Search Results (26)

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

Counterparty risk, which combines market and credit risks, gained prominence after the 2008 financial crisis due to its complexity and systemic implications. Traditional management methods, such as netting and collateralization, have become computationally demanding under frameworks like the Fundamental Review of the Trading Book (FRTB). This paper explores the combined application of Gaussian process regression (GPR) and Bayesian quadrature (BQ) to enhance the efficiency and accuracy of counterparty risk metrics, particularly credit valuation adjustment (CVA). This approach balances excellent precision with significant computational performance gains. Focusing on fixed-income derivatives portfolios, such as interest rate swaps and swaptions, within the One-Factor Linear Gaussian Markov (LGM-1F) model framework, we highlight three key contributions. First, we approximate swaption prices using Bachelier’s formula, showing that forward-starting swap rates can be modeled as Gaussian dynamics, enabling efficient CVA computations. Second, we demonstrate the practical relevance of an analytical approximation for the CVA of an interest rate swap portfolio. Finally, the combined use of Gaussian processes and Bayesian quadrature underscores a powerful synergy between precision and computational efficiency, making it a valuable tool for credit risk management. Full article

The Kennedy model offers a robust framework for modeling forward rates, leveraging Gaussian random fields to accommodate emerging phenomena such as negative rates. In our study, we employ maximum likelihood estimations to determine the parameters of the Kennedy field, utilizing Radon–Nikodym derivatives for enhanced accuracy. We introduce an efficient simulation method for the Kennedy field and develop a Black–Scholes-like analytical pricing formula for diverse financial assets. Additionally, we present a novel parameter estimation algorithm grounded in numerical extreme value optimization, enabling the recalibration of parameters based on observed financial product prices. To validate the efficacy of our approach, we assess its performance using real-world par swap rates in the latter part of this article. Full article

This article estimates the weighted average cost of capital (WACC) for the energy sector in Ecuador, a country with a dollarized economy and illiquid stock markets. Thus, reference companies in the region were taken, and at the same time combined with characteristics of national companies, establishing a useful methodology, which makes sense with the acceptable discount rates in the Ecuadorian economy. For the above, four estimation alternatives were used. In method one, the traditional WACC formula was applied using interest rates and risk premiums from the U.S. market, which resulted in an overestimation due to the double penalty of the country risk and the U.S. market premium. Method two adjusted the market risk premium to consider only the Ecuador-specific risk premium, thus avoiding the double penalty. In method three, the credit default swap (CDS) was used to calculate the country risk premium, and the CDS was excluded from the nominal interest rate, avoiding redundancies. Finally, method four combined the U.S. interest rate with the CDS directly to calculate the market risk premium, more accurately reflecting local economic conditions in a dollarized economy. The WACC results range from 12.63% to 29.70%. In addition, a dummy variable was controlled for during the pandemic period. This article highlights the need for methodologies adapted to emerging markets, since traditional approaches would overestimate the WACC. Full article

The extensive use of polypropylene (PP) in various industries has heightened interest in developing efficient methods for recycling and optimising its mixtures. This study focuses on formulating predictive models for the Melt Flow Rate (MFR) and shear viscosity of PP blends. The investigation involved characterising various grades, including virgin homopolymers, copolymers, and post-consumer recyclates, in accordance with ISO 1133 standards. The research examined both binary and ternary blends, utilising traditional mixing rules and symbolic regression to predict rheological properties. High accuracy was achieved with the Arrhenius and Cragoe models, attaining R² values over 0.99. Symbolic regression further enhanced these models, offering significant improvements. To mitigate overfitting, empirical noise and variable swapping were introduced, increasing the models’ robustness and generalisability. The results demonstrated that the developed models could reliably predict MFR and shear viscosity, providing a valuable tool for improving the quality and consistency of PP mixtures. These advancements support the development of recycling technologies and sustainable practices in the polymer industry by optimising processing and enhancing the use of recycled materials. Full article

Developing countries, including Small Island Developing States (SIDSs) and Least Developed Countries (LDCs), are exceptionally vulnerable to climate change due to their distinct geographical and environmental characteristics. Escalating sea levels and heightened salinity levels imperil freshwater reserves, while warmer ocean temperatures and acidification disrupt water demand, tourism, health services, and fisheries. Concurrently, these countries bear the brunt of water shortages, flooding, and declining water quality. However, significant barriers such as limited financing capacities to fund water security initiatives, exacerbated by a growing debt crisis marked by escalating interest rates and inflation, hinder developmental progress and investments in climate adaptation and mitigation endeavors. Consequently, there arises a critical necessity to harness innovative financial mechanisms to transform these debts into opportunities that support effective climate action. This paper explores the potential of debt-for-climate swaps as a catalyst for advancing transformative wastewater projects, focusing on their strategic deployment to underpin critical initiatives. Through case studies and empirical evidence, the paper elucidates how debt-for-climate swaps can enhance sustainable wastewater management systems in developing countries and delineates best practices for leveraging these mechanisms and the roles and responsibilities of key stakeholders, including governments, policymakers, the private sector, communities, and climate financial institutions. Combining theoretical insights with tangible examples, this paper furnishes a comprehensive framework for harnessing debt-for-climate swaps to enhance water security and resilience in developing countries. It offers actionable strategies for policymakers, practitioners, and stakeholders to navigate the complex terrain of climate change and engender sustainable development. Full article

In this study, the impact of arbitrage resulting from Covered Interest Parity (CIP) deviations on Korea’s long-term interest rates was analyzed, utilizing Vector Error Correction (VEC) models for Granger Causality and Impulse Response Function analyses. This analysis covered the period from February 2002 to September 2023, with a comparative analysis of the periods before and after the Global Financial Crisis (GFC). The Granger Causality analysis indicated that changes in the swap basis reflecting CIP deviation presented a significant Granger causal relationship with the variations in domestic long-term interest rates. Notably, in the post-GFC period, when CIP deviations were relatively pronounced, the incentives for arbitrage trading exhibited a stronger leading effect in terms of inducing changes in domestic long-term interest rates. The Impulse Response Function analysis showed that domestic long-term interest rates significantly and negatively responded to the positive shocks in the swap basis. This response was even more pronounced during the period following the GFC. Additionally, foreign long-term interest rates and monetary policy variables also demonstrated a significant impact on domestic long-term interest rates. These findings imply that the adjustment path back to equilibrium from CIP deviations, driven by arbitrage, was developed more through changes in domestic interest rates rather than exchange rate fluctuations, especially after the GFC. Full article

We propose and investigate a queueing model of a battery swapping and charging station (BSCS) for electric vehicles (EVs). A new approach to the analysis of the queueing model is developed, which combines the representation of the model as a stochastic dynamic system with the use of the methods and results of tropical algebra, which deals with the theory and applications of algebraic systems with idempotent operations. We describe the dynamics of the queueing model by a system of recurrence equations that involve random variables (RVs) to represent the interarrival time of incoming EVs. A performance measure for the model is defined as the mean operation cycle time of the station. Furthermore, the system of equations is represented in terms of the tropical algebra in vector form as an implicit linear state dynamic equation. The performance measure takes on the meaning of the mean growth rate of the state vector (the Lyapunov exponent) of the dynamic system. By applying a solution technique of vector equations in tropical algebra, the implicit equation is transformed into an explicit one with a state transition matrix with random entries. The evaluation of the Lyapunov exponent reduces to finding the limit of the expected value of norms of tropical matrix products. This limit is then obtained using results from the tropical spectral theory of deterministic and random matrices. With this approach, we derive a new exact formula for the mean cycle time of the BSCS, which is given in terms of the expected value of the RVs involved. We present the results of the Monte Carlo simulation of the BSCS’s operation, which show a good agreement with the exact solution. The application of the obtained solution to evaluate the performance of one BSCS and to find the optimal distribution of battery packs between stations in a network of BSCSs is discussed. The solution may be of interest in the case when the details of the underlying probability distributions are difficult to determine and, thus, serves to complement and supplement other modeling techniques with the need to fix a distribution. Full article

Carbon risk, a type of climate risk, is expected to have a crucial impact, especially on high-carbon-emitting, “polluting” firms as opposed to less carbon-intensive, “clean” ones. With a rising number of actions and policies being continuously proposed to mitigate these concerns and an increasing number of investors demanding more climate adaptation initiatives, this transition risk will certainly need to be incorporated into a firm’s credit risk assessment. In this paper, we explore the impact of the carbon risk factor, constructed as the daily median difference in default protection between polluting and clean European firms, on firm creditworthiness using quantile regressions on the tail distribution of credit default swap spreads for different maturities between 2020 and 2023. In particular, the recent European interest rate hikes lead to unexpected conclusions about when the carbon risk factor affects firm creditworthiness and how rapidly the net-zero economy transition must occur. Contrary to the previous literature, we find that investors are expecting the transition to occur in the medium-to-long term. Full article

This paper deals with a credit derivative pricing problem using the martingale approach. We generalize the conventional reduced-form credit risk model for a credit default swap market, assuming that the firms’ default intensities depend on the default states of counterparty firms and that the stochastic interest rate follows a jump-diffusion Cox–Ingersoll–Ross process. First, we derive the joint Laplace transform of the distribution of the vector process $(r_t,R_t)$ by applying piecewise deterministic Markov process theory and martingale theory. Then, using the joint Laplace transform, we obtain the explicit pricing of defaultable bonds and a credit default swap. Lastly, numerical examples are presented to illustrate the dynamic relationships between defaultable securities (defaultable bonds, credit default swap) and the maturity date. Full article

Hydropower as a renewable source can help many countries achieve their sustainable energy and climate goals, but large projects are challenging to finance because of their costs and risks. To fully realize the climate benefits of such projects, sponsors have recently fashioned complex financing arrangements that structure and allocate risks to reduce financing costs. This paper focuses on the blended financing approach adopted for the Nachtigal Hydropower Plant (NHP) in Cameroon. The purpose of the paper is to present a detailed systems analysis of Nachtigal’s financial arrangement to address the question of why the complex financing approach worked in practice. We accomplish this by creating a “financial simulator”—a computational model for evaluating risks and incentives embedded within the financing structure under different contract architectures and risk–event scenarios. Our simulator is a dynamic value–risk calculator that can be easily updated to study other climate-oriented projects that involve complex financial arrangements. We evaluated three aspects of the financing/contractual arrangements that made Nachtigal “bankable:” (i) guarantees that covered nonpayments, (ii) financial options on locally sourced loans; and (iii) an interest rate swap. We found: (i) the guarantees recovered project value threatened by four specific risks often associated with large hydropower investments (cost overruns, schedule delays, offtake risk, and low flow due to climate change); (ii) the mechanism significantly lowered interest rate charges; and (iii) private finance was mobilized—especially due to the options. The financial safeguards employed increased the likelihood of capturing the long-run sustainability benefits from NHP. Full article

Fundamentally, the term premium in long-term nominal yields is compensation to investors for bearing interest rate risk. There is substantial evidence of sizable and time-varying term premia. As opposed to yields, term premia are not directly observable. In this paper, we estimate term premia in Norwegian interest rate swaps from a set of dynamic term structure models, covering the period from 2001/04 until 2022/06. In line with international studies, we find evidence of declining term premia over the sample period. Furthermore, our estimates indicate that term premia have been close to zero, as well as negative in periods, during the last decade of global extraordinary monetary policy measures. We find that the recent rise in Norwegian interest rate swaps is partly caused by increases in term premia. From a practitioner’s perspective, our term premia estimates can be utilized as part of applied management of both investment and debt portfolios. Full article

The privacy of individuals and entire countries is currently threatened by the widespread use of face-swapping DeepFake models, which result in a sizable number of fake videos that seem extraordinarily genuine. Because DeepFake production tools have advanced so much and since so many researchers and businesses are interested in testing their limits, fake media is spreading like wildfire over the internet. Therefore, this study proposes five-layered convolutional neural networks (CNNs) for a DeepFake detection and classification model. The CNN enhanced with ReLU is used to extract features from these faces once the model has extracted the face region from video frames. To guarantee model accuracy while maintaining a suitable weight, a CNN enabled with ReLU model was used for the DeepFake-detection-influenced video. The performance evaluation of the proposed model was tested using Face2Face, and first-order motion DeepFake datasets. Experimental results revealed that the proposed model has an average prediction rate of 98% for DeepFake videos and 95% for Face2Face videos under actual network diffusion circumstances. When compared with systems such as Meso4, MesoInception4, Xception, EfficientNet-B0, and VGG16 which utilizes the convolutional neural network, the suggested model produced the best results with an accuracy rate of 86%. Full article

In Basel III, the credit valuation adjustment (CVA) was given, and it was discussed that a bank covers mark-to-market losses for expected counterparty risk with a CVA capital charge. The purpose of this study is threefold. Using the logistic distribution, it is shown how the expected exposure can be derived for an interest rate swap. Secondly, the risk measure of VaR is contributed for the CVA under this distribution. Thirdly, generalizations for the CVA VaR and CVA CVaR are given by considering both the credit spread and the expected positive exposure to follow the logistic distributions with different parameters. Finally, several simulations are provided to uphold the theoretical discussions. Full article

In this paper, we propose a new exogenous model to address the problem of negative interest rates that preserves the analytical tractability of the original Cox–Ingersoll–Ross (CIR) model with a perfect fit to the observed term-structure. We use the difference between two independent CIR processes and apply the deterministic-shift extension technique. To allow for a fast calibration to the market swaption surface, we apply the Gram–Charlier expansion to calculate the swaption prices in our model. We run several numerical tests to demonstrate the strengths of this model by using Monte-Carlo techniques. In particular, the model produces close Bermudan swaption prices compared to Bloomberg’s Hull–White one-factor model. Moreover, it finds constant maturity swap (CMS) rates very close to Bloomberg’s CMS rates. Full article