An iterative algorithm to determine the number of time steps in path generation methods

The construction of Brownian motion paths is the most important part of simulation methods for option pricing. Particularly, there are several commonly used path generation methods in the context of quasi‐Monte Carlo, including the standard method and the Brownian bridge method. To apply each method, an inevitable step is to decide how many points are used to discretize the time interval. This paper implements an iterative algorithm to select a suitable number of time steps by successively adding discretization nodes until a specific convergence criterion is met. Numerical results with this algorithm are presented in the valuation of Asian options. Copyright © 2016 John Wiley & Sons, Ltd.     

A Useful Extension of Ito＇s Formula with Applications to Optimal Stopping

Given a continuous semimartingale M = （Mt）t≥〉0 and a d-dimensional continuous process of locally bounded variation V = （V^1,……, V^d）, the multidimensional Ito Formula states that f（Mt, Vt） - f（M0, V0） = ∫[0, t] Dx0f（Ms, Vs）dMs＋∑i=1^d∫[0, t] Dxi F（Ms, Vs）dVs^i＋1/2∫[0, t] Dx0^2 f（Ms, Vs）d 〈M〉s if f（x0,……,xd） is of C^2-type with respect to x0 and of C^1-type with respect to the other arguments This formula is very useful when solving various optimal stopping problems based on Brownian motion. However, in such application the function f typically fails to satisfy the stated conditions in that its first partial derivative with respect to x0 is only absolutely continuous. We prove that the formula remains true for such functions and demonstrate its use with two examples from Mathematical Finance.     

带跳随机波动率模型的高阶ADI分裂格式

针对带跳随机波动率模型满足的偏积分微分方程,提出一种新的高阶交替方向隐式（ADI）有限差分格式,该模型是一个具有混合导数和非常数系数的对流扩散型初边值问题.我们将不同的高阶空间离散与时间步ADI分裂格式相结合,得到了一种空间四阶精度、时间二阶精度的有效方法,并采用Fourier方法分析了高阶ADI格式的稳定性.最后,通过对欧式看跌期权定价模型进行数值实验证实了数值方法的高阶收敛性.     

基于分段策略评分的冲突主体偏好排序方法及其应用

冲突中各利益主体的偏好信息对冲突局势的演变和纠纷调解具有重要影响。现有的冲突偏好排序方法主要基于决策者对冲突局势或状态、策略权重和声明信息的主观判断和理解,缺乏科学的数据来源支撑。为准确获取冲突主体的偏好信息,本文提出了一种基于调查法的分段策略冲突偏好排序方法。首先,根据决策者类别将冲突策略集合进行分段,并通过问卷、调研等方法获取每个冲突主体对所有分段策略的重要度评分信息。在此基础上,计算决策者对各个冲突状态的综合偏好评分,进而得到状态偏好的排序结果。最后以医患纠纷为例,对比分析了传统策略权重法和分段策略评分法的偏好排序和稳定性分析结果,进一步验证了所提方法的有效性。     

Pricing vulnerable options under a stochastic volatility model

In this paper, we consider the pricing of vulnerable options when the underlying asset follows a stochastic volatility model. We use multiscale asymptotic analysis to derive an analytic approximation formula for the price of the vulnerable options and study the stochastic volatility effect on the option price. A numerical experiment result is presented to demonstrate our findings graphically.     

Optimal maintenance and scrapping versus the value of back ups

This paper investigates optimal maintenance of equipment under uncertainty and the options of scrapping versus keeping the equipment as a back up (at a cost). This set up is used to analyze three points. The first observation is that the continuous, deterministic and even the unconstrained stochastic problem allow for closed form analytical solutions, realistic constraints require numerical means to solve the corresponding stochastic managerial problem. Second, the possibility to switch at negligible costs between different modes (here running or mothballing the equipment) depending on current states requires a condition in addition to the familiar value matching and smooth pasting conditions, namely continuity of the second derivative of the value function (or super contact). Equipped with these findings the analysis turns to the third point of quantifying numerically the value of keeping equipments as a back-up instead of scrapping.     

Hedging Game Contingent Claims with Constrained Portfolios

Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity. In this paper, we consider the problem of hedging Game Contingent Claims (GCC) in two cases. For the case that portfolio is unconstrained, we provide a single arbitrage-free price $P_0$. Whereas for the constrained case, the price is replaced by an interval $[h_{low},h_{up}]$ of arbitrage-free prices. And for the portfolio with some closed constraints, we give the expressions of the upper-hedging price and lower-hedging price. Finally, for a special type of game option, we provide explicit expressions of the price and optimal portfolio for the writer and holder.     

NEW METHOD TO OPTION PRICING FOR THE GENERAL BLACK-SCHOLES MODEL-AN ACTUARIAL APPROACH

IntroductionRobertMerton[1] startedcontinuous_timefinancialmodelingwithhisexplicitdynamicprogrammingsolutionforoptimalportfolioandconsumptionpolices.Thissetsthestageforhis1973generalequilibriummodelofsecurityprices,anothermilestone .Hismajorcontributionwashisarbitrage_basedproofoftheoptionpricingformulaintroducedbyFisherBlackandMyronScholesin 1973[2 ] ,andhiscontinualdevelopmentofthatapproachtoderivativepricing .Darrelluffie[3 ] derivedtheBlack_ScholesFormulaintraditionaloptionpricingmetho…     

ANALYSIS OF FINANCIAL DERIVATIVES BY MECHANICAL METHOD (Ⅱ)-BASIC EQUATION OF MARKET PRICE OF OPTION

The basic equation of market price of option is formulated by taking assumptions based on the characteristics of option and similar method for formulating basic equations in solid mechanics: hv ₀(t) = m ₁ v ₀ ^–1(t) – n ₁ v ₀(t) + F, where h, m ₁, n ₁, F are constants. The main assumptions are: the ups and downs of market price v ₀(t) are determined by supply and demand of the market; the factors, such as the strike price, tenor, volatility, etc. that affect on v ₀(t) are demonstrated by using proportion or inverse proportion relation; opposite rules are used for purchasing and selling respectively. The solutions of the basic equation under various conditions are found and are compared with the solution v _f (t) of the basic equation of market price of futures. Furthermore the one-one correspondence between v _f and v ₀(t) is proved by implicit function theorem, which forms the theoretic base for study of v _f affecting on the market price of option v ₀(t).