Search Results (147)

This paper develops an explicit positivity-preserving method for the nonlinear Aït-Sahalia interest rate model driven by fractional Brownian motion. To overcome the difficulties in obtaining the convergence rate of this positivity-preserving method, the Lamperti transformation is utilized, which gives an auxiliary equation. And the convergence rate of the numerical method for this auxiliary equation is obtained by virtue of Malliavin calculus. Naturally, the target follows from the inverse of the Lamperti transformation. As a byproduct, the convergence rate of the explicit positivity-preserving method for stochastic differential equations driven by fractional Brownian motion with symmetric coefficients is obtained. Finally, several numerical experiments are performed to verify the theoretical results and demonstrate the advantage of the explicit method. Full article

Investors face the challenge of how to incorporate economic and financial forecasts into their investment strategy, especially in times of financial crisis. To model this situation, we consider a financial market consisting of a risk-free asset with a constant interest rate as well as a risky asset whose drift and volatility is influenced by a stochastic process indicating the probability of potential market downturns. We use a dynamic portfolio optimization approach in continuous time to maximize the expected utility of terminal wealth and solve the corresponding HJB equations for the general class of HARA utility functions. The resulting optimal strategy can be obtained in closed form. It corresponds to a CPPI strategy with a stochastic multiplier that depends on the information from the crisis indicator. In addition to the theoretical results, a performance analysis of the derived strategy is implemented. The specified model is fitted using historic market data and the performance is compared to the optimal portfolio strategy obtained in a Black–Scholes framework without crisis information. The new strategy clearly dominates the BS-based CPPI strategy with respect to the Sharpe Ratio and Adjusted Sharpe Ratio. Full article

This paper develops an analytical pricing formula for vulnerable options with stochastic volatility under a two-factor stochastic interest rate model. We consider the underlying asset price following the Heston stochastic volatility model, while the interest rate is modeled as the sum of two processes. Using the joint characteristic function approach and measure change techniques, we derive an explicit pricing formula for a vulnerable European option. We also conduct numerical experiments to examine the effects of various model parameters on option values. This study provides a more realistic framework for pricing OTC derivatives by incorporating credit risk, stochastic volatility, and stochastic interest rates simultaneously. Full article

This study employs a dynamic stochastic general equilibrium model with Bayesian estimation to rigorously evaluate China’s macroeconomic responses to cost-push, monetary policy, and foreign income shocks. This analysis leverages quarterly data from 2000 to 2024, focusing on critical variables such as the output gap, inflation, interest rates, exchange rates, consumption, investment, and employment. The results demonstrate significant social welfare losses primarily arising from persistent inflation and output volatility due to domestic structural rigidities and global market dependencies. Monetary policy interventions effectively moderate short-term volatility but induce welfare costs if overly restrictive. The findings underscore the necessity of targeted structural reforms to enhance economic flexibility, balanced monetary policy to mitigate aggressive interventions, and diversified economic strategies to reduce external vulnerability. These insights contribute novel policy perspectives for enhancing China’s macroeconomic stability and resilience. Full article

The squared Bessel process plays a central role in stochastic analysis, with broad applications in mathematical finance, physics, and probability theory. While explicit expressions for its transition probability density function (TPDF) under constant parameters are well known, analytical results in the case of time-dependent dimensions remain scarce. In this paper, we address a significantly challenging problem by deriving an analytical formula for the TPDF of a conic combination of independent squared Bessel processes with time-dependent dimensions. The result is expressed in terms of a Laguerre series expansion. Furthermore, we obtain closed-form expressions for the conditional moments of such conic combinations, represented via generalized hypergeometric functions. These results also yield new analytical formulas for the TPDF and conditional moments of both squared Bessel processes and Bessel processes with time-dependent dimensions. The proposed formulas provide a unified analytical framework for modeling and computation involving a broad class of time-inhomogeneous diffusion processes. The accuracy and computational efficiency of our formulas are verified through Monte Carlo simulations. As a practical application, we provide an analytical valuation of an interest rate swap, where the underlying short rate follows a conic combination of independent squared Bessel processes with time-dependent dimensions, thereby illustrating the theoretical and practical significance of our results in mathematical finance. Full article

This study investigates the valuation of Euro-convertible bonds (ECBs) using a novel Markov-modulated cojump-diffusion (MMCJD) model, which effectively captures the dynamics of stochastic volatility and simultaneous jumps (cojumps) in both the underlying stock prices and foreign exchange (FX) rates. Furthermore, we introduce a Markov-modulated Cox–Ingersoll–Ross (MMCIR) framework to accurately model domestic and foreign instantaneous interest rates within a regime-switching environment. To manage computational complexity, the least-squares Monte Carlo (LSMC) approach is employed for estimating ECB values. Numerical analyses demonstrate that explicitly incorporating stochastic volatilities and cojumps significantly enhances the realism of ECB pricing, underscoring the novelty and contribution of our integrated modeling approach. Full article

This study investigated the influence of stochastic fluctuations on financial system stability by analyzing both ordinary and fractional-order financial models under noise. The ordinary financial system experiences perturbations due to bounded random disturbances, whereas the fractional-order counterpart models memory-dependent behaviors by incorporating fractional Gaussian noise (FGN) characterized by a Hurst parameter that governs long-term correlations. This study used data generated through MATLAB simulations based on standard financial models from the literature. Numerical simulations compared system behavior in deterministic and noisy environments. The results reveal that ordinary systems experience transient fluctuations, quickly returning to a stable state, whereas fractional systems exhibit persistent deviations due to historical dependencies. This highlights the fundamental difference between integer-order and fractional-order derivatives in financial modeling. Our key findings indicate that noise significantly impacts interest rates, investment needs, price indices, and profit margins, with the fractional system displaying higher sensitivity to external shocks. These insights emphasize the necessity of incorporating memory effects in financial modeling to improve accuracy in predicting market behavior. The study further underscores the importance of adaptive monetary policies and risk management strategies to mitigate financial instability. Future research should explore hybrid models combining short-term stability with long-term memory effects for enhanced financial forecasting and stability analysis. Full article

The growing interest in machine learning in a critical domain like healthcare emphasizes the need for reliable predictions, as decisions based on these outputs can have significant consequences. This study benchmarks methods for assessing pointwise reliability, focusing on data-driven techniques based on the density principle and the local fit principle. These methods evaluate the reliability of individual predictions by analyzing their similarity to training data and evaluating the performance of the model in local regions. Aiming to establish a standardized comparison, the study introduces a benchmark framework that combines error rate evaluations across reliability intervals with t-distributed Stochastic Neighbor Embedding visualizations to further validate the results. The results demonstrate that methods combining density and local fit principles generally outperform those relying on a single principle, achieving lower error rates for high-reliability predictions. Furthermore, the study identifies challenges such as the adjustment of method parameters and clustering limitations and provides insight into their impact on reliability assessments. Full article

This paper explores the hypothesis that the returns of asset classes can be predicted using common, systematic risk factors represented by the level, slope, and curvature of the US interest rate term structure. These are extracted using the Nelson–Siegel model, which effectively captures the three dimensions of the yield curve. To forecast the factors, we applied autoregressive (AR) and vector autoregressive (VAR) models. Using their forecasts, we predict the returns of government and corporate bonds, equities, REITs, and commodity futures. Our predictions were compared against two benchmarks: the historical mean, and an AR(1) model based on past returns. We employed the Diebold–Mariano test and the Model Confidence Set procedure to assess the comparative forecast accuracy. We found that Nelson–Siegel factors had significant predictive power for one-month-ahead returns of bonds, equities, and REITs, but not for commodity futures. However, for 6-month and 12-month-ahead forecasts, neither the AR(1) nor VAR(1) models based on Nelson–Siegel factors outperformed the benchmarks. These results suggest that the Nelson–Siegel factors affect the aggregate stochastic discount factor for pricing all assets traded in the US economy. Full article

In this study, we aimed to assess the effectiveness of monetary policy in influencing housing prices in Morocco. Bayesian estimation over the period 2007Q2–2017Q2 of a dynamic stochastic general equilibrium model allowed us to reveal a significant impact of the increase in policy interest rates on the prices of residential goods. Indeed, the implementation of a restrictive monetary policy in Morocco will drive the prices of this type of asset downward. Despite this empirical finding, the historical decomposition of shocks impacting the inflation of residential property prices shows that interest rates explain only a small portion of the variations in housing prices in this country. Our results also indicate that an increase in the share of borrowers extends the time required for economic and financial variables to return to their equilibrium state. This is a sign of the potential dangers of fueling housing bubbles through credit booms. Full article

This paper aims to develop optional semimartingale methods in risk theory to allow for a larger class of risk models. Optional semimartingales are left-continuous with right-limit stochastic processes defined on a probability space where the usual conditions—completeness and right-continuity of the filtration—are not assumed. Three risk models are formulated, accounting for inflation, interest rates, and claim occurrences. The first model extends the martingale approach to calculate ruin probabilities, the second employs the Gerber–Shiu function to evaluate the expected discounted penalty from financial oscillations or jumps, and the third introduces a Gaussian risk model using counting processes to capture premium and claim cash flow jumps in insurance companies. Full article

The Heston-Hull-White (HHW) model is a generalization of the classical Heston approach that incorporates stochastic interest rates, making it a more accurate representation of financial markets. In this work, we investigate a computational procedure via a three-dimensional partial differential equation (PDE) to solve option pricing problems under the HHW framework. We propose a local radial basis function–finite difference (RBF–FD) framework under the integration of a new variant of the multiquadric function for efficiently resolving the model. Our study highlights the error analysis of the proposed weights for the first and second derivatives of a suitable function and demonstrates the effectiveness of the RBF–FD approach for this high-dimensional financial model. Full article

The Dupire formula is a very useful tool for pricing financial derivatives. This paper is dedicated to deriving the aforementioned formula for the European call option in the space of distributions by applying a mathematically rigorous approach developed in our previous paper concerning the case of the Margrabe option. We assume that the underlying asset is described by the Merton jump-diffusion model. Using this stochastic process allows us to take into account jumps in the price of the considered asset. Moreover, we assume that the instantaneous interest rate follows the Merton model (1973). Therefore, in contrast to the models combining a constant interest rate and a continuous underlying asset price process, frequently observed in the literature, applying both stochastic processes could accurately reflect financial market behaviour. Moreover, we illustrate the possibility of using the minimal entropy martingale measure as the risk-neutral measure in our approach. Full article

The multivariate Vasicek model is commonly used to capture mean-reverting dynamics typical for short rates, asset price stochastic log-volatilities, etc. Reparametrizing the discretized problem as a VAR(1) model, the parameters are oftentimes estimated using the multivariate least squares (MLS) method, which can be susceptible to outliers. To account for potential model violations, a maximum trimmed likelihood estimation (MTLE) approach is utilized to derive a system of nonlinear estimating equations, and an iterative procedure is developed to solve the latter. In addition to robustness, our new technique allows for reliable recovery of the long-term mean, unlike existing methodologies. A set of simulation studies across multiple dimensions, sample sizes and robustness configurations are performed. MTLE outcomes are compared to those of multivariate least trimmed squares (MLTS), MLE and MLS. Empirical results suggest that MTLE not only maintains good relative efficiency for uncontaminated data but significantly improves overall estimation quality in the presence of data irregularities. Additionally, real data examples containing daily log-volatilities of six common assets (commodities and currencies) and US/Euro short rates are also analyzed. The results indicate that MTLE provides an attractive instrument for interest rate forecasting, stochastic volatility modeling, risk management and other applications requiring statistical robustness in complex economic and financial environments. Full article

Fibers are widely used in concrete structures to control crack propagation and widening due to sustained or impact loads. Nevertheless, the concrete’s mechanical and structural properties are strongly affected by the fibers’ spatial distribution and clumping tendency within the mass material. The main objective of this paper is to assess the efficiency of stochastic finite element modeling to predict the shear strength properties of fiber-reinforced concrete (FRC) beams without stirrups, as tested by four-point loading. Polypropylene and polyvinyl alcohol micro-filament fibers are investigated in this experimental program at relatively high rates, varying from 0.5% to 1% by volume. A stochastic sensitivity analysis is performed using both random fields and random variables to determine the effect of fiber additions on the concrete’s mechanical properties (i.e., splitting tensile strength and modulus of elasticity) including the beam cracking patterns, ductility, mid-span deflection, and ultimate load. Such data could be of interest to civil engineers and structural designers to reduce the effort and resources needed to assess the FRC strength variability and failure behaviors of structural members. Full article