Computable error bounds of multidimensional Euler inversion and their financial applications

Transform inversion is an efficient approximation procedure in operations research, yet the inversion results are sometimes unstable which calls for comprehensive error analysis. This article proposes a multidimensional Euler inversion (MEI) algorithm with computable error bounds. We design mild sufficient conditions that validate the inversion formula, and provide closed-form upper bounds of the inversion errors. Numerical experiments are conducted to compute the joint probability of default and barrier option prices under complicated stochastic models, and output the associated error bounds.     

基于外汇汇率的期权定价及其实证分析

在外汇汇率服从连续扩散过程模型下,研究了外汇汇率的几何平均亚式期权和附有汇率范围的示性函数的新型幂期权定价问题。在实证分析中,通过美元/人民币汇率的真实数据来计算以上所研究期权的价格,并和Black-Scholes模型下的期权定价进行比较,同时对相关期权的隐含波动率进行了分析。     

Market calibration under a long memory stochastic volatility model

In this article, we study a long memory stochastic volatility model (LSV), under which stock prices follow a jump-diffusion stochastic process and its stochastic volatility is driven by a continuous-time fractional process that attains a long memory. LSV model should take into account most of the observed market aspects and unlike many other approaches, the volatility clustering phenomenon is captured explicitly by the long memory parameter. Moreover, this property has been reported in realized volatility time-series across different asset classes and time periods. In the first part of the article, we derive an alternative formula for pricing European securities. The formula enables us to effectively price European options and to calibrate the model to a given option market. In the second part of the article, we provide an empirical review of the model calibration. For this purpose, a set of traded FTSE 100 index call options is used and the long memory volatility model is compared to a popular pricing approach – the Heston model. To test stability of calibrated parameters and to verify calibration results from previous data set, we utilize multiple data sets from NYSE option market on Apple Inc. stock.     

Joint distributions for stochastic functional differential equations

Consider stochastic functional differential equations, whose coefficients depend on past histories. The solution determines a non-Markov process. In the present paper, we shall obtain the existence of smooth densities for joint distributions of solutions, under the uniformly elliptic condition on the diffusion coefficients, via the Malliavin calculus. As an application, we shall study the computations of the Greeks on options associated with the asset price dynamics models with delayed effects.     

Pricing Asian options of discretely monitored geometric average in the regime‐switching model

This paper provides analytic pricing formulas of discretely monitored geometric Asian options under the regime‐switching model. We derive the joint Laplace transform of the discount factor, the log return of the underlying asset price at maturity, and the logarithm of the geometric mean of the asset price. Then using the change of measures and the inversion of the transform, the prices and deltas of a fixed‐strike and a floating‐strike geometric Asian option are obtained. As the numerical results, we calculate the price of a fixed‐strike and a floating‐strike discrete geometric Asian call option using our formulas and compare with the results of the Monte Carlo simulation. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical methods for backward Markov chain driven Black-Scholes option pricing

The drift, the risk-free interest rate, and the volatility change over time horizon in realistic financial world. These frustrations break the necessary assumptions in the Black-Scholes model (BSM) in which all parameters are assumed to be constant. To better model the real markets, a modified BSM is proposed for numerically evaluating options price-changeable parameters are allowed through the backward Markov regime switching. The method of fundamental solutions (MFS) is applied to solve the modified model and price a given option. A series of numerical simulations are provided to illustrate the effect of the changing market on option pricing.     

Weak Galerkin finite element method for valuation of American options

We introduce a weak Galerkin finite element method for the valuation of American options governed by the Black-Scholes equation. In order to implement, we need to solve the optimal exercise boundary and then introduce an artificial boundary to make the computational domain bounded. For the optimal exercise boundary, which satisfies a nonlinear Volterra integral equation, it is resolved by a higher-order collocation method based on graded meshes. With the computed optimal exercise boundary, the front-fixing technique is employed to transform the free boundary problem to a one- dimensional parabolic problem in a half infinite area. For the other spatial domain boundary, a perfectly matched layer is used to truncate the unbounded domain and carry out the computation. Finally, the resulting initial-boundary value problems are solved by weak Galerkin finite element method, and numerical examples are provided to illustrate the efficiency of the method.     

信息不对称下制造商填塞分销渠道策略研究

由制造商和零售商构成的二级供应链,制造商管理者可能使用填塞分销渠道策略最大化自己的效用。本文研究在信息不对称的情形下,制造商填塞分销渠道决策对供应链绩效的影响。研究发现:随着修正财务报告的投资者增多,制造商的库存水平以及制造商管理者的效用都会降低;而随着制造商管理者对市场价值重视程度提高,制造商的利润降低,这表明填塞分销渠道对制造商的真实价值产生负面影响。同时,供应链的利润不仅与管理者填塞分销决策有关,还受到零售价格等外在因素的影响。进一步地,加强外部监管以及设计合理的激励制度,有助于减少管理者填塞分销渠道的行为。     

股价最简微分方程,其解及与Black-Scholes模型的假设的相互关系

在系数的某种等价关系条件下,股价的两类数学表达式,一类是基于明确型描述的由类似固体力学方法导出的最简微分方程(S.D.E.)的解,另一类是基于不确定型描述(即统计理论)的Black-Scholes模型的假设(A.B-S.M.),即股价密度函数服从对数正态分布,可以是完全相同的.S.D.E.的解仅适用于股市的常规情形(无利好或利空消息,等),因此,A.B-S.M.的适用范围也相同.     

带交易费用和红利的欧式期权定价的数值方法

本文在 L eland的带交易费用的欧式期权定价模型基础上 ,先推导出一般费用模型的定价公式 ,然后用二叉树图法给出了带有交易费用和红利的欧式看涨期权定价的数值方法 ,并比较了多头和空头的不同价值。