Pricing Stochastic Barrier Options under Hull-White Interest Rate Model

A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.

Deterministic and Stochastic Analysis of a New Rumor Propagation Model with Nonlinear Propagation Rate in Social Network

This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.

Neural Modeling of Multivariable Nonlinear Stochastic System. Variable Learning Rate Case

The objective of this paper is to develop a variable learning rate for neural modeling of multivariable nonlinear stochastic system. The corresponding parameter is obtained by gradient descent method optimization. The effectiveness of the suggested algorithm applied to the identification of behavior of two nonlinear stochastic systems is demonstrated by simulation experiments.

Stochastic Modeling and Assisted History-Matching Using Multiple Techniques of Multi-Phase Flowback from Multi-Fractured Horizontal Tight Oil Wells

In this paper, the methods developed by?[1] are used to analyze flowback data, which involves modeling flow both before and after the breakthrough of formation fluids. Despite the versatility of these techniques, achieving an optimal combination of parameters is often difficult with a single deterministic analysis. Because of the uncertainty in key model parameters, this problem is an ideal candidate for uncertainty quantification and advanced assisted history-matching techniques, including Monte Carlo (MC) simulation and genetic algorithms (GAs) amongst others. MC simulation, for example, can be used for both the purpose of assisted history-matching and uncertainty quantification of key fracture parameters. In this work, several techniques are tested including both single-objective (SO) and multi-objective (MO) algorithms for history-matching and uncertainty quantification, using a light tight oil (LTO) field case. The results of this analysis suggest that many different algorithms can be used to achieve similar optimization results, making these viable methods for developing an optimal set of key uncertain fracture parameters. An indication of uncertainty can also be achieved, which assists in understanding the range of parameters which can be used to successfully match the flowback data.

随机波动率Hull-White模型参数估计方法

构建随机波动率的两因子模型,应用两阶段半参数方法估计模型中的常系数参数,使用核估计方法估计长期均值函数,给出了两阶段估计方法的相容性和参数的渐近性性质.实证结果表明了对比常系数模型,引入长期均值函数模型将会改善似然函数估计值,而且也能够很好地解释中央银行和政府已实施政策的有效性.此外,可以在不增加维数的条件下,使用该模型对利率衍生品进行更有效地定价.

A unified stochastic damage model for concrete based on multi-scale energy dissipation analysis

This work proposes a unified damage model for concrete within the framework of stochastic damage mechanics. Based on the micro-meso stochastic fracture model(MMSF), the nonlinear energy dissipation process of the microspring from nanoscale to microscale is investigated. In nanoscale, the rate process theory is adopted to describe the crack growth rate;therefore, the corresponding energy dissipation caused by a representative crack propagation can be obtained. The scale gap from nanoscale to microscale is bridged by a crack hierarchy model. Thus, the total energy dissipated by all cracks from the nanoscale to the microscale is gained. It is found that the fracture strain of the microspring can be derived from the above multi-scale energy dissipation analysis. When energy dissipation is regarded as some microdamage to the microspring, the constitutive law of the microspring is no longer linearly elastic, as previously assumed. By changing the expression of the damage evolution law from fracture strain to energy dissipation threshold, the new damage evolution model is derived. The proposed model can not only replicate the original static model but also extend to cases of rate dependence. By deriving the fracture strain under different strain rates, the rate sensitivity of concrete materials can be reflected. The model parameters can be conveniently obtained by identifying them with experimental data. Finally, several numerical examples are presented to verify the proposed model.

GENERALIZED STOCHASTIC DURATION INMARKOVIAN HEATH-JARROW-MORTONFRAMEWORK

This paper focuses on how to measure the interest rate risk. The conventional measure methods of interest rate risk are reviewed and the duration concept is generalized to stochastic duration in the Markovian HJM framework. The generalized stochastic duration of the coupon bond is defined as the time to maturity of a zero coupon bond having the same instantaneous variance as the coupon bond. According to this definition., the authors first present the framework of Markovian HJM model, then deduce the measures of stochastic duration in some special cases which cover some extant interest term structure.

On the Contribution of the Stochastic Integrals to Econometrics

The purpose of this paper is to present the theorical connection between the Itôstochastic calculus and the Financial Econometrics. This paper has two contributions. First, we give the backgrounds on how the stochastic calculus is used to model the real data with the uncertainties. Finally, by using Consumer Price Index (CPI) from the Central Bank of Congo and combining the Itôstochastic calculus and the AR (1)-GARCH (1, 1) model, we estimate the stochastic volatility of inflation rate measuring efficency of monetary policy. Thus the stochastic integrals are the powerful tools of mathematical modelling and econometric analysis.

受媒体信息影响的一类随机传染病模型的研究

考虑到媒体信息对疾病预防和控制具有重要作用,建立了一类受媒体信息影响和具有非线性传染率的随机SEIS传染病模型,并运用随机微分方程的相关理论研究了该模型的绝灭性、持久性和平稳分布.数值模拟验证表明,当环境随机干扰越强或媒体信息报道得越及时时,传染病的绝灭速度越快.该研究结果改进和丰富了文献[12]的相关研究结果,并可为利用媒体信息进行预防和控制疾病提供良好参考。

Option Pricing under the Double Exponential Jump-Diffusion Model with Stochastic Volatility and Interest Rate

This paper proposes an efficient option pricing model that incorporates stochastic interest rate(SIR),stochastic volatility(SV),and double exponential jump into the jump-diffusion settings.The model comprehensively considers the leptokurtosis and heteroscedasticity of the underlying asset’s returns,rare events,and an SIR.Using the model,we deduce the pricing characteristic function and pricing formula of a European option.Then,we develop the Markov chain Monte Carlo method with latent variable to solve the problem of parameter estimation under the double exponential jump-diffusion model with SIR and SV.For verification purposes,we conduct time efficiency analysis,goodness of fit analysis,and jump/drift term analysis of the proposed model.In addition,we compare the pricing accuracy of the proposed model with those of the Black-Scholes and the Kou(2002)models.The empirical results show that the proposed option pricing model has high time efficiency,and the goodness of fit and pricing accuracy are significantly higher than those of the other two models.

Stochastic gradient algorithm for a dual-rate Box-Jenkins model based on auxiliary model and FIR model

Based on the work in Ding and Ding(2008),we develop a modifed stochastic gradient(SG)parameter estimation algorithm for a dual-rate Box-Jenkins model by using an auxiliary model.We simplify the complex dual-rate Box-Jenkins model to two fnite impulse response(FIR)models,present an auxiliary model to estimate the missing outputs and the unknown noise variables,and compute all the unknown parameters of the system with colored noises.Simulation results indicate that the proposed method is efective.

具有随机波动率方差的信用等级迁移模型

考虑到信用等级迁移带来的风险,通过债券定价方式,基于Heston模型建立了具有随机波动率方差的信用等级迁移模型,以此来评估信用风险。根据预先设定的资产阈值将公司债券分为高、低两个信用等级,公司资产的波动率方差在不同的信用等级下有不同的波动性,即波动率方差满足不同的CIR(cox-ingersoll-ross)过程。根据无套利原理等,推导出了高、低等级下债券价值满足的偏微分方程以及耦合边界处满足的条件。利用隐格式差分方法对债券价值求取数值解,并进行参数分析。

基于随机森林模型的辽宁省收缩城市未来发展趋势探究

由于城镇水平的高速发展,如何快速有效地遏制收缩城市的进程已然成为人们关注的重点。该文针对收缩城市的分类、影响收缩城市的重要因素和收缩城市未来发展趋势进行分析与讨论。通过对常住人口增长率、随机森林模型的计算,筛选出了2009—2020年辽宁省30个城市中的收缩城市与影响收缩的较大因素,将数据绘制成城市发展指数变化折线图,针对曲线的趋势,对各个收缩城市的未来发展进行合理的分析与预测。

具有非线性波动的运费率模型的渐近性质

研究具有非线性波动的运费率模型的渐近性质.利用马尔可夫不等式,证明解的随机最终有界性.通过取适当函数,利用指数鞅不等式、Borel-Cantelli引理,得到解的轨道估计仅与模型的漂移项系数有关.最后,通过数值模拟,验证了模型的合理性.

Stochastic Volatility Model and Technical Analysis of Stock Price

In the stock market, some popular technical analysis indicators （e.g. Bollinger Bands, RSI, ROC, ...） are widely used by traders. They use the daily （hourly, weekly, ...） stock prices as samples of certain statistics and use the observed relative frequency to show the validity of those well-known indicators. However, those samples are not independent, so the classical sample survey theory does not apply. In earlier research, we discussed the law of large numbers related to those observations when one assumes Black-Scholes＇ stock price model. In this paper, we extend the above results to the more popular stochastic volatility model.

Upper Bounds for Ruin Probabilities under Stochastic Interest Rate and Optimal Investment Strategies

In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross （CIR） model. For the stock price process, we consider both the case of constant volatility （driven by an O U process） and the case of stochastic volatility （driven by a CIR model）. In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.

多货币债券定价的跳跃扩散模型随机路径分析

针对同一债券特别是主权债券以不同币种发行时所产生的违约信用风险进行研究,同时关注回收率对汇率形成的影响。研究认为:以远期汇率为对冲工具的组合无效,而同时考虑违约及不违约情况的期望汇率定价是一个有效选择。在这一理念基础上,研究还讨论了确定期望汇率的分析框架,并利用跳跃扩散模型复制策略进行风险对冲,然后对不同币种债券定价,最后利用蒙特卡洛技术模拟汇率生成的随机路径。

汇率衍生品多因子定价模型

汇率是非常重要的宏观变量之一,在如今中国经济加速与世界融合的大背景下,汇率金融衍生品是兼顾投资、保值和规避风险等较为全面功能的交易品种。本文紧密联系当前国际上关于汇率随机模型研究的前沿理论,创新性地在仿射模型框架下提出将汇率和利率共同建模并引入汇率的随机波动率与跳跃,推导了本国零息债券价格的解析解、外国零息债券价格的解析解和基于傅里叶变换的汇率欧式期权价格的半解析解,这对于中国汇率衍生品定价的协调一致性与风险管理有着非常重要的意义。同时,使用最小化损失函数的方法进行参数校准,并利用蒙特卡洛模拟验证了方法的有效性,进而作为例子将其应用到人民币美元汇率期权的实证数据中,得到了参数校准的结果。

随机利率背景下具有一般违约负相关结构公司债券的定价

为了更准确分析关联公司之间违约负相关因素对于公司债券估值的影响,在随机利率背景下,考虑具有一般违约负相关结构公司债券定价问题。采用n+1家关联公司的违约强度的双曲衰减相关性模型描述第n+1家公司和前n家关联公司之间因具有违约负相关而形成的一般违约负相关性结构,利用约化法建立了具有一般违约负相关结构公司债券定价的数学模型。基于随机分析方法和依条件独立法,推导出公司债券定价的显式表达式,并基于数值计算分析违约负相关因素对公司债券定价的影响。

Ait-Sahalia利率模型数值解收敛性分析

【目的】为研究一类高度非线性的广义Ait-Sahalia利率模型,对其数值解的收敛性进行证明。【方法】首先引入迭代方法证明方程存在唯一的全局正解;然后从经典欧拉(Euler-Maruyama,EM)数值格式出发,得到了广义Ait-Sahalia利率模型的驯服(tamed)欧拉数值解;最后修正方程系数所满足的条件,证明方程的驯服欧拉数值解依概率收敛于方程的解析解。【结果】对于漂移项和扩散项都高度非线性的随机微分方程,通过改进经典欧拉方法及处理方程漂移项和扩散项的系数条件,可获得具有依概率收敛性质的数值解。【结论】本研究结果可推广至其他类型的利率模型数值解研究,对金融衍生品分析和定价具有一定的指导意义。