触销式双障碍卖权价值过程分析及其定价

主要证明了在不存在交易成本的完全市场条件下连续时间欧式触销式双障碍卖权贴现到0时刻的价值过程{V(t∧τL∧τH,Sl∧τL∧τH)；0≤t≤T}为鞅，并且给出了对应单障碍卖权价值过程的鞅性质。同时还讨论了美式触销式双障碍卖权的定价问题，给出了任意时刻t(0≤t≤T)其内在价值的表达式。     

双障碍幂型期权定价公式

为了进一步完善障碍期权理论,更好地适应金融市场的需求,本文在完全市场条件下,利用连续时间的双障碍幂型期权买权过程的鞅性和等价鞅测度变换的方法,得到了双障碍幂型期权定价模型的显式解.     

一类双标的型欧式买权的定价

文献[1]中讨论了双标的欧式期权的特殊情形,本文讨论一般情形:无风险资产(债券或银行存单)有依赖时间参数的利率rt,两种风险资产(股票)连续支付红利,并且分别有依赖时间参数的期望收益率μ1t,μ2 t,波动率σ1t,σ2 t,红利率q1t,q2 t以及两风险资产瞬时报酬率的相关系数ρt.在此基础上,构造了一类较为复杂的双标的型欧式买权,利用二维Girsanov定理以及鞅方法,得到买权的定价公式与避险参数Delta     

非局部柯西问题弱解的衰减速度（英文）

考虑如(1)所示的非局部柯西问题弱解(u_t)_t≥0的渐近性质.仅利用跳核J(x,y)当|x-y|充分大时下界的性质,本文证明了对于任意1≤qp∞及充分大t,‖u_t‖_p≤c(t)‖u_0‖_q成立,同时给出c(t)的最优显示估计式.     

Vasicěk随机利率模型下指数O-U过程的幂型期权鞅定价

研究了Vasicěk随机利率模型中一维标准Brown运动与资产价格服从指数Ornstein-Uhlenbeck过程中一维标准Brown运动的相关系数为ρ(-1≤ρ≤1)的情形下的幂型期权鞅定价问题.推广了基于Vasicěk随机利率模型下基于Black-Scholes公式的两种幂型期权定价问题.并利用Girsanov定理和等价鞅测度,给出了基于Vasicěk随机利率模型下服从指数Ornstein-Uhlenbeck过程的两种欧式幂型期权鞅定价公式.     

稀疏过程下带有退保和分红策略的相依风险模型

本文在保费收入为复合Poisson过程,索赔次数{N_(1)(t),t≥0},退保次数{N_(2)(t),t≥0}和支付红利的保单数{N_(3)(t),t≥0}分别是保单到达数{M(t),t≥0}的p_(1),p_(2),p_(3)-稀疏过程的假定下,建立带有干扰的风险模型,运用鞅方法讨论该模型盈余过程的性质,给出其最终破产概率的表达式和Lundberg上界,并给出具体实例.     

Hardy-Orlicz-amalgam鞅空间的原子分解

引入了Hardy-Orlicz-amalgam鞅空间,当Φ为凹函数且0 Φ≤q_Φ≤q≤1时,建立了Hardy-Orlicz-amalgam鞅空间H₍(Φ,q))^s的原子分解定理.作为应用,以此为工具给出了其共轭空间的刻画.     

具有一般跳过程的期权无差异效用价值过程的定价模型

本文采用指数效用最大化的方法研究了期权的动态无差异效用价值过程Ct(H;α).考虑股票价格过程为具有基于随机测度的一般跳的半鞅模型,且期权的无差异效用价值过程的Doob-Meyer分解的鞅部分的GKW(Galtchouk-Kunita-Watanabe)分解满足Jacod鞅表示定理.利用无差异效用价值过程在最小熵测度和最优投资策略下为鞅的事实构建了一个倒向随机微分方程.通过概率测度变换将方程的鞅部分和生成元转化为BMO(bounded mean oscillation)鞅,证明了该方程的解的唯一性.并将方程的生成元分成[?A=0]和[?A≠0],证明了最优投资策略存在.从而给出期权无差异效用价值过程的倒向随机微分方程的表达形式.     

连续支付红利的美式障碍期权定价的数值方法

本文利用显式差分格式为连续支付红利的向下触销型美式障碍期权定价.由于障碍的影响,定价模型的边值条件含有间断,故把结点设在障碍水平上,并在障碍附近的区域内运用局部网格加密技术,这样就可以得到较精确的期权价格.本文给出数值算例,验证算法的有效性,并分析障碍对期权价格的影响.     

《数学年刊》第8卷B辑第1期1987——目录和提要

正鞅和随机测度Kahane Jean-pierre对以 t 为指标的正鞅 Q_n(t)(n=0,1,…),(t∈T,T 为紧度量空间)和测度:σ∈M~ (G),随机测度Qσ定义为 Q_nσ的极限.一般来说,EQσ≤σ.本文给出的条件保证了 EQσ=0(退化)或者 EQσ=σ(完全作用),当 Q_n(t)为独立权函数的乘积这一特殊情况下,σ能分解成两个互相奇异的测度之和σ=σ′ σ″,使得 Q 在σ′,上为完全作用,而在σ″上是退化的,EQ 是一个射影算子.本文还给出了一些例子和应用(例如随机覆盖,B.Mandelbrot 鞅以及乘法浑沌).     

支付离散红利的交换期权定价

在标的资产支付离散红利的情形下,对交换期权定价问题进行了讨论,并采用Dai和Lyuu（2008）的股票支付离散红利的期权定价方法,给出了支付离散红利的交换期权的闭式解。     

Valuation of life insurance surrender and exchange options

In this paper I analyze two American-type options related to life and pension insurance contract. I use Monte Carlo simulations combined with the Longstaff and Schwartz approach for the valuation of American options to find the value of a typical surrender option. I find that the values may be much lower than previously indicated. This reduction of value is due to a different treatment of bonuses, limiting the customers’ ability to forecast the return of their policies. The numerical results show that the value may be higher than the corresponding surrender option.     

Two Exotic Lookback Options

This paper formally analyses two exotic options with lookback features, referred to as extreme spread lookback options and look‐barrier options, first introduced by Bermin. The holder of such options receives partial protection from large price movements in the underlying, but at roughly the cost of a plain vanilla contract. This is achieved by increasing the leverage through either floating the strike price (for the case of extreme spread options) or introducing a partial barrier window (for the case of look‐barrier options). We show how to statically replicate the prices of these hybrid exotic derivatives with more elementary European binary options and their images, using new methods first introduced by Buchen and Konstandatos. These methods allow considerable simplification in the analysis, leading to closed‐form representations in the Black–Scholes framework.     

前向打靶格方法计算巴拉和巴黎期权的价格

本文采用前向打靶格方法计算了巴拉期权和巴黎期权的价格.     

Approximation of Non-Lipschitz SDEs by Picard Iterations

In this article, we propose an approximation method based on Picard iterations deduced from the Doléans–Dade exponential formula. Our method allows to approximate trajectories of Markov processes in a large class, e.g., solutions to non-Lipchitz stochastic differential equation. An application to the pricing of Asian-style contingent claims in the constant elasticity of variance model is presented and compared to other methods of the literature.     

A New Approach to Pricing Double-Barrier Options with Arbitrary Payoffs and Exponential Boundaries

Abstract

We consider in this article the arbitrage free pricing of double knock-out barrier options with payoffs that are arbitrary functions of the underlying asset, where we allow exponentially time-varying barrier levels in an otherwise standard Black–Scholes model. Our approach, reminiscent of the method of images of electromagnetics, considerably simplifies the derivation of analytical formulae for this class of exotics by reducing the pricing of any double-barrier problem to that of pricing a related European option. We illustrate the method by reproducing the well-known formulae of Kunitomo and Ikeda (1992 Kunitomo, N. and Ikeda, M. 1992. Pricing options with curved boundaries. Mathematical Finance, 2: 276–298.  [Google Scholar]) for the standard knock-out double-barrier call and put options. We give an explanation for the rapid rate of convergence of the doubly infinite sums for affine payoffs in the stock price, as encountered in the pricing of double-barrier call and put options first observed by Kunitomo and Ikeda (1992 Kunitomo, N. and Ikeda, M. 1992. Pricing options with curved boundaries. Mathematical Finance, 2: 276–298.  [Google Scholar]).     

High-Order Methods for Exotic Options and Greeks Under Regime-Switching Jump-Diffusion Models

This paper aims to develop high-order numerical methods for solving the system partial differential equations (PDEs) and partial integro-differential equations (PIDEs) arising in exotic option pricing under regime-switching models and regime-switching jump-diffusion models, respectively. Using cubic Hermite polynomials, the high-order collocation methods are proposed to solve the system PDEs and PIDEs. This collocation scheme has the second-order convergence rates in time and fourth-order rates in space. The computation of the Greeks for the options is also studied. Numerical examples are carried out to verify the high-order convergence and show the efficiency for computing the Greeks.     

Calibration of a basket option model applied to company valuation

Applying real options thinking to company valuation seems theoretically and intuitively appealing. However, the real option analogy of a single European option as well as the compound option proxy perform poorly when applied to company valuation. We therefore suggest to rework the building blocks of real option applications to corporate valuation.  We introduce a framework to delineate the distribution of the underlying asset in the risk neutral world, which is important in order to value any derivative. This is achieved by an algorithm to calibrate a basket option model using real world data of observed share prices. The fitting takes account of the class of stable distributions. The index of stability of asymmetric α stable distribution serves as an over-all parameter to characterise the specific distribution.     

The Valuation of American Options with Stochastic Stopping Time Constraints

Abstract

This paper concerns the pricing of American options with stochastic stopping time constraints expressed in terms of the states of a Markov process. Following the ideas of Menaldi et al., we transform the constrained into an unconstrained optimal stopping problem. The transformation replaces the original payoff by the value of a generalized barrier option. We also provide a Monte Carlo method to numerically calculate the option value for multidimensional Markov processes. We adapt the Longstaff–Schwartz algorithm to solve the stochastic Cauchy–Dirichlet problem related to the valuation problem of the barrier option along a set of simulated trajectories of the underlying Markov process.     

依赖时间参数的几种有固定执行价格的亚式期权定价

本文在假定标的资产模型依赖时间参数（即无风险利率,标的资产的期望收益率,波动率及红利率）,利用已建立的亚式期权定价模型,讨论了上限型期权、抵付型期权、双向型期权等,得到相应的期权定价解析公式．