Journal articles: 'One-factor interest rate models'

1

Canabarro, Eduardo. "Wher do One-Factor Interest Rate Models Fail?" Journal of Fixed Income 5, no. 2 (September 30, 1995): 31–52. http://dx.doi.org/10.3905/jfi.1995.408145.

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2

Hull, John, and Alan White. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities." Journal of Financial and Quantitative Analysis 28, no. 2 (June 1993): 235. http://dx.doi.org/10.2307/2331288.

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3

Kuan, Grace C. H., and Nick Webber. "Pricing Barrier Options with One-Factor Interest Rate Models." Journal of Derivatives 10, no. 4 (May 31, 2003): 33–50. http://dx.doi.org/10.3905/jod.2003.319204.

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4

Zhu, You-Lan. "Three-factor interest rate models." Communications in Mathematical Sciences 1, no. 3 (2003): 557–73. http://dx.doi.org/10.4310/cms.2003.v1.n3.a8.

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joonhee Rhee, Hoon Park, JongWoo Park, and Young-Gwon Choi. "GMM Estimation of Vasicek Types One Factor Interest Rate Models." Productivity Review 27, no. 4 (December 2013): 321–44. http://dx.doi.org/10.15843/kpapr.27.4.201312.321.

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Rogers, L. C. G., and Wolfgang Stummer. "Consistent fitting of one-factor models to interest rate data." Insurance: Mathematics and Economics 27, no. 1 (August 2000): 45–63. http://dx.doi.org/10.1016/s0167-6687(00)00039-1.

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7

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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8

Sorwar, Ghulam. "Estimating single factor jump diffusion interest rate models." Applied Financial Economics 21, no. 22 (July 21, 2011): 1679–89. http://dx.doi.org/10.1080/09603107.2011.591729.

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Sorwar, Ghulam, Giovanni Barone-Adesi, and Walter Allegretto. "Valuation of derivatives based on single-factor interest rate models." Global Finance Journal 18, no. 2 (January 2007): 251–69. http://dx.doi.org/10.1016/j.gfj.2006.04.005.

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JAIMUNGAL, SEBASTIAN, and VLADIMIR SURKOV. "VALUING EARLY-EXERCISE INTEREST-RATE OPTIONS WITH MULTI-FACTOR AFFINE MODELS." International Journal of Theoretical and Applied Finance 16, no. 06 (September 2013): 1350034. http://dx.doi.org/10.1142/s0219024913500349.

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Multi-factor interest-rate models are widely used. Contingent claims with early exercise features are often valued by resorting to trees, finite-difference schemes and Monte Carlo simulations. When jumps are present, however, these methods are less effective. In this work we develop an algorithm based on a sequence of measure changes coupled with Fourier transform solutions of the pricing partial integro-differential equation to solve the pricing problem. The new algorithm, which we call the irFST method, also neatly computes option sensitivities. Furthermore, we are also able to obtain closed-form formulae for accrual swaps and accrual range notes. We demonstrate the versatility and precision of the method through numerical experiments on European, Bermudan and callable bond options, accrual swaps and accrual range notes.

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11

Mari, Carlo. "Single factor models with Markovian spot interest rate: an analytical treatment." Decisions in Economics and Finance 26, no. 1 (May 1, 2003): 39–52. http://dx.doi.org/10.1007/s102030300002.

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12

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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LIM, K. G., SHIWEI CHANG, and TSUI KAI CHONG. "DEFAULTABLE DEBT PRICING IN MULTI-FACTOR MODELS." International Journal of Theoretical and Applied Finance 05, no. 08 (December 2002): 823–44. http://dx.doi.org/10.1142/s0219024902001742.

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This paper employs the structural approach to study defaultable debt pricing under multi-factor models. We extend existing results under the structural approach in two directions. By incorporating multiple factors, we can capture the impact of other economic variables on the debt prices apart from the interest rate factor. In our approach, we provide credit spread pricing using both the real interest rate and inflation rate as state variables. We also extend the analyses to a more general default boundary. In our paper we assume that default happens when the firm value hits a given fraction of the corresponding risk-free debt for the first time. This is also the recovery rate of the defaulted debt. Analytical solutions for both the case of constant recovery rate and the extended case of recovery rate being a deterministic function of time in the multi-factor models are provided in our study. We also provide comparison of the performance of our model with other relevant credit spread models.

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14

CHU, CHI CHIU, and YUE KUEN KWOK. "VALUATION OF GUARANTEED ANNUITY OPTIONS IN AFFINE TERM STRUCTURE MODELS." International Journal of Theoretical and Applied Finance 10, no. 02 (March 2007): 363–87. http://dx.doi.org/10.1142/s0219024907004160.

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We propose three analytic approximation methods for numerical valuation of the guaranteed annuity options in deferred annuity pension policies. The approximation methods include the stochastic duration approach, Edgeworth expansion, and analytic approximation in affine diffusions. The payoff structure in the annuity policies is similar to a quanto call option written on a coupon-bearing bond. To circumvent the limitations of the one-factor interest rate model, we model the interest rate dynamics by a two-factor affine interest rate term structure model. The numerical accuracy and the computational efficiency of these approximation methods are analyzed. We also investigate the value sensitivity of the guaranteed annuity option with respect to different parameters in the pricing model.

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15

Di Persio, Luca, Gregorio Pellegrini, and Michele Bonollo. "Polynomial Chaos Expansion Approach to Interest Rate Models." Journal of Probability and Statistics 2015 (2015): 1–24. http://dx.doi.org/10.1155/2015/369053.

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The Polynomial Chaos Expansion (PCE) technique allows us to recover a finite second-order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochastic quantityξ, hence acting as a kind of random basis. The PCE methodology has been developed as a mathematically rigorous Uncertainty Quantification (UQ) method which aims at providing reliable numerical estimates for some uncertain physical quantities defining the dynamic of certain engineering models and their related simulations. In the present paper, we use the PCE approach in order to analyze some equity and interest rate models. In particular, we take into consideration those models which are based on, for example, the Geometric Brownian Motion, the Vasicek model, and the CIR model. We present theoretical as well as related concrete numerical approximation results considering, without loss of generality, the one-dimensional case. We also provide both an efficiency study and an accuracy study of our approach by comparing its outputs with the ones obtained adopting the Monte Carlo approach, both in its standard and its enhanced version.

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16

Gómez-Valle, L., and J. Martínez-Rodríguez. "Estimation of risk-neutral processes in single-factor jump-diffusion interest rate models." Journal of Computational and Applied Mathematics 291 (January 2016): 48–57. http://dx.doi.org/10.1016/j.cam.2015.02.031.

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17

Lioui, Abraham, and Paulo Maio. "Interest Rate Risk and the Cross Section of Stock Returns." Journal of Financial and Quantitative Analysis 49, no. 2 (March 10, 2014): 483–511. http://dx.doi.org/10.1017/s0022109014000131.

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AbstractWe derive a macroeconomic asset pricing model in which the key factor is the opportunity cost of money. The model explains well the cross section of stock returns in addition to the excess market return. The interest rate factor is priced and seems to drive most of the explanatory power of the model. In this model, both value stocks and past long-term losers enjoy higher average (excess) returns because they have higher interest rate risk than growth/past winner stocks. The model significantly outperforms the nested models (capital asset pricing model (CAPM) and consumption CAPM (CCAPM)) and compares favorably with alternative macroeconomic models.

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18

Lo, C. F. "Lie-Algebraic Approach for Pricing Zero-Coupon Bonds in Single-Factor Interest Rate Models." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/276238.

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The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

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19

HELL, PHILIPP, THILO MEYER-BRANDIS, and THORSTEN RHEINLÄNDER. "CONSISTENT FACTOR MODELS FOR TEMPERATURE MARKETS." International Journal of Theoretical and Applied Finance 15, no. 04 (June 2012): 1250027. http://dx.doi.org/10.1142/s0219024912500276.

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We propose an approach for pricing and hedging weather derivatives based on including forward looking information about the temperature available to the market. This is achieved by modeling temperature forecasts by a finite dimensional factor model. Temperature dynamics are then inferred in the short end. In analogy to interest rate theory, we establish conditions which guarantee consistency of a factor model with the martingale dynamics of temperature forecasts. Finally, we consider a specific two-factor model and examine in more detail pricing and hedging of weather derivatives in this context.

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20

GAN, JUNWU. "ANALYTIC BACKWARD INDUCTION OF OPTION CASH FLOWS: A NEW APPLICATION PARADIGM FOR THE MARKOVIAN INTEREST RATE MODELS." International Journal of Theoretical and Applied Finance 08, no. 08 (December 2005): 1019–57. http://dx.doi.org/10.1142/s0219024905003384.

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This paper develops a unified formulation and a new computational methodology for the entire class of the multi-factor Markovian interest rate models. The early exercise premium representation for general American options is derived for all Markovian models. The option cash flow functions are decomposed into fast and slowly varying components. The fast varying components have the same expression for all options within a model. They are calculated analytically. Only the slowly varying components are option specific. Their backward induction for a finite time interval is carried out from Taylor expansion expressions. The small coefficient of the expansion is the product of the variance and the width of the time interval. The option price is calculated by dividing its time horizon into smaller intervals and numerically iterating the Taylor expansion expressions of one time interval. Other new results include: (i) The derivation of a new "almost" Markovian LIBOR market model and its related Markovian short-rate model; (ii) the universal form of the critical boundary near the maturity for the American options in the one-factor Markovian models; and (iii) approximate analytic expressions for the entire critical boundary of the American put stock option. The put price calculated from the boundary has relative precision better than 10-5.

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21

Tran, Ngoc-Khanh. "The Functional Stochastic Discount Factor." Quarterly Journal of Finance 09, no. 04 (December 2019): 1950013. http://dx.doi.org/10.1142/s2010139219500137.

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By assuming that the stochastic discount factor (SDF) [Formula: see text] is a proper but unspecified function of state variables [Formula: see text], we show that this function [Formula: see text] must solve a simple second-order linear differential equation specified by state variables’ risk-neutral dynamics. Therefore, this assumption determines the most general possible SDFs and associated preferences, that are consistent with the given risk-neutral state dynamics and interest rate. A consistent SDF then implies the corresponding state dynamics in the data-generating measure. Our approach offers novel flexibilities to extend several popular asset pricing frameworks: affine and quadratic interest rate models, as well as models built on linearity-generating processes. We illustrate the approach with an international asset pricing model in which (i) interest rate has an affine dynamic term structure and (ii) the forward premium puzzle is consistent with consumption-risk rationales; the two asset pricing features previously deemed conceptually incompatible.

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22

Brody, Dorje C., Lane P. Hughston, and Ewan Mackie. "General theory of geometric Lévy models for dynamic asset pricing." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2142 (February 29, 2012): 1778–98. http://dx.doi.org/10.1098/rspa.2011.0670.

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The geometric Lévy model (GLM) is a natural generalization of the geometric Brownian motion (GBM) model used in the derivation of the Black–Scholes formula. The theory of such models simplifies considerably if one takes a pricing kernel approach. In one dimension, once the underlying Lévy process has been specified, the GLM has four parameters: the initial price, the interest rate, the volatility and the risk aversion. The pricing kernel is the product of a discount factor and a risk aversion martingale. For GBM, the risk aversion parameter is the market price of risk. For a GLM, this interpretation is not valid: the excess rate of return is a nonlinear function of the volatility and the risk aversion. It is shown that for positive volatility and risk aversion, the excess rate of return above the interest rate is positive, and is increasing with respect to these variables. In the case of foreign exchange, Siegel's paradox implies that one can construct foreign exchange models for which the excess rate of return is positive for both the exchange rate and the inverse exchange rate. This condition is shown to hold for any geometric Lévy model for foreign exchange in which volatility exceeds risk aversion.

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23

Toczydlowska, Dorota, and Gareth Peters. "Financial Big Data Solutions for State Space Panel Regression in Interest Rate Dynamics." Econometrics 6, no. 3 (July 18, 2018): 34. http://dx.doi.org/10.3390/econometrics6030034.

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A novel class of dimension reduction methods is combined with a stochastic multi-factor panel regression-based state-space model in order to model the dynamics of yield curves whilst incorporating regression factors. This is achieved via Probabilistic Principal Component Analysis (PPCA) in which new statistically-robust variants are derived also treating missing data. We embed the rank reduced feature extractions into a stochastic representation for state-space models for yield curve dynamics and compare the results to classical multi-factor dynamic Nelson–Siegel state-space models. This leads to important new representations of yield curve models that can be practically important for addressing questions of financial stress testing and monetary policy interventions, which can incorporate efficiently financial big data. We illustrate our results on various financial and macroeconomic datasets from the Euro Zone and international market.

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Bhar, Ramaprasad, and Damien Lee. "Alternative characterization of volatility of short-term interest rate." International Journal of Financial Engineering 05, no. 02 (June 2018): 1850018. http://dx.doi.org/10.1142/s2424786318500184.

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Most reported stochastic volatility (SV) model for interest rates only deals with an AR specification for the latent factor process. We show in this paper the technical details for specifying the SV model for interest rates that includes an ARMA structure, a jump component and additional exogenous variables for the latent factor process. We demonstrate the efficacy of this approach with an application to the US short-term interest rate data. We find that the elasticity parameter of the variance is closer to 0.5, i.e., similar to that of the Cox–Ingersoll–Ross (1985) model of interest rates. This is quite a contrast to the finding Chan et al. [Chan, KC, GA Karolyi, F Longstaff and A Sanders (1992). The volatility of short-term interest rates: An empirical comparison of alternative models of term structure of interest rates, Journal of Finance, 47, 1209–1227]. who found the elasticity to be close to 1.5.

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Jeffrey, Andrew. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics." Journal of Financial and Quantitative Analysis 30, no. 4 (December 1995): 619. http://dx.doi.org/10.2307/2331280.

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Gómez-Valle, L., and J. Martínez-Rodríguez. "The Role of the Risk-Neutral Jump Size Distribution in Single-Factor Interest Rate Models." Abstract and Applied Analysis 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/805695.

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We obtain a result that relates the risk-neutral jump size of interest rates with yield curve data. This function is unobservable; therefore, this result opens a way to estimate the jump size directly from data in the markets together with the risk-neutral drift and jump intensity estimations. Then, we investigate the finite sample performance of this approach with a test problem. Moreover, we analyze the effect of estimating the risk-neutral jump size instead of assuming that it is artificially absorbed by the jump intensity, as usual in the interest rate literature. Finally, an application to US Treasury Bill data is also illustrated.

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27

CHENG, SI, and MICHAEL R. TEHRANCHI. "POLYNOMIAL TERM STRUCTURE MODELS." International Journal of Theoretical and Applied Finance 24, no. 02 (March 2021): 2150009. http://dx.doi.org/10.1142/s0219024921500096.

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In this paper, we explore a class of tractable interest rate models that have the property that the price of a zero-coupon bond can be expressed as a polynomial of a state diffusion process. Our results include a classification of all such time-homogeneous single-factor models in the spirit of Filipović’s maximal degree theorem for exponential polynomial models, as well as an explicit characterization of the set of feasible parameters in the case when the factor process is bounded. Extensions to time-inhomogeneous and multi-factor polynomial models are also considered.

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Qudratullah, Mohammad Farhan. "Zakah Rate In Islamic Stock Performance Models: Evidence From Indonesia." IQTISHADIA 13, no. 1 (June 15, 2020): 107. http://dx.doi.org/10.21043/iqtishadia.v13i1.6004.

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<p>There are three models commonly used to measure the performance of Islamicstocks, named Treynor Ratio, Sharpe Ratio, and Jansen Index. One component of the three models is risk-free returns which are usually approached with interest rates, whereas interest rates are prohibited in the concept of Islamic finance. This paper will approach a risk-free return with zakat-rate on the Islamic capital market in Indonesia from January 2011 - July 2018, then compare it with a model that uses interest rates. The results obtained by the model with interest rates and zakah-rate in this third model have very high suitability values, so that zakah-rate can be used as an alternative substitute for interest rates in measuring the Islamic stock performance. Beside not contradicting the concept of Islamic economics, calculation of models with zakah-rate is simpler than models with interest rates.</p>

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Maio, Paulo, and Pedro Santa-Clara. "Short-Term Interest Rates and Stock Market Anomalies." Journal of Financial and Quantitative Analysis 52, no. 3 (June 2017): 927–61. http://dx.doi.org/10.1017/s002210901700028x.

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We present a simple 2-factor model that helps explain several capital asset pricing model (CAPM) anomalies (value premium, return reversal, equity duration, asset growth, and inventory growth). The model is consistent with Merton’s intertemporal CAPM (ICAPM) framework, and the key risk factor is the innovation on a short-term interest rate, the federal funds rate, or the T-bill rate. This model explains a large fraction of the dispersion in the average returns of the joint market anomalies. Moreover, the model compares favorably with alternative multifactor models widely used in the literature. Hence, short-term interest rates seem to be relevant for explaining several dimensions of cross-sectional equity risk premia.

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Anderson, Bing, Peter J. Hammond, and Cyrus A. Ramezani. "Affine Models of the Joint Dynamics of Exchange Rates and Interest Rates." Journal of Financial and Quantitative Analysis 45, no. 5 (August 13, 2010): 1341–65. http://dx.doi.org/10.1017/s0022109010000438.

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AbstractThis paper extends the affine class of term structure models to describe the joint dynamics of exchange rates and interest rates. In particular, the issue of how to reconcile the low volatility of interest rates with the high volatility of exchange rates is addressed. The incomplete market approach of introducing exchange rate volatility that is orthogonal to both interest rates and the pricing kernels is shown to be infeasible in the affine setting. Models in which excess exchange rate volatility is orthogonal to interest rates but not orthogonal to the pricing kernels are proposed and validated via Kalman filter estimation of maximal 5-factor models for 6 country pairs.

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Kim, Sunghyun Henry, and M. Ayhan Kose. "DYNAMICS OF OPEN-ECONOMY BUSINESS-CYCLE MODELS: ROLE OF THE DISCOUNT FACTOR." Macroeconomic Dynamics 7, no. 2 (January 16, 2003): 263–90. http://dx.doi.org/10.1017/s1365100501010252.

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This paper examines the dynamic implications of different preference formulations in open-economy business-cycle models with incomplete asset markets. In particular, we study two preference formulations: a time-separable preference formulation with a fixed discount factor, and a time-nonseparable preference structure with an endogenous discount factor. We analyze the moment implications of two versions of an otherwise identical open-economy model—one with a fixed discount factor and the other with an endogenous discount factor—and study impulse responses to productivity and world real-interest-rate shocks. Our results suggest that business-cycle implications of the two models are quite similar under conventional parameter values. We also find that the approximation errors associated with the solutions of these two models are of the same magnitude.

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Chiarella, Carl, Sara Pasquali, and Wolfgang J. Runggaldier. "On filtering in Markovian term structure models: an approximation approach." Advances in Applied Probability 33, no. 04 (December 2001): 794–809. http://dx.doi.org/10.1017/s0001867800011204.

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We consider a parametrization of the Heath-Jarrow-Morton (HJM) family of term structure of interest rate models that allows a finite-dimensional Markovian representation of the stochastic dynamics. This parametrization results from letting the volatility function depend on time to maturity and on two factors: the instantaneous spot rate and one fixed-maturity forward rate. Our main purpose is an estimation methodology for which we have to model the observations under the historical probability measure. This leads us to consider as an additional third factor the market price of interest rate risk, that connects the historical and the HJM martingale measures. Assuming that the information comes from noisy observations of the fixed-maturity forward rate, the purpose is to estimate recursively, on the basis of this information, the three Markovian factors as well as the parameters in the model, in particular those in the volatility function. This leads to a nonlinear filtering problem, for the solution of which we describe an approximation methodology, based on time discretization and quantization. We prove the convergence of the approximate filters for each of the observed trajectories.

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Chiarella, Carl, Sara Pasquali, and Wolfgang J. Runggaldier. "On filtering in Markovian term structure models: an approximation approach." Advances in Applied Probability 33, no. 4 (December 2001): 794–809. http://dx.doi.org/10.1239/aap/1011994030.

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We consider a parametrization of the Heath-Jarrow-Morton (HJM) family of term structure of interest rate models that allows a finite-dimensional Markovian representation of the stochastic dynamics. This parametrization results from letting the volatility function depend on time to maturity and on two factors: the instantaneous spot rate and one fixed-maturity forward rate. Our main purpose is an estimation methodology for which we have to model the observations under the historical probability measure. This leads us to consider as an additional third factor the market price of interest rate risk, that connects the historical and the HJM martingale measures. Assuming that the information comes from noisy observations of the fixed-maturity forward rate, the purpose is to estimate recursively, on the basis of this information, the three Markovian factors as well as the parameters in the model, in particular those in the volatility function. This leads to a nonlinear filtering problem, for the solution of which we describe an approximation methodology, based on time discretization and quantization. We prove the convergence of the approximate filters for each of the observed trajectories.

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34

Rhee, Joon Hee. "Theoretical Identifications of the Market Price of Risk under the Affine Interest Rate Model with Jumps." Journal of Derivatives and Quantitative Studies 13, no. 2 (November 30, 2005): 133–43. http://dx.doi.org/10.1108/jdqs-02-2005-b0006.

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Any finance models must specify the market prices of risk that determines the relationship between the two probability measures. Although the general form of the change of measure is well known, few papers have investigated the change of measure for interest rate models and their implications for the way a model can fit to empirical facts about the behaviour of interest rates. This paper demonstrates that arbitrary specifications of market price of risk in empirical studies under the two factor affine interest rate model with jumps are not compatible with the theory of original interest rate model. Particularly, the empirical models of Duffee (2002) and Duarte (2003) may be wrong specifications in some parts under a rigorous theoretical interest rate theory.

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Kim, Don H., and Athanasios Orphanides. "Term Structure Estimation with Survey Data on Interest Rate Forecasts." Journal of Financial and Quantitative Analysis 47, no. 1 (December 16, 2011): 241–72. http://dx.doi.org/10.1017/s0022109011000627.

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AbstractThe estimation of dynamic no-arbitrage term structure models with a flexible specification of the market price of risk is beset by severe small-sample problems arising from the highly persistent nature of interest rates. We propose using survey forecasts of a short-term interest rate as an additional input to the estimation to overcome the problem. To illustrate the methodology, we estimate the 3-factor affine-Gaussian model with U.S. Treasury yields data and demonstrate that incorporating information from survey forecasts mitigates the small-sample problem. The model thus estimated for the 1990–2003 sample generates a stable and sensible estimate of the expected path of the short rate, reproduces the well-known stylized patterns in the expectations hypothesis tests, and captures some of the short-run variations in the survey forecast of the changes in longer-term interest rates.

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BERMÚDEZ, ANA, and MARÍA R. NOGUEIRAS. "NUMERICAL SOLUTION OF TWO-FACTOR MODELS FOR VALUATION OF FINANCIAL DERIVATIVES." Mathematical Models and Methods in Applied Sciences 14, no. 02 (February 2004): 295–327. http://dx.doi.org/10.1142/s0218202504003246.

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In this paper we propose a general methodology to solve partial differential inequalities arising in the valuation of financial derivatives. Firstly we show how to build up a weak formulation and how to discretize it by implicit finite difference schemes in time and finite elements in space and we propose an iterative algorithm to solve the discrete variational inequality. Although the methodology is quite general, here it is applied to solve two important two-factor models: one for valuation of dividend paying Amerasian options and another for convertible bonds with stochastic interest rate and call and put features. In both cases we validate our results with some others existing in the literature.

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Srivastava, Suresh C., Shahid Hamid, and Askar H. Choudhury. "Stock And Bond Market Linkage In The Empirical Study Of Interest Rate Sensitivity Of Bank Returns." Journal of Applied Business Research (JABR) 15, no. 1 (August 31, 2011): 47. http://dx.doi.org/10.19030/jabr.v15i1.5689.

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<span>The bank stocks equilibrium pricing relation is the traditional CAPM augmented by a second factor to account for the unexpected changes in the interest rates. This paper examines the methodological issue of constructing an interest rate variable that is orthogonal to the market index. We test a new approach in which the interest rate variable and the market return are treated as the components of a bivariate vector, a suitable vector ARMA model is determined, and then the appropriate whitened residuals are used as the interest rate factor in the two-factor model. Results are compared with the results from other models in which prevailing orthogonalization procedure is used. Our investigation indicates that the robustness of the result depends, to a limited extent, on the procedure employed to orthogonalize the two factors.</span>

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McGibany, James M., and Farrokh Nourzad. "Tax Rate Changes, Interest Rate Volatility, And The Decline In Velocity, 1981-1983." Journal of Applied Business Research (JABR) 3, no. 1 (November 1, 2011): 62. http://dx.doi.org/10.19030/jabr.v3i1.6549.

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One of the most puzzling economic events in the U.S. during this decade has been the dramatic decline in the growth rate of the income velocity of money. From the fourth quarter of 1981 to the second quarter of 1983, the velocity growth rate fell by nearly 4% as opposed to its 3% trend growth rate. Traditional models have been unable to fully capture this unusual behavior of velocity, over predicting its rate of growth. The present study is concerned with this over prediction problem and attempts to more accurately explain the decline in the velocity growth rate in the 1981-1983 period. It examines the extent to which increased interest rate volatility in the early 1980s and the Reagan tax cuts may be contributed to the decline of the velocity growth rate from 1981 to 1983.

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Fama, Eugene F. "Interest Rates and Inflation Revisited." Review of Asset Pricing Studies 9, no. 2 (February 8, 2019): 197–209. http://dx.doi.org/10.1093/rapstu/raz004.

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Abstract The continuously compounded (CC) interest rate on a one-month Treasury bill observed at the end of month t–1 is the sum of a CC expected real return and a CC expected inflation rate, Rt–1 = Et–1(rt) + Et–1(It). Two approaches are used to split Rt–1 between its two components. In the first, models for rt produce estimates of Et–1(rt), which are used to infer Et–1(It) as Rt–1 – Et–1(rt). The second approach models It to produce estimates of Et–1(It) and infer Et–1(rt) as Rt–1 – Et–1(It). By design, the estimates of Et–1(rt) and Et–1(It) from both approaches have the properties implied by rational bill prices. Received October 10, 2018; Editorial decision December 31, 2018 By Editor Jeffrey Pontiff

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Rhee, Wooheon. "CAN RBC MODELS EXPLAIN BUSINESS CYCLES IN KOREA?" Macroeconomic Dynamics 21, no. 3 (April 26, 2016): 599–623. http://dx.doi.org/10.1017/s1365100515000619.

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I examine whether an RBC model can generate a higher volatility of consumption relative to output, a strong negative correlation between output and the trade balance, and a weak countercyclicality of the real interest rate, phenomena that have been observed in the business cycles of emerging economies, including Korea. From an RBC model with recursive utility, I show that it is not the degree of relative risk aversion, but the elasticity of intertemporal substitution (EIS), that governs the movements of the variables of the model in the log linearized environment. The Bayesian estimation results based on Korean data from the period 1987 to 2013 suggest that there are some elements of success in describing the Korean economy based on the simple RBC model both with the EIS larger than one and with an error term for the real interest rate equation. An EIS larger than one improves the performance of the simple RBC model mainly in the direction of raising the volatility of consumption relative to output. Simulation results show that the error term for the real interest rate process mostly reflects the endogenous channel of financial frictions where the domestic real interest rate depends negatively on the expected (transitory) productivity shock.

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Baños, David, Marc Lagunas-Merino, and Salvador Ortiz-Latorre. "Variance and Interest Rate Risk in Unit-Linked Insurance Policies." Risks 8, no. 3 (August 6, 2020): 84. http://dx.doi.org/10.3390/risks8030084.

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One of the risks derived from selling long-term policies that any insurance company has arises from interest rates. In this paper, we consider a general class of stochastic volatility models written in forward variance form. We also deal with stochastic interest rates to obtain the risk-free price for unit-linked life insurance contracts, as well as providing a perfect hedging strategy by completing the market. We conclude with a simulation experiment, where we price unit-linked policies using Norwegian mortality rates. In addition, we compare prices for the classical Black-Scholes model against the Heston stochastic volatility model with a Vasicek interest rate model.

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Levin, Alexander. "Deriving Closed-Form Solutions for Gaussian Pricing Models: A Systematic Time-Domain Approach." International Journal of Theoretical and Applied Finance 01, no. 03 (July 1998): 349–76. http://dx.doi.org/10.1142/s0219024998000205.

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A systematic time-domain approach is presented to the derivation of closed-form solutions for interest-rate contingent assets. A financial system "asset — interest rate market" is assumed to follow an any-factor system of linear stochastic differential equations and some piece-wise defined algebraic equations for the payoffs. Closed-form solutions are expressed through the first two statistical moments of the state variables that are proven to satisfy a deterministic linear system of ordinary differential equations. A number of examples are given to illustrate the method's effectiveness. With no restrictions on the number of factors, solutions are derived for randomly amortizing loans and deposits; any European-style swaptions, caps, and floors; conversion options; Asian-style options, etc. A two-factor arbitrage-free Gaussian term structure is introduced and analyzed.

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Cairns, Andrew J. G., David Blake, and Kevin Dowd. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk." ASTIN Bulletin 36, no. 01 (May 2006): 79–120. http://dx.doi.org/10.2143/ast.36.1.2014145.

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It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

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Cairns, Andrew J. G., David Blake, and Kevin Dowd. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk." ASTIN Bulletin 36, no. 1 (May 2006): 79–120. http://dx.doi.org/10.1017/s0515036100014410.

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It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

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Poměnková, J., and S. Kapounek. "Interest rates and prices causality in the Czech Republic – Granger approach." Agricultural Economics (Zemědělská ekonomika) 55, No. 7 (August 6, 2009): 347–56. http://dx.doi.org/10.17221/2/2009-agricecon.

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Monetary policy analysis concerns both the assumptions of the transmission mechanism and the direction of causality between the nominal (i.e. the money) and real economy. The traditional channel of monetary policy implementation works via the interest rate changes and their impact on the investment activity and the aggregate demand. Altering the relationship between the aggregate demand and supply then impacts the general price level and hence inflation. Alternatively, the Post-Keynesians postulate money as a residual. In their approach, banks credit in response to the movements in investment activities and demand for money. In this paper, the authors use the VAR (i.e. the vector autoregressive) approach applied to the “Taylor Rule” concept to identify the mechanism and impact of the monetary policy in the small open post-transformation economy of the Czech Republic. The causality (in the Granger sense) between the interest rate and prices in the Czech Republic is then identified. The two alternative modelling approaches are tested. First, there is the standard VAR analysis with the lagged values of interest rate, inflation and economic growth as explanatory variables. This model shows one way causality (in the Granger sense) between the inflation rate and interest rate (i.e. the inflation rate is (Granger) caused by the lagged interest rate). Secondly, the lead (instead of lagged) values of the interest rate, inflation rate and real exchange rate are used. This estimate shows one way causality between the inflation rate and interest rate in the sense that interest rate is caused by the lead (i.e. the expected future) inflation rate. The assumptions based on money as a residual of the economic process were rejected in both models.

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Gatarek, Dariusz, and Juliusz Jabłecki. "Between Scylla and Charybdis: The Bermudan Swaptions Pricing Odyssey." Mathematics 9, no. 2 (January 6, 2021): 112. http://dx.doi.org/10.3390/math9020112.

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Bermudan swaptions are options on interest rate swaps which can be exercised on one or more dates before the final maturity of the swap. Because the exercise boundary between the continuation area and stopping area is inherently complex and multi-dimensional for interest rate products, there is an inherent “tug of war” between the pursuit of calibration and pricing precision, tractability, and implementation efficiency. After reviewing the main ideas and implementation techniques underlying both single- and multi-factor models, we offer our own approach based on dimension reduction via Markovian projection. Specifically, on the theoretical side, we provide a reinterpretation and extension of the classic result due to Gyöngy which covers non-probabilistic, discounted, distributions relevant in option pricing. Thus, we show that for purposes of swaption pricing, a potentially complex and multidimensional process for the underlying swap rate can be collapsed to a one-dimensional one. The empirical contribution of the paper consists in demonstrating that even though we only match the marginal distributions of the two processes, Bermudan swaptions prices calculated using such an approach appear well-behaved and closely aligned to counterparts from more sophisticated models.

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Brachetta, Matteo, and Claudia Ceci. "Optimal Excess-of-Loss Reinsurance for Stochastic Factor Risk Models." Risks 7, no. 2 (May 1, 2019): 48. http://dx.doi.org/10.3390/risks7020048.

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We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer’s surplus is governed by a marked point process with dual-predictable projection affected by an environmental factor and that the insurance company can borrow and invest money at a constant real-valued risk-free interest rate r. Our model allows for stochastic risk premia, which take into account risk fluctuations. Using stochastic control theory based on the Hamilton-Jacobi-Bellman equation, we analyze the optimal reinsurance strategy under the criterion of maximizing the expected exponential utility of the terminal wealth. A verification theorem for the value function in terms of classical solutions of a backward partial differential equation is provided. Finally, some numerical results are discussed.

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Ahmed, Doaa Akl, and Mamdouh Abdelmoula M. Abdelsalam. "Inflation Instability Impact on Interest Rate in Egypt: Augmented Fisher Hypothesis Test." Applied Economics and Finance 5, no. 1 (November 30, 2017): 1. http://dx.doi.org/10.11114/aef.v5i1.2709.

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The paper aims at examining an augmented version of Fisher hypothesis that include inflation instability. According to this hypothesis, there is a positive relation between interest rates and expected inflation. In contrast, there is a debate regarding the impact of inflation uncertainty on interest rate. According to the portfolio theory and models of asset pricing, inflation instability positively affects the interest rate. The reason is that risk-averse investors must be compensated with higher returns for higher risks. In contrast, the loanable funds theory implies a negative impact of inflation instability and interest rates since high uncertainty leads consumers to protect themselves against inflation by raising their savings which lowers consumption and interest rates. To compute inflation volatility, we applied different Autoregressive Conditional Heteroscedasticity models. The simple and augmented versions of Fisher hypothesis are examined using Markov Switch Model to account for possible regime shift in that relationship. For the original Fisher hypothesis, there is an evidence of supporting it in the first regime while that hypothesis does not hold in the second one. In the augmented version of Fisher hypothesis, portfolio theory hypothesis is verified in the first regime whereas the loanable funds hypothesis is confirmed in the second one.

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Draijer, Jael Marjan, Arthur Bakker, Esther Slot, and Sanne Akkerman. "The Multidimensional Structure of Interest." Frontline Learning Research 8, no. 4 (June 15, 2020): 18–36. http://dx.doi.org/10.14786/flr.v8i4.577.

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There is increasing attention for interest as a powerful, complex, and integrative construct, ranging in appearance from entirely momentary states of interest to longer-term interest pursuits. Developmental models have shown how these situational interests can develop into individual interests over time. As such, these models have helped to integrate more or less separate research traditions and focus the attention of the field more on the developmental dynamics. This, however, also raises subsequent questions, one being how development can be understood in terms of interest structure. The developmental models seem to suggest that development occurs roughly along the line of six dimensions, which we summarize as the dimensions of historicity, value, agency, frequency, intensity, and mastery. Using an experience sampling method that was implemented in a smartphone application, we prompted 94 adolescents aged 13 to 16 (60% female) to rate each interest they experienced during two weeks on these six dimensions. A latent profile analysis on 1247 interests showed six distinct multidimensional patterns, indicating both a homogeneous and heterogeneous structure of interest. Four homogeneous patterns were indicated by more or less equal levels on all six dimensions in varying degrees, and contained 86% of the interests. Two heterogeneous patterns were found, describing variations of interest that are interpreted and discussed. These results endorse the complexity of the construct of interest and provide suggestions for identifying different manifestations of interest.

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Purbayati, Radia. "EVALUASI PRAKTEK PERBANKAN SYARIAH DI INDONESIA : INTEREST RATE FREE?" Ekspansi: Jurnal Ekonomi, Keuangan, Perbankan dan Akuntansi 11, no. 2 (November 30, 2019): 231–50. http://dx.doi.org/10.35313/ekspansi.v11i2.1575.

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The aim of this study is to evaluate Islamic Banking practice truly interest rate free on determining funding and financing pricing. The object of this study are Islamic and Conventional Banking in Indonesia 2014-2018. Variables used in the study consists of equivalent rate (interest rate) of demand deposit, saving deposit, time deposit, working capital financing (loan) and financing (loan) in Islamic and Conventional Banking. VAR / VECM Modelling and Granger Causality Test applied on these 5 Models. The evidence shows that at that time there are only Model 2 and Model 5 were Granger Cause at one way in the short run. On the other hand, pricing on funding and financing product at islamic banking were determined by its time lag of pricing on funding and financing products at islamic and conventional banking , vice and versa. The shocks at the short run will be adjusted as its shocks response into long run equilibrium. It means the practicing Islamic banking in Indonesia is not truly interest rate free. Keywords : Pricing on funding and financing products, Islamic Banking, Conventional Banking, VAR/VECM Modelling, Granger Causality.

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Journal articles on the topic 'One-factor interest rate models'

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