Interest Rate Dynamics Research Articles

Hybrid Lévy Models: Design and Computational Aspects

ABSTRACTA hybrid model is a model, where two markets are studied jointly such that stochastic dependence can be taken into account. Such a dependence is well known for equity and interest rate markets on which we focus here. Other pairs can be considered in a similar way. Two different versions of a hybrid approach are developed. Independent time-inhomogeneous Lévy processes are used as the drivers of the dynamics of interest rates and equity. In both versions, the dynamics of the interest rate side is described by an equation for the instantaneous forward rate. Dependence between the markets is generated by introducing the driver of the interest rate market as an additional term into the dynamics of equity in the first version. The second version starts with the equity dynamics and uses a corresponding construction for the interest rate side. Dependence can be quantified in both cases by a single parameter. Numerically efficient valuation formulas for interest rate and equity derivatives are developed. Using market quotes for liquidly traded assets we show that the hybrid approach can be successfully calibrated.

Global real interest rate dynamics from the late 19th century to today

There is a long-standing economic debate to what extent interest rates are determined by domestic versus international forces. Using a time series factor model, we estimate two common global factors for the short-term real interest rate for a panel of 17 advanced economies from 1871 to 2013. Our analysis shows that more than 50% of the variation in national real interest rates can be explained by our two international factors alone. While our data encompasses several macroeconomic regime changes, we find in general that real interest rates are more responsive to international conditions during times of high international capital mobility, such as the post Bretton Woods period. Our first common global factor can be interpreted as an approximation of the global short-term equilibrium real interest rate. Using an error-correction approach, we show that that the global real interest rate acts as a force of attraction for national real interest rates. Moreover, our factor analysis can also explain the long-term downward trend of national real interest rates that started in the 1980s, meaning that the forces of secular stagnation have acted on a global level. Finally, we estimate a Panel-VAR model, which allows us to show that the national business cycle is highly responsive to our two common global factor variables, thus indicating that small economies have increasing difficulties to insulate themselves from international macroeconomic conditions. Our analysis is important insofar as it shows that during periods of high capital mobility Central Banks might have even less influence in setting the domestic short-term real interest rate than what is commonly assumed by most neo-keynesian macroeconomic models.

A Shannon wavelet method for pricing foreign exchange options under the Heston multi-factor CIR model

We present a robust and highly efficient Shannon wavelet pricing method for plain-vanilla foreign exchange European options under the jump-extended Heston model with multi-factor CIR interest rate dynamics. Under a Monte Carlo and partial differential equation hybrid computational framework, the option price can be expressed as an expectation, conditional on the variance factor, of a convolution product that involves the densities of the time-integrated domestic and foreign multi-factor CIR interest rate processes. We propose an efficient treatment to this convolution product that effectively results in a significant dimension reduction, from two multi-factor interest rate processes to only a single-factor process. By means of a state-of-the-art Shannon wavelet inverse Fourier technique, the resulting convolution product is approximated analytically and the conditional expectation can be computed very efficiently. We develop sharp approximation error bounds for the option price and hedging parameters. Numerical experiments confirm the robustness and efficiency of the method.

Scenario Prediction of Dynamics of Interest Rates and Internal Credit Volume in Russia for 2018−2022

This article proposes a model of internal credit driven by variations in interest rates of loans for end borrowers. The variations in internal credit after the interest rate crises that have taken place around the world in recent years are analyzed by international panel comparison, and the median elasticity is evaluated. A prediction of internal credit variations in Russia in the near future is given in light of various scenarios of interest rate fluctuations.

The Dynamics of Inflation, Money Growth, Exchange Rates And Interest Rates in Ghana

The Dynamics of Inflation, Money Growth, Exchange Rates And Interest Rates in Ghana

Economic Uncertainty, Precautionary Savings, and Treasury Yield Dynamics

We show there is a much stronger negative dynamic relation between changes in economic uncertainty and Treasury yields over weaker-economic times since at least 1990. We document this economic-state variation in uncertainty-yield dynamics for weekly and monthly change horizons, for nominal yields and real-yield proxies, for multiple economic-state identification methods, and for different economic-uncertainty metrics. We provide additional evidence to probe interpretation, especially relying on survey-based expected economic growth and inflation. Our collective evidence suggests that short-term fluctuations in precautionary-savings and consumption-smoothing forces are particularly influential on interest rate dynamics during weaker-economic times.

Financial Big Data Solutions for State Space Panel Regression in Interest Rate Dynamics

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.

The Real and Nominal Determinants of Stock and Bond Returns Comovement

The comovement between returns to stocks and nominal Treasury bonds varies over time in both magnitude and direction. Earlier research attempts to interpret this phenomenon as a consequence of variations in the link between inflation and future economic activity. I present some opposing empirical evidence, and instead argue that in the data, the comovement between stock and nominal bond returns is driven by real factors. I build a New Keynesian model that generates this behavior through the joint dynamics of output, inflation, and interest rates. The model features two types of persistent shocks to productivity growth: mean-reverting “cyclical” shocks and permanent “trend” shocks. The relative importance of these two shocks varies stochastically over time. The model quantitatively explains the observed patterns in stock-bond return comovement.

A simple analytics framework for evaluating mean escape time in different term structures with stochastic volatility

The aim of this paper is to propose a simple framework for analyzing the mean escape time of interest rate product in different term structures with stochastic volatility. In the modeling perspective, we utilize the one factor Hull–White model to design the dynamics of interest rate returns whose stochastic volatility term is assumed to follow the Cox–Ingersoll–Ross process. Furthermore, we apply the Nelson–Siegel function to simulate various scenarios of term structure based on the US Treasury bill and European bond. Then, we analyze the mean escape time surfaces of different term structures for theoretical flat yield curves and two empirical S-shaped yield curves whose term structures of short-, mid-, and long-term maturities are shifted by the modified parameters of the Nelson–Siegel function. We observe that the survival probability begins with one and reduces to zero with different rate of decay for different interest rates and volatilities. Furthermore, the results of empirical term structures imply that the adjustment in the yield of long-term maturity changes the structure of MET surface more significantly than that of short- and long-term maturities. Lastly, we detect the noise enhanced stability phenomenon from the mean escape time for all cases of flat yield, Treasury bill, and European bond.

Financial Big Data Solutions for State Space Panel Regression in Interest Rates Dynamics

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 dynamic 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 data sets from the Euro Zone and international market.

The determinants of the benchmark interest rates in China

This paper empirically investigates the determinants of the two key benchmark interest rates in China using an array of constrained ordered probit models for quarterly frequency data from 1987 to 2013. Specifically, we estimate the behavioral equation of the People's Bank of China that models its decision-making process for revisions of the benchmark deposit rate and the lending rate. Our findings imply that the PBC's policy decisions are better understood as responses to changes in inflation and money growth, while output gaps and the exchange rate play negligible roles. We also implement in-sample fit analyses and out-of-sample forecast exercises. Our empirical findings show robust and reasonably good performances of our models in understanding dynamics of these benchmark interest rates.

Interest Rate Deregulation and Dynamics of Industrial Sector’s Productivity in Nigeria

The systematic deregulation of interest rate in Nigeria in 1987 has continued to generate unending controversies among policy makers and other key stakeholders about its spill-over effects on sectoral performance and economy wide aggregate. In view the growing controversies, this paper analyzed the long-term implication of interest rate deregulation on the productivity of the industrial sector in Nigeria between 1987 and 2016. Specifically, this paper focused attention on the impacts of prime lending rate, deposit rate, monetary policy rate and cash reserve ratio on industrial output. The datasets on each of the variables were culled from the Central Bank of Nigeria Statistical Bulletin. The Autoregressive Distributive Lag (ARDL) model was adopted for the estimation of the long run behavior of the exogenous variables. The Augmented Dickey-Fuller (ADF) stationarity test approach and ARDL based bounds test approach to cointegration were applied to test the null hypotheses of a unit root and no long run relationship respectively. It was found from the ADF tests results that the variables are fractionally integrated. The bounds test result also indicates that the variables are long run relationship, hence necessitating the rejection of the null hypothesis of no cointegration. The long run regression result shows that at 10 percent level, prime lending is positively related to industrial output. This finding is in contrary to the theoretical expectations. It was equally uncovered from the result that monetary policy rate negatively impacted on industrial output at 5 percent level. Similarly, the deposit rate contracts the productivity of the industrial sector in the long run. In of these findings, this paper recommends among others that the Central Bank of Nigeria should ensure that interest rate deregulation is frequently monitored and primarily tailored towards ensuring that the prevailing market rate of interest provides opportunity for improved performance of the industrial sector.

Анализ влияния процентной политики Банка России на инфляцию и динамику процентных ставок коммерческих банков

Анализ влияния процентной политики Банка России на инфляцию и динамику процентных ставок коммерческих банков

PDE formulation of some SABR/LIBOR market models and its numerical solution with a sparse grid combination technique

SABR models have been used to incorporate stochastic volatility to LIBOR market models (LMM) in order to describe interest rate dynamics and price interest rate derivatives. From the numerical point of view, the pricing of derivatives with SABR/LIBOR market models (SABR/LMMs) is mainly carried out with Monte Carlo simulation. However, this approach could involve excessively long computational times. For first time in the literature, in the present paper we propose an alternative pricing based on partial differential equations (PDEs). Thus, we pose original PDE formulations associated to the SABR/LMMs proposed by Hagan and Lesniewsk (2008), Mercurio and Morini (2009) and Rebonato and White (2008). Moreover, as the PDEs associated to these SABR/LMMs are high dimensional in space, traditional full grid methods (like standard finite differences or finite elements) are not able to price derivatives over more than three or four underlying interest rates. In order to overcome this curse of dimensionality, a sparse grid combination technique is proposed. A comparison between Monte Carlo simulation results and the ones obtained with the sparse grid technique illustrates the performance of the method.

Drug trafficking, money laundering and the business cycle: Does secular stagnation include crime?

AbstractThe aim of the paper is to analyze theoretically and empirically the impact the macroeconomic cycle has on the accumulation of capital by organized crime, using estimates for the global drug market. So far, the economic literature has neglected the relationships existing between illegal markets, money laundering and the business cycle. We propose a dynamic model where the business cycle influences the criminal economy via two different channels. On the one side, illegal markets grow at variable rates, depending on the health of the legal economy. Second, a pass‐through effect can exist, since the business cycle affects the legal markets which criminal operators use to launder their revenues. Furthermore, we analyze the consequences of a ‘saturation effect’ limiting maximum accumulation of illegal capital. We find that overall illegal capital is affected by the business cycle through a capital multiplier; in addition to this, the dynamics of interest rates in financial markets can influence such multiplier.

Exchange Rates, Interest Rates and the Global Carry Trade

We empirically examine how the global carry trade affects the dynamics of spot exchange rates and interest rates across 13 countries from 2000, through the world financial crisis, until the end of 2011. Our model identifies the weekly carry trade position in each currency by matching data on forex trading flows with the predictions of a dynamic portfolio allocation problem that exploits the predictability in excess currency returns (deviations from uncovered interest parity). Using these carry positions produce two surprising results: First, in nine countries carry trades are an economically significant driver of interest rate differentials (vs. U.S. rates). Second, the carry trade only affects the dynamics of spot exchange rates insofar as it is contributes to total forex order flow; (i.e., flows generated by the carry trade and all other trading motives). These findings contradict the conventional view that sudden large movements in exchange rates are attributable to the carry trade. They suggest, instead, that the effects of the global carry trade are primarily concentrated in bond markets.

Dynamic derivative strategies with stochastic interest rates and model uncertainty

We obtain a closed-form solution to the investment problem of an ambiguity averse investor in complete and incomplete markets with stochastic changes in volatility and interest rates. The investor can have different levels of uncertainty about the dynamics of stock price, interest rates, and stock price volatility. We employ the Continuum-Generalized Method of Moments to estimate the model parameters based on S&P500 and 10-year Treasury bond prices data. Most importantly, we demonstrate the relevance of modelling ambiguity jointly, instead of modelling it separately for each variable. In addition, we find that in the incomplete markets bond investment is quite sensitive to the interest rate ambiguity, whereas volatility ambiguity does not have any substantial effect on the optimal portfolio. Welfare loss analysis reveals that ignoring volatility ambiguity can be very costly in complete markets and ignoring interest rate ambiguity results in somewhat significant and similar losses in both types of market.

Financial frictions, interest rate dynamics, and international business cycle synchronization

AbstractA two‐country real business cycle model with national endogenous borrowing constraints and working capital requirements can account for the high level of international co‐movements. The effects of technology shocks are transmitted internationally through the dynamics of the interest rate. Specifically, the borrowing mechanism brings about a wedge between the real interest rate and the expected marginal product of capital, such that interest rates fall following positive technology shocks. A lower interest rate induces more investment by Foreign firms, which in turn contribute to greater synchronization of economic activities across countries. Moreover, terms of trade amplify the effects of technology shocks.

A Shannon Wavelet Method for Pricing Foreign Exchange Options under the Heston Multi-Factor CIR Model

We present a robust and highly efficient Shannon wavelet pricing method for plain-vanilla foreign exchange European options under the jump-extended Heston model with multi-factor CIR interest rate dynamics. Under a Monte Carlo and partial differential equation hybrid computational framework, the option price can be expressed as an expectation, conditional on the variance factor, of a convolution product that involves the densities of the time-integrated domestic and foreign multi-factor CIR interest rate processes. We propose an efficient treatment to this convolution product that effectively results in a significant dimension reduction, from two multi-factor interest rate processes to only a one-factor process. By means of a state-of-the-art Shannon wavelet inverse Fourier technique, the resulting convolution product is approximated analytically and the conditional expectation can be computed very efficiently. We develop sharp approximation error bounds for the option price and hedging parameters. Numerical experiments confirm the robustness and impressive efficiency of the method.

Consistent recalibration of yield curve models

AbstractThe analytical tractability of affine (short rate) models, such as the Vasiček and the Cox–Ingersoll–Ross (CIR) models, has made them a popular choice for modeling the dynamics of interest rates. However, in order to properly account for the dynamics of real data, these models must exhibit time‐dependent or even stochastic parameters. This breaks their tractability, and modeling and simulating become an arduous task. We introduce a new class of Heath–Jarrow–Morton (HJM) models that both fit the dynamics of real market data and remain tractable. We call these models consistent recalibration (CRC) models. CRC models appear as limits of concatenations of forward rate increments, each belonging to a Hull–White extended affine factor model with possibly different parameters. That is, we construct HJM models from “tangent” affine models. We develop a theory for continuous path versions of such models and discuss their numerical implementations within the Vasiček and CIR frameworks.