, the probability of generating a path of this process that does not satisfy the constraint is valued using some results related to the hitting times. Lastly, the proposed approach is applied to various interest rates sensitive contracts and is illustrated by some numerical examples.

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Tanaka, Katsuto, Weilin Xiao, and Jun Yu. "Maximum Likelihood Estimation for the Fractional Vasicek Model." Econometrics 8, no. 3 (August 12, 2020): 32. http://dx.doi.org/10.3390/econometrics8030032.

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This paper estimates the drift parameters in the fractional Vasicek model from a continuous record of observations via maximum likelihood (ML). The asymptotic theory for the ML estimates (MLE) is established in the stationary case, the explosive case, and the boundary case for the entire range of the Hurst parameter, providing a complete treatment of asymptotic analysis. It is shown that changing the sign of the persistence parameter changes the asymptotic theory for the MLE, including the rate of convergence and the limiting distribution. It is also found that the asymptotic theory depends on the value of the Hurst parameter.

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Driss, Ezouine, and Idrissi Fatima. "Predicting Exchange Rates of Morocco Using an Econometric and a Stochastic Model." International Journal of Accounting and Finance Studies 1, no. 1 (April 18, 2018): 54. http://dx.doi.org/10.22158/ijafs.v1n1p54.

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<p><em>To predict the exchange rate EUR / MAD & USD / MAD in Morocco we used two most answered methods in the theory: the Box-Jenkins econometric model and the stochastic model of Vasicek then the comparison of the forecasted data for the month of March 2018 of the two methods with the exchange rates actually observed allowed us to retain the econometric the autoregressive integrated moving average model ARIMA (2,1,2) for EUR / MAD and (3,1,2) for USD / MAD rather than the Vasicek model.</em><em></em></p>

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Liu, Yinglin, Ruili Hao, and Zuhua Wang. "Pricing Loan CDS with Vasicek Interest Rate under the Contagious Model." Journal of Mathematical Finance 06, no. 03 (2016): 416–30. http://dx.doi.org/10.4236/jmf.2016.63033.

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Beliaeva, Natalia A., Sanjay K. Nawalkha, and Gloria M. Soto. "Pricing American Interest Rate Options under the Jump-Extended Vasicek Model." Journal of Derivatives 16, no. 1 (August 31, 2008): 29–43. http://dx.doi.org/10.3905/jod.2008.710896.

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39

Tarelli, Andrea. "No-arbitrage one-factor term structure models in zero- or negative-lower-bound environments." Investment Management and Financial Innovations 17, no. 1 (March 25, 2020): 197–212. http://dx.doi.org/10.21511/imfi.17(1).2020.18.

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One-factor no-arbitrage term structure models where the instantaneous interest rate follows either the process proposed by Vasicek (1977) or by Cox, Ingersoll, and Ross (1985), commonly known as CIR, are parsimonious and analytically tractable. Models based on the original CIR process have the important characteristic of allowing for a time-varying conditional interest rate volatility but are undefined in negative interest rate environments. A Shifted-CIR no-arbitrage term structure model, where the instantaneous interest rate is given by the sum of a constant lower bound and a non-negative CIR-like process, allows for negative yields and benefits from similar tractability of the original CIR model. Based on the U.S. and German yield curve data, the Vasicek and Shifted-CIR specifications, both considering constant and time-varying risk premia, are compared in terms of information criteria and forecasting ability. Information criteria prefer the Shifted-CIR specification to models based on the Vasicek process. It also provides similar or better in-sample and out-of-sample forecasting ability of future yield curve movements. Introducing a time variation of the interest rate risk premium in no-arbitrage one-factor term structure models is instead not recommended, as it provides worse information criteria and forecasting performance.

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Fink, Holger, Claudia Klüppelberg, and Martina Zähle. "Conditional Distributions of Processes Related to Fractional Brownian Motion." Journal of Applied Probability 50, no. 01 (March 2013): 166–83. http://dx.doi.org/10.1017/s0021900200013188.

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Conditional distributions for affine Markov processes are at the core of present (defaultable) bond pricing. There is, however, evidence that Markov processes may not be realistic models for short rates. Fractional Brownian motion (FBM) can be introduced by an integral representation with respect to standard Brownian motion. Using a simple prediction formula for the conditional expectation of an FBM and its Gaussianity, we derive the conditional distributions of FBM and related processes. We derive conditional distributions for fractional analogies of prominent affine processes, including important examples like fractional Ornstein–Uhlenbeck or fractional Cox–Ingersoll–Ross processes. As an application, we propose a fractional Vasicek bond market model and compare prices of zero-coupon bonds to those achieved in the classical Vasicek model.

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Fink, Holger, Claudia Klüppelberg, and Martina Zähle. "Conditional Distributions of Processes Related to Fractional Brownian Motion." Journal of Applied Probability 50, no. 1 (March 2013): 166–83. http://dx.doi.org/10.1239/jap/1363784431.

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Conditional distributions for affine Markov processes are at the core of present (defaultable) bond pricing. There is, however, evidence that Markov processes may not be realistic models for short rates. Fractional Brownian motion (FBM) can be introduced by an integral representation with respect to standard Brownian motion. Using a simple prediction formula for the conditional expectation of an FBM and its Gaussianity, we derive the conditional distributions of FBM and related processes. We derive conditional distributions for fractional analogies of prominent affine processes, including important examples like fractional Ornstein–Uhlenbeck or fractional Cox–Ingersoll–Ross processes. As an application, we propose a fractional Vasicek bond market model and compare prices of zero-coupon bonds to those achieved in the classical Vasicek model.

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Mallier, R., and A. S. Deakin. "A Green′s function for a convertible bond using the Vasicek model." Journal of Applied Mathematics 2, no. 5 (2002): 219–32. http://dx.doi.org/10.1155/s1110757x02203058.

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We consider a convertible security where the underlying stock price obeys a lognormal random walk and the risk-free rate is given by the Vasicek model. Using a Laplace transform in time and a Mellin transform in the stock price, we derive a Green′s function solution for the value of the convertible bond.

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Zhang, Chubing, and Ximing Rong. "Optimal Investment Strategies for DC Pension with Stochastic Salary under the Affine Interest Rate Model." Discrete Dynamics in Nature and Society 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/297875.

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We study the optimal investment strategies of DC pension, with the stochastic interest rate (including the CIR model and the Vasicek model) and stochastic salary. In our model, the plan member is allowed to invest in a risk-free asset, a zero-coupon bond, and a single risky asset. By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the CRRA and CARA utility functions, respectively.

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Cordoni, Francesco, and Luca Di Persio. "Invariant measure for the Vasicek interest rate model in the Heath–Jarrow–Morton–Musiela framework." Infinite Dimensional Analysis, Quantum Probability and Related Topics 18, no. 03 (September 2015): 1550022. http://dx.doi.org/10.1142/s0219025715500228.

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In this paper we study a particular class of forward rate problems, related to the Vasicek model, where the driving equation is a linear Gaussian stochastic partial differential equation. We first give an existence and uniqueness results of the related mild solution in infinite dimensional setting, then we study the related Ornstein–Uhlenbeck semigroup with respect to the determination of a unique invariant measure for the associated Heath–Jarrow–Morton–Musiela model.

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Yun, Yanan, and Lingyun Gao. "Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model." International Journal of Theoretical and Applied Mathematics 6, no. 2 (2020): 19. http://dx.doi.org/10.11648/j.ijtam.20200602.11.

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Al-Saadony, M. F., and W. J. Al-Obaidi. "Estimation the vasicek interest rate model driven by fractional Lévy processes with application." Journal of Physics: Conference Series 1897, no. 1 (May 1, 2021): 012017. http://dx.doi.org/10.1088/1742-6596/1897/1/012017.

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Djeutcha, Eric, and Louis Aime Fono. "Pricing for options in a Hull-White-Vasicek volatility and interest rate model." Applied Mathematical Sciences 15, no. 8 (2021): 377–84. http://dx.doi.org/10.12988/ams.2021.914516.

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ALBANESE, CLAUDIO, and ALEXEY KUZNETSOV. "AFFINE LATTICE MODELS." International Journal of Theoretical and Applied Finance 08, no. 02 (March 2005): 223–38. http://dx.doi.org/10.1142/s0219024905002986.

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We introduce a new class of lattice models based on a continuous time Markov chain approximation scheme for affine processes, whereby the approximating process itself is affine. A key property of this class of lattice models is that the location of the time nodes can be chosen in a payoff dependent way and one has the flexibility of setting them only at the relevant dates. Time stepping invariance relies on the ability of computing node-to-node discounted transition probabilities in analytically closed form. The method is quite general and far reaching and it is introduced in this article in the framework of the broadly used single-factor, affine short rate models such as the Vasiček and CIR models. To illustrate the use of affine lattice models in these cases, we analyze in detail the example of Bermuda swaptions.

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Yoon, Ji-Hun, Jeong-Hoon Kim, Sun-Yong Choi, and Youngchul Han. "Stochastic volatility asymptotics of defaultable interest rate derivatives under a quadratic Gaussian model." Stochastics and Dynamics 17, no. 01 (December 15, 2016): 1750003. http://dx.doi.org/10.1142/s0219493717500034.

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Stochastic volatility of underlying assets has been shown to affect significantly the price of many financial derivatives. In particular, a fast mean-reverting factor of the stochastic volatility plays a major role in the pricing of options. This paper deals with the interest rate model dependence of the stochastic volatility impact on defaultable interest rate derivatives. We obtain an asymptotic formula of the price of defaultable bonds and bond options based on a quadratic term structure model and investigate the stochastic volatility and default risk effects and compare the results with those of the Vasicek model.

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Xiao, Weilin, Weiguo Zhang, Xili Zhang, and Xiaoyan Chen. "The valuation of equity warrants under the fractional Vasicek process of the short-term interest rate." Physica A: Statistical Mechanics and its Applications 394 (January 2014): 320–37. http://dx.doi.org/10.1016/j.physa.2013.09.033.

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