Modelling electricity prices: a time change approach

To capture mean reversion and sharp seasonal spikes observed in electricity prices, this paper develops a new stochastic model for electricity spot prices by time changing the Jump Cox-Ingersoll-Ross (JCIR) process with a random clock that is a composite of a Gamma subordinator and a deterministic clock with seasonal activity rate. The time-changed JCIR process is a time-inhomogeneous Markov semimartingale which can be either a jump-diffusion or a pure-jump process, and it has a mean-reverting jump component that leads to mean reversion in the prices in addition to the smooth mean-reversion force. Furthermore, the characteristics of the time-changed JCIR process are seasonal, allowing spikes to occur in a seasonal pattern. The Laplace transform of the time-changed JCIR process can be efficiently computed by Gauss–Laguerre quadrature. This allows us to recover its transition density through efficient Laplace inversion and to calibrate our model using maximum likelihood estimation. To price electricity derivatives, we introduce a class of measure changes that transforms one time-changed JCIR process into another time-changed JCIR process. We derive a closed-form formula for the futures price and obtain the Laplace transform of futures option price in terms of the Laplace transform of the time-changed JCIR process, which can then be efficiently inverted to yield the option price. By fitting our model to two major electricity markets in the US, we show that it is able to capture both the trajectorial and the statistical properties of electricity prices. Comparison with a popular jump-diffusion model is also provided.     

De Moivre's Poisson Approximation to the Binomial

In his first work on probability, written in 1711, Abraham De Moivre looked at the problem of finding the number of trials required in a binomial experiment to achieve a probability of 1/2 of finding at least some given number of successes. He looked at two cases: when the probability of success  p  = 1/2 and when  p  is small but  n , the number of trials, is large. In the latter case, unlike other problems that he solved in probability, De Moivre never revealed his method of solution. We explore the solution that De Moivre originally suggests and find that his method does not work. We explore other numerical solutions and put forward the suggestion that De Moivre relied on a very cumbersome and tedious method of solution based on his earlier work on series in the 1690s. Since his method was neither quick nor mathematically elegant, he never revealed the method that he used to obtain his numerical solutions.     

一种低复杂度的降低MIMO—OFDM峰平比的CARI方法

天线旋转取反算法(CARI)是降低MIMO-OFDM系统峰平功率比(PAPR)的一种性能较优的算法,不足之处是其迭代次数很大。CARI的次最优算法逐次次最优天线旋转取反(SS-CARI)算法虽然可以减小迭代次数,但性能损失又比较大。针对这一问题,提出了一种用滑动窗搜索旋转取反组合的次最优CARI方法,利用滑动窗搜索局部最优的旋转取反组合,既可以避免整体的遍历搜索大大减小CARI算法的计算复杂度,又可以改善SS-CARI的PAPR减小性能。仿真结果表明,该方法能够在系统复杂度与PAPR降低性能上取得很好的折衷。     

COMPLEX LOGARITHMS IN HESTON‐LIKE MODELS

The characteristic functions of many affine jump‐diffusion models, such as Heston's stochastic volatility model and all of its extensions, involve multivalued functions such as the complex logarithm. If we restrict the logarithm to its principal branch, as is done in most software packages, the characteristic function can become discontinuous, leading to completely wrong option prices if options are priced by Fourier inversion. In this paper, we prove without any restrictions that there is a formulation of the characteristic function in which the principal branch is the correct one. Because this formulation is easier to implement and numerically more stable than the so‐called rotation count algorithm of Kahl and Jäckel, we solely focus on its stability in this paper. This paper shows how complex discontinuities can be avoided in the Variance Gamma and Schöbel–Zhu models, as well as in the exact simulation algorithm of the Heston model, recently proposed by Broadie and Kaya.     

基于SVPWM的轻型直流输电控制策略研究

文章针对VSC采用SVPWM的控制方式，分析研究了SVPWM的等效三角载波PWM。以VSC的稳态模型为基础，通过坐标变换推导出VSC功率传输方程的直角坐标形式，并且求得控制量同功率值之间的解析关系式。采用逆系统方法设计了VSC的功率传榆控制系统，以及基于有功、无功独立调节的VSC—HVDC控制系统。仿真结果表明，建立的VSC—HVDC系统能较好地向无源网络供电，实现了VSC传输功率的独立、灵活调节。     

Value-at-Risk computation by Fourier inversion with explicit error bounds

The Value-at-Risk of a delta–gamma approximated derivatives portfolio can be computed by numerical integration of the characteristic function. However, while the choice of parameters in any numerical integration scheme is paramount, in practice it often relies on ad hoc procedures of trial and error. For normal and multivariate t-distributed risk factors, we show how to calculate the necessary parameters for one particular integration scheme as a function of the data (the distribution of risk factors, and delta and gamma) in order to satisfy a given error tolerance. This allows for implementation in a fully automated risk management system. We also demonstrate in simulations that the method is significantly faster than the Monte Carlo method, for a given error tolerance.     

Jason地震反演技术分析

文章分析了Jason反演软件对基础地震资料品质的要求和如何建立符合实际地质情况的地质模型。讨论了层位控制测井外推趋势及反演参数中入值的合理选择问题。该项研究有助于地震反演技术的推广应用。     

Double-sided Parisian option pricing

In this paper we derive Fourier transforms for double-sided Parisian option contracts. The double-sided Parisian option contract is triggered by the stock price process spending some time above an upper level or below some lower level. The double-sided Parisian knock-in call contract is the general type of Parisian contract from which also the single-sided contract types follow. The paper gives an overview of the different types of contracts that can be derived from the double-sided Parisian knock-in calls, and, after discussing the Fourier inversion, it concludes with various numerical examples, explaining the, sometimes peculiar, behavior of the Parisian option. The paper also yields a nice result on standard Brownian motion. The Fourier transform for the double-sided Parisian option is derived from the Laplace transform of the double-sided Parisian stopping time. The probability that a standard Brownian motion makes an excursion of a given length above zero before it makes an excursion of another length below zero follows from this Laplace transform and is not very well known in the literature. In order to arrive at the Laplace transform, a very careful application of the strong Markov property is needed, together with a non-intuitive lemma that gives a bound on the value of Brownian motion in the excursion.      

Ruin time and aggregate claim amount up to ruin time for the perturbed risk process

We consider the classical Sparre-Andersen risk process perturbed by a Wiener process, and study the joint distribution of the ruin time and the aggregate claim amounts until ruin by determining its Laplace transform. This is first done when the claim amounts follow respectively an exponential/Phase-type distribution, in which case we also compute the distribution of recovery time and study the case of a barrier dividend. Then the general distribution is considered when ruin occurs by oscillation, in which case a renewal equation is derived.     

现阶段我国粮食价格倒挂的判断与应对策略

粮食价格倒挂是近年来国内粮食市场呈现的典型价格现象,也是制约现阶段粮食托市收购政策可持续性的重大难题。尽管现阶段粮食价格倒挂的政策性起因与“统购统销”和“双轨制”时期的粮食价格倒挂相似,但已从绝对倒挂转变为相对倒挂,应对环境也已发生根本性变化。面对现阶段粮食价格倒挂问题,既不能走计划经济的下游管控老路,又不可能在短期内实现目标价格政策的推广,加上近年来国际粮价低迷以及WTO规则的约束,近期的粮食价格倒挂可能会成为一种常态。粮食价格倒挂问题的解决,需要积极推进全产业链的市场化改革,做到市场化目标下的短期适应（粮食加工业转型升级）与长期改革（粮食流通体制改革）相结合。