A new closed-form solution as an extension of the Black–Scholes formula allowing smile curve plotting

In this paper, as a generalization of the Black–Scholes (BS) model, we elaborate a new closed-form solution for a uni-dimensional European option pricing model called the J-model. This closed-form solution is based on a new stochastic process, called the J-process, which is an extension of the Wiener process satisfying the martingale property. The J-process is based on a new statistical law called the J-law, which is an extension of the normal law. The J-law relies on four parameters in its general form. It has interesting asymmetry and tail properties, allowing it to fit the reality of financial markets with good accuracy, which is not the case for the normal law. Despite the use of one state variable, we find results similar to those of Heston dealing with the bi-dimensional stochastic volatility problem for pricing European calls. Inverting the BS formula, we plot the smile curve related to this closed-form solution. The J-model can also serve to determine the implied volatility by inverting the J-formula and can be used to price other kinds of options such as American options.     

Post‐Retirement Financial Strategies: Forecasts and Valuation

This paper uses a discrete‐time, discrete‐state Monte Carlo simulation model to evaluate representative strategies for investing and spending a fixed sum designed to fund consumption during the period after retirement. Two assets are considered – one providing a riskless real return, the other a market portfolio of bonds and stocks. A stochastic process for the returns from the market portfolio is proposed. Then a set of Arrow‐Debreu state prices is obtained on the assumption that the market portfolio is an efficient investment strategy. The model is used to forecast ranges of consumption and ranges of the ratios of year‐to‐year consumption, and also to estimate the values of components of future consumption.     

Pricing of vanilla and first-generation exotic options in the local stochastic volatility framework: survey and new results

Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices and so on. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes. Many issues remain, though, including the efficacy of the standard alternating direction implicit (ADI) numerical methods for solving SV and LSV pricing problems. In general, the amount of required computations for these methods is very substantial. In this paper, we address some of these issues and propose a viable alternative to the standard ADI methods based on Galerkin-Ritz ideas. We also discuss various approaches to solving the corresponding pricing problems in a semi-analytical fashion. We use the fact that in the zero correlation case some of the pricing problems can be solved analytically, and develop a closed-form series expansion in powers of correlation. We perform a thorough benchmarking of various numerical solutions by using analytical and semi-analytical solutions derived in the paper.     

灰铸铁端盖消失模铸造工艺设计及数值模拟

为了解决端盖消失模铸造过程中易产生气孔、夹渣、缩松、缩孔等问题、提高铸件合格率及工艺出品率,依据端盖铸件的工艺特点,设计了顶注、中注、底注3种浇注工艺方案。利用计算机模拟软件研究了浇注温度、负压度对消失模铸造端盖充型、凝固过程及铸件孔隙体积的影响;采用正交试验的方法研究了实施底注浇注工艺方案时浇注温度、负压度对端盖铸件孔隙体积的影响;按照优选出的浇注温度、负压度工艺参数进行生产验证。结果表明：顶注、中注浇注方案在铸件的顶部均出现了明显的缩孔,底注浇注工艺方案较好;优选出的浇注温度为1 420 ℃、负压度为0.06 MPa,采用此工艺参数时端盖铸件孔隙的缺陷体积最小,为3.005 cm³,工艺出品率为77.7%,铸件的组织和性能均满足要求。研究结果可为端盖类铸铁件消失模铸造工艺的设计提供参考依据,具有实际应用价值。     

Option pricing with the control variate technique beyond Monte Carlo simulation

Although mostly used alongside Monte Carlo simulation, the control-variate (CV) technique can be applied to other numerical algorithms in option pricing. This paper studies the conditions under which a numerical method (simulation-based or not) can benefit from the CV technique and what approximators can serve as CVs. We demonstrate the ideas with Carr and Madan’s Fourier transform-based algorithm, convolution-based pricing algorithms, and classic binomial trees. Numerical results are provided to show that the CV-enhanced versions are more efficient than the original algorithms.     

加氢处理过程模型的研究

为了改善重油品质以及优化炼厂加氢装置操作,本文开发了用于预测特定条件下加氢产品品质的加氢处理过程模型。在建立模型过程中,对一些相关重要问题进行了阐述,并对与上述问题有关的研究成果进行了综述。加氢过程模拟是设计新装置以及现有装置改扩建的必要环节。在超低硫含量操作装置中如何预测不同进料以及操作条件下的加氢操作性能,是炼油厂要面临的重要挑战之一。     

物资配装——运送模拟模型

本文针对克拉克（Ｃｌａｒｋ）物资配送节约法的局限性，设计了多目标物资配装──运送模拟系统。配装运送是物资配送的重要环节。本系统在配装运送过程模型化的基础上，模拟期望载荷水平下最适配车结构和最佳行车路线。通过多目标控制的“二次寻优”策略实现配送系统合理化的总目标。因而较之“节约法”更有效地提高了配送计划的决策水平。     

Smoothing the payoff for efficient computation of Basket option prices

We consider the problem of pricing basket options in a multivariate Black–Scholes or Variance-Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high-dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse-grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster than Monte Carlo or Quasi Monte Carlo methods in dimensions up to 35.     

基于混沌加密的小波域音频盲水印算法

本文将混沌理论引入到了音频水印系统的研究中,设计了一种将一段简短的音频用混沌序列进行加密后,作为载体嵌入到原始音频信号的小波域中。先将作为水印的音频信号利用混沌映射进行置乱,然后再利用混沌序列实现对隐藏位置的保密。这种方法既保证了水印的安全性又实现了水印的盲提取。实验表明,此方法具有很高的安全性和鲁棒性。     

能源使用的技术无效性及其收敛性分析

在影响能源使用技术无效的因素分析中,研究表明,引进国外技术与购买国内技术对能源使用的技术效率存在显著的正向效用,而且购买国内技术表现出更高的能源使用效率的提升作用。在进一步对能源使用技术无效性收敛情况的分析中,研究表明全国各省市区更倾向于沿特定轨迹持续发展而不是稳定于一特定态。而对三大地区的分析表明东部地区存在俱乐部收敛(绝对β收敛)的情况,即东部地区各省市收敛于同一稳定态,但对于中西部的省市区则表现出与全国研究类似的结论,说明各地能源消耗的技术无效性将在一定时间内持续降低。