The affine Heston model with correlated Gaussian interest rates for pricing hybrid derivatives

In this article we define a multi-factor equity–interest rate hybrid model with non-zero correlation between the stock and interest rate. The equity part is modeled by the Heston model and we use a Gaussian multi-factor short-rate process. By construction, the model fits in the framework of affine diffusion processes, allowing fast calibration to plain vanilla options. We also provide an efficient Monte Carlo simulation scheme.     

On break-even correlation: the way to price structured credit derivatives by replication

We consider the pricing of European-style structured credit pay-off under the Gaussian Copula Model (GCM). When no sudden jump-to-default events occur, the perfect replication of these pay-offs under the GCM is obtained if and only if the underlying single-name credit spreads follow a particular family of dynamics and if the pricing parameters are given by so-called ‘break-even’ correlations. We exhibit a class of Merton-style models that are consistent with this result. We calculate break-even correlations explicitly to price nth-to-default baskets under the GCM. Finally, we illustrate the usefulness of this concept as a relative-value tool.     

1 kW微波源机箱电磁耦合的并行FDTD模拟

微波源机箱的不同面板上开有不同数量和大小的矩形孔缝和散热通风孔,电磁脉冲可以通过机箱上的孔缝耦合进入微波源内部,对内部电路和设备造成干扰。通过自动网格剖分技术实现了1 kW微波源的快速建模,采用并行时域有限差分（FDTD）算法模拟了不同极化方向下高斯脉冲正入射1 kW微波源机箱的耦合问题,分析了微波源机箱的电磁脉冲耦合规律。研究结果表明,数值计算结果与电磁软件仿真结果吻合得比较好,电磁脉冲的极化方向对耦合进入微波源箱体内的电场强度影响不大,微波源机箱中心点的谐振特性明显。     

Fisher information under Gaussian quadrature models

This paper develops formulae to compute the Fisher information matrix for the regression parameters of generalized linear models with Gaussian random effects. The Fisher information matrix relies on the estimation of the response variance under the model assumptions. We propose two approaches to estimate the response variance: the first is based on an analytic formula (or a Taylor expansion for cases where we cannot obtain the closed form), and the second is an empirical approximation using the model estimates via the expectation–maximization process. Further, simulations under several response distributions and a real data application involving a factorial experiment are presented and discussed. In terms of standard errors and coverage probabilities for model parameters, the proposed methods turn out to behave more reliably than does the ‘disparity rule’ or direct extraction of results from the generalized linear model fitted in the last expectation–maximization iteration.     

Modeling electric taxis' charging behavior using real-world data

Charging behavior is critical to the development and deployment of electric vehicle (EV) systems, given its impacts in EV adoption, the energy and environmental performance of EVs, potential load change to the electric grid, etc. However, the general characteristics of practical charging behavior have not been well studied. Existing studies are mostly based on travel data from conventional internal combustion engine vehicles, modeled with assumed and simplified charging scenarios. The use of public charging infrastructure is often neglected. Few studies evaluate real-world charging behaviors of EVs currently in operation using public charging stations. To address this gap, this study analyzes the data of 39,372 charging events from 129 unique electric taxis in Shenzhen, China to study the distributions of daily charging frequency, charging start time, and charging duration. The insights we learned from this study are: 1) the daily frequency for a vehicle to visit charging stations is unlikely to exceed five times; 2) the distribution of charging start time have multiple peaks and can be fitted with Gaussian Mixture Models; 3) charging duration is influenced by charging start time; and 4) charging dynamics can be modeled using the distributions of daily charging frequency, charging start time, and charging duration. Results from this study can inform charging behavior modeling for EVs and charging infrastructure development.     

The normal, the natural, and the harmonic

Use is made of rigorous definitions for the terms normal, natural, and harmonic to reveal a number of unfamiliar aspects about them. The Gaussian distribution is not sufficient to determine who is normal, and fluctuations above or below a natural-growth curve may or may not be natural. A recipe for harmonically sustained natural growth requires that the overlap during the substitution process must be limited. As a consequence the overall growth process must experience good as well as bad “seasons”.     

Estimating a distribution function in the presence of auxiliary information

For estimating the distribution functionF of a population, the empirical or sample distribution functionF _n has been studied extensively. Qin and Lawless (1994) have proposed an alternative estimator for estimatingF in the presence of auxiliary information under a semiparametric model. They have also proved the point-wise asymptotic normality of . In this paper, we establish the weak convergence of to a Gaussian process and show that the asymptotic variance function of is uniformly smaller than that ofF _n . As an application of , we propose to employ the mean and varianceŜ _n ² of to estimate the population mean and variance in the presence of auxiliary information. A simulation study is presented to assess the finite sample performance of the proposed estimators , andŜ _n ² .     

Machine learning for quantitative finance: fast derivative pricing,hedging and fitting

In this paper, we show how we can deploy machine learning techniques in the context of traditional quant problems. We illustrate that for many classical problems, we can arrive at speed-ups of several orders of magnitude by deploying machine learning techniques based on Gaussian process regression. The price we have to pay for this extra speed is some loss of accuracy. However, we show that this reduced accuracy is often well within reasonable limits and hence very acceptable from a practical point of view. The concrete examples concern fitting and estimation. In the fitting context, we fit sophisticated Greek profiles and summarize implied volatility surfaces. In the estimation context, we reduce computation times for the calculation of vanilla option values under advanced models, the pricing of American options and the pricing of exotic options under models beyond the Black–Scholes setting.     

Repeated measures and longitudinal data analysis using higher‐order entropies

This paper implements the generalized maximum entropy (GME) method in longitudinal data setup to investigate the regression para meters and correlation among the repeated measurements. We derive the GME system using Shannon classical entropy as well as some higher‐order entropies assuming an autoregressive correlation structure. This method is illustrated using two simulated examples to study the effect of changing the support range and compare the performance of the GME approach with the classical estimation methods.