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This paper studies the optimal investment and benefit payment strategies for target benefit (TB) pension plans. The pension fund receives contributions from active members and pays benefits to retirees. Meanwhile, the accumulated wealth is invested in financial market consisting of one risk-free asset and one risky asset, in which the risk-free interest rate is described by the Vasicek model. The general hyperbolic absolute risk aversion (HARA) utility is adopted to describe pension fund managers' risk preferences. Using the dynamic programming approach, we construct the Hamilton–Jacobi–Bellman (HJB) equation and obtain explicit expressions for optimal investment and benefit payment strategies using the Legendre transform-dual technique. Finally, numerical analysis is presented to illustrate the sensitivity of the optimal strategies to model parameters. [ABSTRACT FROM AUTHOR]

After the 2007 financial crisis, many central banks adopted policies to lower their interest rates; the dynamics of these rates cannot be captured using classical models. Recently, Meucci and Loregian proposed an approach to estimate nonnegative interest rates using the inverse-call transformation. Despite the fact that their work is distinguished from others in the literature by their consideration of practical aspects, some technical difficulties still remain, such as the lack of analytic expression for the zero-coupon bond (ZCB) price. In this work, we propose novel approximate closed-form solutions for the ZCB price in the zero lower bound (ZLB) framework, when the underlying shadow rate is assumed to follow the classical one-factor Vasicek model. Then, a filtering procedure is performed using the Unscented Kalman Filter (UKF) to estimate the unobservable state variable (the shadow rate), and the model calibration is proceeded by estimating the model parameters using the Particle Swarm Optimization (PSO) algorithm. Further, empirical illustrations are given and discussed using (as input data) the interest rates of the AAA-rated bonds compiled by the European Central Bank ranging from 6 September 2004 to 21 June 2012 (a period that concerns the ZLB framework). Our approximate closed-form solution is able to show a good match between the actual and estimated yield-rate values for short and medium time-to-maturity values, whereas, for long time-to-maturity values, it is able to estimate the trend of the yield rates. [ABSTRACT FROM AUTHOR]

In this paper, we consider one-dimensional generalized affine processes under the paradigm of Knightian uncertainty (the so-called nonlinear generalized affine models). This extends and generalizes previous results in Fadina et al. (2019) and Lütkebohmert et al. (2022). In particular, we study the case when the payoff is allowed to depend on the path, like it is the case for barrier options or Asian options. To this end, we develop the path-dependent setting for the value function relying on functional Itô calculus. We establish a dynamic programming principle which then leads to a functional nonlinear Kolmogorov equation describing the evolution of the value function. While for Asian options, the valuation can be traced back to PDE methods, this is no longer possible for more complicated payoffs like barrier options. To handle such payoffs in an efficient manner, we approximate the functional derivatives with deep neural networks and show that the numerical valuation under parameter uncertainty is highly tractable. Finally, we consider the application to structural modelling of credit and counterparty risk, where both parameter uncertainty and path-dependence are crucial and the approach proposed here opens the door to efficient numerical methods in this field. [ABSTRACT FROM AUTHOR]

Tempered fractional Brownian motion (TFBM) and tempered fractional Brownian motion of the second kind (TFBMII) modify the power-law kernel in the moving average representation of fractional Brownian motion by introducing exponential tempering. We construct least-square estimators for the unknown drift parameters within Vasicek models that are driven by these processes. To demonstrate their strong consistency, we establish asymptotic bounds with probability 1 for the rate of growth of trajectories of tempered fractional processes. [ABSTRACT FROM AUTHOR]

After the 2007 financial crisis, many central banks adopted policies to lower their interest rates; the dynamics of these rates cannot be captured using classical models. Recently, Meucci and Loregian proposed an approach to estimate nonnegative interest rates using the inverse-call transformation. Despite the fact that their work is distinguished from others in the literature by their consideration of practical aspects, some technical difficulties still remain, such as the lack of analytic expression for the zero-coupon bond (ZCB) price. In this work, we propose novel approximate closed-form solutions for the ZCB price in the zero lower bound (ZLB) framework, when the underlying shadow rate is assumed to follow the classical one-factor Vasicek model. Then, a filtering procedure is performed using the Unscented Kalman Filter (UKF) to estimate the unobservable state variable (the shadow rate), and the model calibration is proceeded by estimating the model parameters using the Particle Swarm Optimization (PSO) algorithm. Further, empirical illustrations are given and discussed using (as input data) the interest rates of the AAA-rated bonds compiled by the European Central Bank ranging from 6 September 2004 to 21 June 2012 (a period that concerns the ZLB framework). Our approximate closed-form solution is able to show a good match between the actual and estimated yield-rate values for short and medium time-to-maturity values, whereas, for long time-to-maturity values, it is able to estimate the trend of the yield rates.

This paper investigates the pricing formula for geometric Asian options where the underlying asset is driven by the sub-fractional Brownian motion with interest rate satisfying the sub-fractional Vasicek model. By applying the sub-fractional $ {\rm{It\hat o}} $ formula, the Black-Scholes (B-S) type Partial Differential Equations (PDE) to Asian geometric average option is derived by Delta hedging principle. Moreover, the explicit pricing formula for Asian options is obtained through converting the PDE to the Cauchy problem. Numerical experiments are conducted to test the impact of the stock price, the Hurst index, the speed of interest rate adjustment, and the volatilities and their correlation for the Asian option and the interest rate model, respectively. The results show that the main parameters such as Hurst index have a significant influence on the price of Asian options.

In this paper, we concentrate on the European option pricing problem in incomplete markets by taking Vasicek stochastic interest rate model into account and expanding it in accordance with a Lévy process named Variance Gamma (VG) process. In doing so, first, we prove the existence and uniqueness of the solution to the stochastic differential equation of this model. Then, by the means of the hedging and replicating techniques, pricing formulas for the bond and, in succession, for European options are established. Finally, from a numerical point of view, we will analyze the value of a bond based on our consideration model and also, we will study a European call option bond price. All these results are reported through the Monte-Carlo simulation method. [ABSTRACT FROM AUTHOR]

The unbiased expectation theory stipulates that long-term interest rates are determined by the market's expectations of future short-term interest rates. According to this hypothesis, if investors have unbiased expectations about future interest rate movements, the forward interest rates should be good predictors of future spot interest rates. This hypothesis of the term structure of interest rates has long been a subject of debate due to empirical and theoretical challenges. Despite extensive research, a satisfactory explanation for the observed systematic difference between future spot interest rates and forward interest rates has not yet been identified. In this study, we approach this issue from an arbitrage theory perspective, leveraging on the connection between the expectation hypothesis and changes in probability measures. We propose that the observed bias can be explained by two adjustments: a risk premia adjustment, previously considered in the literature, and a stochastic adjustment that has been overlooked until now resulting from two measure changes. We further demonstrate that for specific instances of the Vasicek and Cox, as well as the Ingersoll and Ross, stochastic interest rate models, quantifying these adjustments reveals that the stochastic adjustment plays a significant role in explaining the bias, and ignoring it may lead to an overestimation of the required risk premia/aversion adjustment. Our findings extend beyond the realm of financial economic theory to have tangible implications for interest rate modelling. The capacity to quantify and distinguish between risk and stochastic adjustments empowers modellers to make more informed decisions, leading to a more accurate understanding of interest rate dynamics over time. [ABSTRACT FROM AUTHOR]

The aim of this study is to analyze bifurcation points in financial models using colored noise as a stochastic component. The research investigates the impact of colored noise on change-points and approach to their detection via neural networks. The paper presents a literature review on the use of colored noise in complex systems. The Vasicek stochastic model of interest rates is the object of the research. The research methodology involves approximating numerical solutions of the model using the Euler–Maruyama method, calibrating model parameters, and adjusting the integration step. Methods for detecting bifurcation points and their application to the data are discussed. The study results include the outcomes of an LSTM model trained to detect change-points for models with different types of noise. Results are provided for comparison with various change-point windows and forecast step sizes. [ABSTRACT FROM AUTHOR]

The inferred rate of default (IRD) was first introduced as an indicator of default risk computable from information publicly reported by the Bulgarian National Bank. We have provided a more detailed justification for the suggested methodology for forecasting the IRD on the bank-group- and bank-system-level based on macroeconomic factors. Furthermore, we supply additional empirical evidence in the time-series analysis. Additionally, we demonstrate that IRD provides a new perspective for comparing credit risk across bank groups. The estimation methods and model assumptions agree with current Bulgarian regulations and the IFRS 9 accounting standard. The suggested models could be used by practitioners in monthly forecasting the point-in-time probability of default in the context of accounting reporting and in monitoring and managing credit risk. [ABSTRACT FROM AUTHOR]

Analysis of traffic flow signals plays an important role in traffic prediction and management. As an intrinsic property, the singular point of a traffic flow signal labels a new nonsteady status. Therefore, detecting the singular point is an effective approach to determine the moment of traffic flow prediction. In this paper, an improved wavelet transform is proposed to detect singular points of real-time traffic flow signals. The number of detected singular points is output via the heuristic selection of multiple scales. Then, a weighted similarity measurement of historical traffic flow signals is utilized to predict the next singular point. The position of the next singular point decides the duration of prediction adaptively. The detected and predicted singular points are applied to dynamically update the unequal interval prediction of traffic flow. Furthermore, a Vasicek model is used to predict the traffic flow by minimizing the sum of the relative mean standard error (RMSE) between the traffic flow increment in the predicted interval and the sampled increments of previous intervals. A decomposition method is used to solve the unequal matrix problem. Based on the scenario and traffic flow imported from the real-world map, the simulation results show that the proposed algorithm outperforms existing approaches with high prediction accuracy and much lower computing cost. [ABSTRACT FROM AUTHOR]

Asian rainbow options provide investors with a new option solution as an effective tool for asset allocation and risk management. In this paper, we address the pricing problem of Asian rainbow options with stochastic interest rates that obey the Vasicek model. By introducing the Vasicek model as the change process of the stochastic interest rate, based on the non-arbitrage principle and the stochastic differential equation, the number of assets of the Asian rainbow option is expanded to n dimensions, and the pricing formulas of the Asian rainbow option with multiple (n) assets under the Vasicek interest rate model are obtained. The multi-asset pricing results under stochastic interest rates provide more possibilities for Asian rainbow options. Furthermore, Monte Carlo simulation experiments show that the pricing formula is accurate and efficient under double stochastic errors. Finally, we perform parameter sensitivity analysis to further justify the pricing model.

This paper investigates the pricing formula for geometric Asian options where the underlying asset is driven by the sub-fractional Brownian motion with interest rate satisfying the sub-fractional Vasicek model. By applying the sub-fractional I t o ^ formula, the Black-Scholes (B-S) type Partial Differential Equations (PDE) to Asian geometric average option is derived by Delta hedging principle. Moreover, the explicit pricing formula for Asian options is obtained through converting the PDE to the Cauchy problem. Numerical experiments are conducted to test the impact of the stock price, the Hurst index, the speed of interest rate adjustment, and the volatilities and their correlation for the Asian option and the interest rate model, respectively. The results show that the main parameters such as Hurst index have a significant influence on the price of Asian options. This paper investigates the pricing formula for geometric Asian options where the underlying asset is driven by the sub-fractional Brownian motion with interest rate satisfying the sub-fractional Vasicek model. By applying the sub-fractional formula, the Black-Scholes (B-S) type Partial Differential Equations (PDE) to Asian geometric average option is derived by Delta hedging principle. Moreover, the explicit pricing formula for Asian options is obtained through converting the PDE to the Cauchy problem. Numerical experiments are conducted to test the impact of the stock price, the Hurst index, the speed of interest rate adjustment, and the volatilities and their correlation for the Asian option and the interest rate model, respectively. The results show that the main parameters such as Hurst index have a significant influence on the price of Asian options. [ABSTRACT FROM AUTHOR]

In this article, the spectral collocation method based on radial basis functions is used to solve the mentioned models. The advantage of this method is that it converts the equations into a system of algebraic equations. Therefore, we can solve this problem with Newton's method. The purpose of this article is to numerically solve stochastic models such as the Heston model, Vasicek model, Cox-Ingersoll and Ross model and a model of the Black-Scholes called the Genral Stock model. The method is computationally attractive, and numerical examples confirm the validity and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a time-consistent and arbitrage-free state space for the one-, two-, and three-factor Vasicek models for long-term bonds is constructed. To account for the uncertainty in long-term bond yields, we propose a stochastic time-dependent mean-reversion model. The state-space model allows for the computation of measurement errors from observed yields. Appropriate state and measurement linear equations are derived to allow the use of the Kalman filter for model implementation. Based on weekly South African Government Bonds from February 2010 to February 2021, we give parameter estimates for the one-factor, two-factor, and three-factor models. The results from the study show that the developed model can fit the term structure of very long-term bonds. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the shapes of forward curves and yield curves that can be attained in the two-factor Vasicek model. We show how to partition the state space of the model, such that each partition is associated to a particular shape (normal, inverse, humped, etc.). The partitions and the corresponding shapes are determined by the winding number of a single curve with possible singularities and self-intersections, which can be constructed as the envelope of a family of lines. Building on these results, we classify possible transitions between term structure shapes, give results on attainability of shapes conditional on the level of the short rate, and propose a simple method to determine the relative frequency of different shapes of the forward curve and the yield curve. [ABSTRACT FROM AUTHOR]

This article develop an inference problem for Vasicek model driven by a general Gaussian process. We construct a least squares estimator and a moment estimator for the drift parameters of the Vasicek model, and we prove the consistency and the asymptotic normality. Our approach partially extended the result of Xiao and Yu for the case when noise is a fractional Brownian motion with Hurst parameter H ∈ [ 1 / 2 , 1). The strategy is to exploit the Garsia–Rodemich–Rumsey inequality since the theorem of Pickands cannot be used any more in our case. [ABSTRACT FROM AUTHOR]

Tempered fractional Brownian motion (TFBM) and tempered fractional Brownian motion of the second kind (TFBMII) modify the power-law kernel in the moving average representation of fractional Brownian motion by introducing exponential tempering. We construct least-square estimators for the unknown drift parameters within Vasicek models that are driven by these processes. To demonstrate their strong consistency, we establish asymptotic bounds with probability 1 for the rate of growth of trajectories of tempered fractional processes.

The unbiased expectation theory stipulates that long-term interest rates are determined by the market’s expectations of future short-term interest rates. According to this hypothesis, if investors have unbiased expectations about future interest rate movements, the forward interest rates should be good predictors of future spot interest rates. This hypothesis of the term structure of interest rates has long been a subject of debate due to empirical and theoretical challenges. Despite extensive research, a satisfactory explanation for the observed systematic difference between future spot interest rates and forward interest rates has not yet been identified. In this study, we approach this issue from an arbitrage theory perspective, leveraging on the connection between the expectation hypothesis and changes in probability measures. We propose that the observed bias can be explained by two adjustments: a risk premia adjustment, previously considered in the literature, and a stochastic adjustment that has been overlooked until now resulting from two measure changes. We further demonstrate that for specific instances of the Vasicek and Cox, as well as the Ingersoll and Ross, stochastic interest rate models, quantifying these adjustments reveals that the stochastic adjustment plays a significant role in explaining the bias, and ignoring it may lead to an overestimation of the required risk premia/aversion adjustment. Our findings extend beyond the realm of financial economic theory to have tangible implications for interest rate modelling. The capacity to quantify and distinguish between risk and stochastic adjustments empowers modellers to make more informed decisions, leading to a more accurate understanding of interest rate dynamics over time.

The inferred rate of default (IRD) was first introduced as an indicator of default risk computable from information publicly reported by the Bulgarian National Bank. We have provided a more detailed justification for the suggested methodology for forecasting the IRD on the bank-group- and bank-system-level based on macroeconomic factors. Furthermore, we supply additional empirical evidence in the time-series analysis. Additionally, we demonstrate that IRD provides a new perspective for comparing credit risk across bank groups. The estimation methods and model assumptions agree with current Bulgarian regulations and the IFRS 9 accounting standard. The suggested models could be used by practitioners in monthly forecasting the point-in-time probability of default in the context of accounting reporting and in monitoring and managing credit risk.

Catastrophic losses induced by natural disasters are receiving growing attention because of the severe increases in their magnitude and frequency. We first investigated the extreme tail behavior of flood-caused economic losses and maximum point precipitation based on the peaks-over-threshold method and point process (PP) model and its extreme tail dependence. We found that both maximum point precipitation and direct economic losses are well-modeled by the PP approach with certain tail dependence. These findings were further utilized to design a layered compensation insurance scheme using estimated value-at-risk (VaR) and conditional VaR (CVaR) among all stakeholders. To diversify the higher level of losses due to extreme precipitation, we designed a coupon paying catastrophe bond triggered by hierarchical maximum point precipitation level, based on the mild assumption on the independence between flood-caused risk and financial risk. The pricing sensitivity was quantitatively analyzed in terms of the tail risk of the flood disaster and the distortion magnitude and the market risk in Wang's transform. Our trigger process was carefully designed using a compound Poisson process, modeling both the frequency and the layered intensity of flood disasters. Lastly, regulations and practical suggestions are provided regarding the flood risk prevention and warning. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate option pricing using stochastic interest rates and compare the performance of each of them with options pricing using non-stochastic interest rates (Black, Scholes and Merton model) in Tehran Stock Exchange. In this study, our data are option data traded in Tehran Stock Exchange from March 2018 to December 2022. During the research, the theoretical prices achieved from each model compared with the prices traded in the Tehran Stock Exchange. Based on the Root Mean Squared Error (RMSE) criterion and regression results, It was found that in the valuation of short-term options, there is not much difference between the option pricing using stochastic interest rate models and Black, Scholes and Merton model. While the pricing of long-term options have performed better than the Black, Scholes, and Merton models under stochastic interest rate. Also, using Vasicek interest rate model in option pricing is the most accurate option pricing result compared to other models. After that, Merton model and CIR model have been most accurate. [ABSTRACT FROM AUTHOR]

Exit times of diffusion processes play an important role in the application of finance, insurance, biology, engineering, and so on. This article investigates the two-side exit time problems for the Vasicek model. By using Strong Markov property, the Laplace–Stieltjes transform (LST) of some exit times are obtained. And then the results are used to figure out the probability and mathematical expectation of the exit times. Finally, numerical examples are given to illustrate the applications of the LST of some exit times. [ABSTRACT FROM AUTHOR]

Bu çalışmada stokastik diferansiyel denklemlerine dayanan Vasicek ve CIR modelleri gösterge faiz oranına uygulanarak, modellerin faiz oranı öngörü performansları incelenmiş, getiri eğrisi ve forward verim eğrisi tahmin edilmiştir. Analizler tüm dönemin yanı sıra ICSS algoritmasına bağlı olarak belirlenen farklı volatilite dönemleri dikkate alınarak da yapılmıştır. Modellerin performanslarının analizinde RMSE, ME, MSE, MAE, MAPE ve Theil’s U kriterlerinden yararlanılmıştır. Bulgular, belirgin bir şekilde CIR modelinin performansının Vasicek modelinin performansından daha iyi olduğu sonucuna işaret etmektedir. Çalışma bulgularının para politikası uygulamaları, sabit getirili finansal varlıkların fiyatlanması ve getiri eğrilerinin tahmini gibi konular açısından oldukça önemli bilgiler sunduğu düşünülmektedir.

Analysis of traffic flow signals plays an important role in traffic prediction and management. As an intrinsic property, the singular point of a traffic flow signal labels a new nonsteady status. Therefore, detecting the singular point is an effective approach to determine the moment of traffic flow prediction. In this paper, an improved wavelet transform is proposed to detect singular points of real-time traffic flow signals. The number of detected singular points is output via the heuristic selection of multiple scales. Then, a weighted similarity measurement of historical traffic flow signals is utilized to predict the next singular point. The position of the next singular point decides the duration of prediction adaptively. The detected and predicted singular points are applied to dynamically update the unequal interval prediction of traffic flow. Furthermore, a Vasicek model is used to predict the traffic flow by minimizing the sum of the relative mean standard error (RMSE) between the traffic flow increment in the predicted interval and the sampled increments of previous intervals. A decomposition method is used to solve the unequal matrix problem. Based on the scenario and traffic flow imported from the real-world map, the simulation results show that the proposed algorithm outperforms existing approaches with high prediction accuracy and much lower computing cost.

Interest rate derivatives are often characterized by jumps of different magnitudes due to abnormal occurrences from certain sudden or rare events. Adequate pricing of such derivatives require the use of Lévy processes. In order to manage risks, it is necessary to study the effects of changes in a model's parameters. In this paper, we extend an existing Vasicek interest rate model with a Brownian motion as an underlying to a subordinated Lévy market with a variance gamma process as an underlying. We derive an expression for the price of an interest rate derivative called a 'zero-coupon bond' in the market. We employ Malliavin calculus to determine the sensitivity of the model to changes in some critical parameters of the associated interest rate derivatives by computing the greeks: delta and gamma. These are important riskmeasuring quantities in a financial market, especially a variance gamma Lévy market. [ABSTRACT FROM AUTHOR]

Interest rate derivatives being financial instruments whose values are affected by movements in interest rates experience jumps due to many unforeseen circumstances, and thus, require adequate modelling and sensitivity analysis that consider such scenarios in order to minimize risks. This paper derives expressions for the greeks from parameters of a variance gamma process required when computing the sensitivities of the parameters of an interest rate derivative called zero-coupon bond driven by the variance gamma process. [ABSTRACT FROM AUTHOR]

This paper incorporates state dependent correlations (those that vary systematically with the state of the economy) into the Vasicek default model. Other approaches to randomizing correlation in the Vasicek model have either assumed that correlation is independent of the systematic risk factor (zero state dependence) or is an explicit function of the systematic risk factor (perfect state dependence). By contrast, our approach allows for an arbitrary degree of state dependence and includes both zero and perfect state dependence as special cases. This is accomplished by expressing the factor loading as a function of an auxiliary (Gaussian) variable that is correlated with the systematic risk factor. Using Federal Reserve data on delinquency rates we use maximum likelihood to estimate the parameters of the model, and find the empirical degree of state dependence to be quite high (but generally not perfect). We also find that randomizing correlation, without allowing for state dependence, does not improve the empirical performance of the Vasicek model.

Globally, Africa's food security is the lowest but an in -depth quantitative analysis on its food system is still lacking. To achieve this, food production is used as the indicator for food availability and food price, as the proxy for food access at the continental and regional level respectively. The different dimensions studied focused on the crop production-population (cpp) system and food price correlations/tail dependence. The cpp was found to be stable and the preservation of this stability under a reduced (constant) crop production (population) was verified by the Vasicek model. In contrast, an increase in the population destabilized the system. Given that food insecurity is much more prevalent in East Africa (EA), the extreme quarterly maize prices in Kenya, Ethiopia and Somalia were analyzed using rank correlation measures, copulas, univariate and bivariate generalized extreme value theory. For all years (2006 - 2019), Kenya-Ethiopia exhibited the highest correlation while Somalia-Kenya, the lowest. Across different periods, the global food crises (global stressor) stimulated a higher correlation between price-pairs than the widespread drought (local stressor) in EA. Tail dependence is present but asymptotic dependence is absent for all pairs. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Catastrophic losses induced by natural disasters are receiving growing attention because of the severe increases in their magnitude and frequency. We first investigated the extreme tail behavior of flood-caused economic losses and maximum point precipitation based on the peaks-over-threshold method and point process (PP) model and its extreme tail dependence. We found that both maximum point precipitation and direct economic losses are well-modeled by the PP approach with certain tail dependence. These findings were further utilized to design a layered compensation insurance scheme using estimated value-at-risk (VaR) and conditional VaR (CVaR) among all stakeholders. To diversify the higher level of losses due to extreme precipitation, we designed a coupon paying catastrophe bond triggered by hierarchical maximum point precipitation level, based on the mild assumption on the independence between flood-caused risk and financial risk. The pricing sensitivity was quantitatively analyzed in terms of the tail risk of the flood disaster and the distortion magnitude and the market risk in Wang’s transform. Our trigger process was carefully designed using a compound Poisson process, modeling both the frequency and the layered intensity of flood disasters. Lastly, regulations and practical suggestions are provided regarding the flood risk prevention and warning.

Interbank rate is an important benchmark used to gauge the impact of monetary policy on the economic activities of a country. It serves not only as the basis of financial market operations but also acts as an effective tool of the central bank, which uses it to control the flow of funds, both in terms of domestic and foreign currencies. In the past, researchers used time series methodology to analyse the volatility of interbank rates which has a few drawbacks. This study, however, attempted to model the mean reversion and volatility of interbank rate by applying the Vasicek stochastic model using the maximum likelihood estimation (MLE) technique. In order to get precise observations, the study applied Monte Carlo simulation in R. The results suggested that the long term mean and speed of mean reversion behaved in a contrasting manner over different time horizons in the interbank market of Pakistan. [ABSTRACT FROM AUTHOR]

We provide a full classification of all attainable term structure shapes in the two-factor Vasicek model of interest rates. In particular, we show that the shapes normal, inverse, humped, dipped and hump-dip are always attainable. In certain parameter regimes, up to four additional shapes can be produced. Our results apply to both forward and yield curves and show that the correlation and the difference in mean-reversion speeds of the two factor processes play a key role in determining the scope of attainable shapes. The key mathematical tool is the theory of total positivity, pioneered by Samuel Karlin and others in the 1950s. [ABSTRACT FROM AUTHOR]

The path integral method is applied to investigation of time dependence of interest rate of Merton and Vasicek stochastic models. The path integral is based on Wiener integral by means of variable substitution based on stochastic equations of the models. The results were obtained for term structure of interest rates in Merton and Vasicek models. The path integral method is applied to the investigation of the time dependence of the interest rate in the Merton and Vasicek stochastic models. The path integral is based on the Wiener integral by means of variable substitution based on stochastic equations of the models. The results were obtained for the term structure of interest rates in the Merton and Vasicek models. As is known, the drawback of those models is that they allow for negative values of the interest rate. Hence, one should introduce boundary conditions, which limit the stochastic variable domain to positive values. During the construction of the path integral for respective mean values, one needs use a transition probability that satisfies those boundary conditions. However, the construction of such path integral for average values, which contains an exponent dependent on some functional of integration variables, is in general a very complicated task. In the work, an easier approach is used that consists in limiting the integral domain in path integrals for the Merton and Vasicek models. In particular, in path integrals the integral domain is limited using condition ⟆t t0 r(τ )dτ > 0, which is given by the Heaviside step function θ(x). It is shown that limiting the integral domain in such a way allows us to get rid of negative values of the term structure of interest rates. The path integrals for the limited integral domain are calculated using the transformation of the Heaviside step function into a complex plane. During the calculation of mean values, a normalization of the measure is applied to a selected domain. As a result, in the models where the interest rate takes only positive values, equations for the term structure of interest rates were obtained. Positive values of interest rates are visually demonstrated by means of asymptotic analysis of their time dependence. The obtained functional forms of the interest rates dependencies can be used to calibrate models with the help of respective optimization procedures, which minimize deviation of theoretical and experimental values. Expressions found in the work allow one to accomplish the above procedures using numeric methods. [ABSTRACT FROM AUTHOR]

Copyright of Mexican Journal of Economics & Finance / Revista Mexicana de Economia y Finanzas is the property of Instituto Mexicano de Ejecutivos de Finanzas and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper proposes an approximate formula to measure the credit risk of portfolios under random recoveries. This formula is based on a Taylor expansion and enables having recoveries that are correlated with the default rates over the business cycle. We show how to calibrate the corresponding models and the accuracy of the approximation using defaulted corporate bonds data for the period 1982–2014. Our results show that the proposed formula can be used to approximate the loss distribution of a portfolio under random correlated recoveries in a very satisfactory way. Moreover, this kind of recovery models could be easily implemented under the Basel capital requirements regulation to improve the credit risk measurement. [ABSTRACT FROM AUTHOR]

In this paper we assume the insurance wealth process is driven by the compound Poisson process. The discounting factor is modelled as a geometric Brownian motion at first and then as an exponential function of an integrated Ornstein-Uhlenbeck process. The objective is to maximize the cumulated value of expected discounted dividends up to the time of ruin. We give an explicit expression of the value function and the optimal strategy in the case of interest rate following a geometric Brownian motion. For the case of the Vasicek model, we explore some properties of the value function. Since we can not find an explicit expression for the value function in the second case, we prove that the value function is the viscosity solution of the corresponding HJB equation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a new methodology that allows forecasting, through Vasicek and CIR models, of future expected interest rates based on rolling windows from observed financial market data. The novelty, apart from the use of those models not for pricing but for forecasting the expected rates at a given maturity, consists in an appropriate partitioning of the data sample. This allows capturing all the statistically significant time changes in volatility of interest rates, thus giving an account of jumps in market dynamics. The new approach is applied to different term structures and is tested for both models. It is shown how the proposed methodology overcomes both the usual challenges (e.g., simulating regime switching, volatility clustering, skewed tails) as well as the new ones added by the current market environment characterized by low to negative interest rates. [ABSTRACT FROM AUTHOR]