有限状态Q过程波动率与跳组合情形的期权定价

引入了有限状态Q过程随机波动率与复合Poisson过程组合的资产价格动态模型,得到了该组合模型下欧式看涨期权定价的一般公式,推广了Hull和White的结论.最后通过数值模拟,充分体现了期权价格对初始时刻波动率大小的依赖.     

非仿射随机波动率跳扩散模型的利差期权定价

在两标的资产价格满足一类随机利率、随机波动率及跳跃均存在于资产价格和波动率的非仿射跳扩散模型下考察了利差期权的定价.首先,利用泰勒公式将非线性微分方程线性化,得到了两标的资产对数价格的近似联合密度特征函数;然后,使用Fourier逆变换等方法,获得了利差期权定价理论的半封闭公式,并将其推广到价差期权的定价.最后,通过数值实验,表明非仿射随机波动率跳扩散的利差期权定价模型比仿射随机波动率模型具有更高的精确性,并且扩散波动和跳跃波动对期权价格影响显著.     

快速均值回归随机波动率模型参数估计及应用

基于快速均值回归随机波动率模型, 研究双限期权的定价问题, 同时推导了考虑均值回归随机波动率的双限期权的定价公式。 根据金融市场中SPDR S&P 500 ETF期权的隐含波动率数据和标的资产的历史收益数据, 对快速均值回归随机波动率模型中的两个重要参数进行估计。 利用估计得到的参数以及定价公式, 对双限期权价格做了数值模拟。 数值模拟结果发现, 考虑了随机波动率之后双限期权的价格在标的资产价格偏高的时候会小于基于常数波动率模型的期权价格。     

高维欧式期权定价模型的奇摄动解

讨论了一类欧式期权定价问题的随机波动率模型,其随机波动率采用快速均值回归的随机波动率模型.通过采用奇摄动方法,得到了多风险资产欧式期权价格的形式渐近展开式,得到该合成展开式的一致有效误差估计.     

基于动态VaR约束与随机波动率模型的最优投资策略

研究Stein-Stein随机波动率模型下带动态VaR约束的最优投资组合选择问题. 假设投资者的目标是最大化终端财富的期望幂效用,可投资于无风险资产和一种风险资产, 风险资产的价格过程由Stein-Stein随机波动率模型刻画. 同时, 投资者期望能在投资过程中利用动态VaR约束控制所面对的风险.运用Bellman动态规划方法和Lagrange乘子法, 得到了该约束问题最优策略的解析式及特殊情形下最优值函数的解析式; 并通过理论分析和数值算例, 阐述了动态VaR约束与随机波动率对最优投资策略的影响.     

基于带跳随机波动率模型的双币种重置期权定价研究

研究了外国标的资产价格,汇率及其波动率过程满足仿射跳扩散模型的双币种重置期权定价问题,其中波动率过程与标的资产,汇率相关,且具有共同跳跃风险成分.利用多维Feynman-Kac定理,Fourier逆变换等方法,获得了双币种重置期权价格的表达式.应用数值计算分析了波动率过程主要参数对期权价格的影响.数值结果表明,波动率因素以及跳跃风险参数对期权价格的影响是显著的.     

不确定环境下的欧式期权定价

正1引言Black-Scholes~([1])(B-S)期权定价模型是金融市场上为人所熟知的研究期权价格的经典模型.然而,实证研究表明B-S模型暴露出一些与市场实际信息相违背的现象,其中有两点引起市场的广泛关注.第一点是基础资产,如股票的价格与B-S假设的正态分布相比表现的是偏峰厚尾的特性;其次是波动率曲线是敲定价格的凸曲线,即波动率微笑.为了在B-S模型中引入偏峰厚尾特性,一些模型和理论,如分数布朗运动及一些广义双曲模型~([2,3])描述基础资产的价格.另一方面,为了解释波动率微笑,一些自回归异方差(ARCH)~([4])、常弹性模型(CEV)~([5])等期权定价理论被相继提出.Merton~([6])为了同时考虑基础资产的偏     

在4/2随机波动率下正态调和稳态过程模型对期权的定价和对冲

本文把4/2随机波动率添加到用于模拟资产价格的正态调和稳态过程中,得到了一种全新的Lévy随机波动率模型.更进一步地,本文在此基础上还构造了考虑杠杆效应的Lévy随机波动率模型.本文从数学上证明了模型可行性,并且推导了在这种模型下可被半显式表达出来的期权定价公式和对冲策略公式.作为应用,本文还推导了在上面模型下VIX(波动率指数)波动率衍生品的定价公式,最后数值检验证实了模型的实用性.     

最小化破产概率的保险人鲁棒投资再保险策略研究

在模型不确定条件下,研究以破产概率最小化为目标的模糊厌恶型保险公司的最优投资再保险问题. 假设保险公司可投资于一种风险资产,也可购买比例再保险. 分别考虑风险资产的价格过程服从随机波动率模型和非随机波动率模型的两种情况,根据动态规划原理建立相应的HJB方程,得到保险公司的最优鲁棒投资再保险策略和价值函数的解析解. 最后,通过数值模拟分析了各模型参数对最优策略和价值函数的影响.     

带跳随机利率与波动率模型的远期生效期权定价

本文研究了市场利率,基础资产价格及其波动率过程满足一类多元仿射跳扩散模型的远期生效期权定价问题,其中市场利率和波动率过程与基础资产相关且具有共同跳跃风险成分.利用Fourier反变换和远期测度技术,获得了欧式远期生效看涨期权价格的解析显示解.应用数值计算比较了利率,波动率过程对期权价格的不同表现,并分析了模型中主要参数对期权价格和对冲策略的影响.数值结果表明,利率和波动率因素,以及跳跃风险参数对期权价格有显著作用,这表明了多元仿射跳扩散模型具有较好拟合实际的能力.     

The Height Process of a Continuous-State Branching Process with Interaction

Journal of Theoretical Probability - For a generalized continuous-state branching process with non-vanishing diffusion part, finite expectation and a directed (“left-to-right”)...     

On the Existence of a Small Parameter for a Semi-Markov Process

The problem of existence of a small parameter for a decomposable semi-Markov process with a finite number of states E is investigated in the case where the phase space E of the process can be represented in the form of the union of disjoint sets E ₁,...,E_r of ergodic states. The asymptotic behavior of transition probabilities of the semi-Markov process with phase space , where E ₀ is the set of unessential states and E _k, k=1,...,r, are classes of ergodic states, is studied.     

On the Ranked Excursion Heights of a Kiefer Process

Let (K(s,t), 0s1, t1) be a Kiefer process, i.e., a continuous two-parameter centered Gaussian process indexed by [0,1]×₊ whose covariance function is given by (K(s₁,t₁) K(s₂,t₂))=(s₁s₂-s₁s₂)t₁t₂, 0s₁, s₂1, t₁, t₂ 0. For each t>0, the process K(·,t) is a Brownian bridge on the scale of . Let M ₁ ^* (t) M ₂ ^* (t) M _j ^* (t) 0 be the ranked excursion heights of K(,t). In this paper, we study the path properties of the process tM _j ^* (t). Two laws of the iterated logarithm are established to describe the asymptotic behaviors of M _j ^* (t) as t goes to infinity.     

On the First-Passage Area of a One-Dimensional Jump-Diffusion Process

For a one-dimensional jump-diffusion process X(t), starting from x?>?0, it is studied the probability distribution of the area A(x) swept out by X(t) till its first-passage time below zero. In particular, it is shown that the Laplace transform and the moments of A(x) are solutions to certain partial differential-difference equations with outer conditions. The distribution of the maximum displacement of X(t) is also studied. Finally, some explicit examples are reported, regarding diffusions with and without jumps.     

Bootstrapping the Empirical Distribution Function of a Spatial Process

In this article, we consider a stationary α-mixing random field in IR ^d. Under a large-sample scheme that is a mixture of the so-called “infill” and “increasing domain” asymptotics, we establish a functional central limit theorem for the empirical processes of this random field. Further, we apply a blockwise bootstrap to the samples. Under the condition that the side length of the block for some 0 < β < 1, where λ _n is the growth rate in the increasing domain asymptotics, we show that the bootstrapped empirical process converges weakly to the same limiting Gaussian process almost surely. Extension to multivariate random fields and application to differentiable statistical functionals are also given. A spatial version of the Bernstein’s inequality is developed, which may be of some independent interest. In final form 13 December 2004     

Functional Estimation of the Random Rate of a Cox Process

The intensity of a doubly stochastic Poisson process (DSPP) is also a stochastic process whose integral is the mean process of the DSPP. From a set of sample paths of the Cox process we propose a numerical method, preserving the monotone character of the mean, to estimate the intensity on the basis of the functional PCA. A validation of the estimation method is presented by means of a simulation as well as a comparison with an alternative estimation method.     

On Estimation of the Intensity Function of a Point Process

In this paper we review techniques for estimating the intensity function of a spatial point process. We present a unified framework of mass preserving general weight function estimators that encompasses both kernel and tessellation based estimators. We give explicit expressions for the first two moments of these estimators in terms of their product densities, and pay special attention to Poisson processes.     

Properties of the Boundary Flux of a Singular Diffusion Process

Consider a nonhomogeneous fluid flowing through a homogeneous porous medium occupyinga bounded domain ΩR~n.Let u=u(x,t)represent the density of the fluid at the positionx∈Ω and time t,which satisfies the following singular diffusion equation