Option Pricing by the Legendre Wavelets Method

Computational Economics - This paper presents the numerical solution of the Black–Scholes partial differential equation (PDE) for the evaluation of European call and put options. The proposed...     

Pricing Credit Default Swaps Under Multifactor Reduced-Form Models: A Differential Quadrature Approach

We present a new numerical method for pricing credit default swaps under fully correlated multifactor reduced-form models. In particular, the proposed approach combines an implicit/explicit operator splitting procedure with the harmonic differential quadrature scheme, and is so efficient that it can be applied to models with up to six stochastic factors. This is a remarkable advantage, as we can use two factors to describe the interest rate, other two factors to describe the default probability, and other two factors to take into account, for example, the so-called counterparty risk. The performances of the novel method are demonstrated by extensive simulation, in which various kinds of models with four and six fully correlated factors are considered.     

An Implementation of Bouchouev's Method for a Short Time Calibration of Option Pricing Models

We analyse the Bouchouev integral equation for the deterministic volatility function in the Black–Scholes option pricing model. We areable to reduce Bouchouev's original triple integral equation to a single integral equation and describe its numerical solution. Moreover we show empirically that the most complex term in the equation may often be safely ignored for the purposes of numerical calculations. We present a selection of numerical examples indicating the range of time values for which we would expect the equation to be valid.     

A Dimension Reduction Shannon-Wavelet Based Method for Option Pricing

We present a robust and highly efficient dimension reduction Shannon-wavelet method for computing European option prices and hedging parameters under a general jump-diffusion model with square-root stochastic variance and multi-factor Gaussian interest rates. Within a dimension reduction framework, the option price can be expressed as a two-dimensional integral that involves only (i) the value of the variance at the terminal time, and (ii) the time-integrated variance process conditional on this value. A Shannon wavelet inverse Fourier technique is developed to approximate the conditional density of the time-integrated variance process. Furthermore, thanks to the excellent approximation properties of Shannon wavelets, the overall pricing procedure is reduced to the evaluation of just a single integral that involves only the density of the terminal variance value. This single integral can be accurately evaluated, since the density of the variance at the terminal time is known in closed-form. We develop sharp approximation error bounds for the option price and hedging parameters. Numerical experiments confirm the robustness and impressive efficiency of the method.     

Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models

In mathematical finance a popular approach for pricing options under some Lévy model would be to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a partial integro-differential equation (PIDE) that usually does not allow an analytical solution, while a numerical solution also faces some problems. In this paper we develop a new approach on how to transform the PIDE into a class of so-called pseudo-parabolic equations which are well known in mathematical physics but are relatively new for mathematical finance. As an example we will discuss several jump-diffusion models which Lévy measure allows such a transformation.     

一类地产期权的微分方程定价模型及其计算

该文以北京西奥中心写字楼为例,分析“以租待售”型房地产营销工具具有的分期付款期权特性,运用Δ-对冲技巧和Ito引理,构造了美式分期付款地产期权的微分方程定价模型,并确定了定价模型中各个变量的内涵,包括标的资产价格、波动率、期限和执行价等。针对北京西奥中心写字楼的具体市场数据,应用有限差分策略进行数值计算,得到了相应的期权价值。     

Utility-Based Pricing,Timing and Hedging of an American Call Option Under an Incomplete Market with Partial Information

This paper studies the pricing, timing and hedging of an American call option written on a non-tradable asset whose mean appreciation rate is not observable but is known to be a Gaussian random variable. Our goal is to analyze the effects of the partial information on investment in the American option under an incomplete market. The objective of the option holder is to maximize the expected discounted utility of consumption over an infinite lifetime. Thanks to consumption utility-based indifference pricing principal, stochastic control and filtering theory, under CARA utility, we derive the value and the exercise time of the American call option, which are determined by a semi-closed-form solution of a free-boundary PDE problem with a finite time horizon. We provide numerical results by finite difference methods and compare the results with those under a fully observable case. Numerical calculations demonstrate that partial information leads to a significant loss of the implied value of the American call option. This loss increases with the uncertainty of the mean appreciation rate. If the option holder is risk-averse enough, a growth of the systematic/idiosyncratic risk will increase/decrease the implied option value and the option is exercised later/sooner. Whether a stronger positive correlation between the tradable asset and the non-tradable underlying asset increases the option value and the information value depends on the risk attitude of the option holder. On the contrary, a stronger negative correlation will definitely make the option and the information more valuable. In addition, explicit expressions of the utility-based pricing for a perpetual American call are presented if the tradable risky asset is perfectly correlated with the underlying asset.     

期权定价理论在风险投资决策中的应用

在研究了风险投资的含义和基本特点的基础上，介绍了传统的投资决策方法即净现值法和内部收益率法的基本原理，并且指出现有的建立在净现值法基础之上的评价方法由于难以操作或不符合风险投资的特点，很难对风险投资项目进行有效的评价。在对风险投资行为特征进行深入分析的基础上，认为风险投资具有期权性质，提出了一种基于B1ack-Scholes定价公式的风险投资项目评价方法，从而有效克服了传统净现值法的局限，增加了风险项目投资决策的合理性和科学性。     

Consumption Utility-Based Pricing and Timing of the Option to Invest with Partial Information

This paper extends real options theory to consider the situation where the mean appreciation rate of the value of an irreversible investment project is not observable and governed by an Ornstein–Uhlenbeck process. Our main purpose is to analyze the impact of the uncertainty of the mean appreciation rate on the pricing and investment timing of the option to invest under incomplete markets with partial information. We assume that an investor aims to maximize expected discounted utility of lifetime consumption. Based on consumption utility indifference pricing method, stochastic control and filtering theory, we obtain under CARA utility the implied values and the optimal investment thresholds of the option to invest, which are determined by a semi-closed-form solution to a free-boundary partial differential equation (PDE) problem. The solution is independent of the utility time-discount rate. We provide numerical results by finite difference methods and compare the results with those under a fully observable case. Numerical calculations show that partial information leads to a significant loss of the implied value of the option to invest. This loss, called implied information value, IIV increases quickly with the uncertainty of the mean appreciation rate. A high volatility of project values might decrease the IIV, as well as the implied value of the option.     

AzureOP:基于Windows Azure云并行计算的期权定价SaaS

计算速度对于期权交易者至关重要,关系到如何有效地制定价格并评估相应的风险,而云并行计算提供的随收随付制（Pay-as-You-Go）可以实现低成本运行。在微软云平台Windows Azure的基础上,开发了基于云并行计算的期权定价试点云软件AzureOP,该软件以较低的费用提供了低风险和高速度,并给出了AzureOP对于美式期权价格的模拟结果,绘制了对应的期权价格定价曲线和定价曲面。最后,对云并行计算在金融应用上的优势和不足进行了总结和讨论,同时举例说明了试点云软件AzureOP的具体细节。     

A Robust Numerical Scheme For Pricing American Options Under Regime Switching Based On Penalty Method

This paper is devoted to develop a robust numerical method to solve a system of complementarity problems arising from pricing American options under regime switching. Based on a penalty method, the system of complementarity problems are approximated by a set of coupled nonlinear partial differential equations (PDEs). We then introduce a fitted finite volume method for the spatial discretization along with a fully implicit time stepping scheme for the PDEs, which results in a system of nonlinear algebraic equations. We show that this scheme is consistent, stable and monotone, hence convergent. To solve the system of nonlinear equations effectively, an iterative solution method is established. The convergence of the solution method is shown. Numerical tests are performed to examine the convergence rate and verify the effectiveness and robustness of the new numerical scheme.     

振动式微陀螺正交误差自补偿方法

微陀螺正交误差会影响陀螺的零偏稳定性,为了提高微陀螺的性能,必须减小正交误差。针对正交误差处理中存在的问题,推导了包含交叉耦合误差效应的驱动模态和检测模态的动力学方程,研究了交叉耦合误差引起的正交误差表达式,提出了一种正交误差闭环控制自补偿方法。通过将经正交误差幅值调幅控制的驱动位移信号闭环反馈作用到检测模态的输出,实现正交误差的自补偿。制作PCB电路测试了微陀螺的性能。正交误差自补偿后微陀螺零偏输出均值从778 mV减小到了2 mV,零偏稳定性从75°/h提高到了34.5°/h。实验结果表明,此方法是可行的。     

Convergence Analysis of Iterative Laplace Transform Methods for the Coupled PDEs from Regime-Switching Option Pricing

This paper aims to analyze the convergence rates of the iterative Laplace transform methods for solving the coupled PDEs arising in the regime-switching option pricing. The so-called iterative Laplace transform methods are described as follows. The semi-discretization of the coupled PDEs with respect to the space variable using the finite difference methods (FDMs) gives the coupled ODE systems. The coupled ODE systems are solved by the Laplace transform methods among which an iteration algorithm is used in the computational process. Finally, the numerical contour integral method is used as the Laplace inversion to restore the solutions to the original coupled PDEs from the Laplace space. This Laplace approach is regarded as a better alternative to the traditional time-stepping method. The errors of the approach are caused by the FDM semi-discretization, the iteration algorithm and the Laplace inversion using the numerical contour integral. This paper provides the rigorous error analysis for the iterative Laplace transform methods by proving that the method has a second-order convergence rate in space and exponential-order convergence rate with respect to the number of the quadrature nodes for the Laplace inversion.     

距离比较法构建酪氨酸酶抑制剂的药效团模型

运用距离比较法程序建立了酪氨酸酶抑制剂的药效团模型，以此为提问结构对Maybridge和NCI，2个数据库进行搜索，得到了一系列新型的可能具有高活性的黑色素合成抑制剂。     

The Role of Additional Information in Option Pricing: Estimation Issues for the State Space Model

We consider two competing financial state space models and investigate whether additional information in the form of option price data is helpful to the estimation of either the unobservable state variable (volatility) or the unknown parameters in the model. The complete discussion of the estimation problem in the presence of additional information involves decisions about filtering methods, the quality of the new information, the correlation between state variables and out-of-sample forecast performance. It is found that the state variable estimation is more sensitive than the parameter estimation to the correlation, information quality and the assumed linearity or non-linearity of the underlying model. As a result of the investigation of these factors, the particle filter is shown to be an attractive method for computing posterior distributions for these models.