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。     

考虑价值漏损的研发项目实物期权定价模型

提出了一种考虑价值漏损的研发项目期权定价决策模型。针对研发项目投资决策中隐含的扩张期权,以及期权中以现金流或便利收益存在的价值漏损,在传统的二叉树定价模型的基础上,给出了包含价值漏损的单期、两期和三期二叉树期权定价方法,建立了考虑价值漏损的研发项目期权定价模型。通过算例将两种结果进行了比较分析,结果表明考虑价值漏损的实物期权定价能更准确、有效地估算研发项目的价值。     

不确定环境下项目评估的期权决策树研究

在不确定环境下,传统的净现值(NPV)项目评估方法由于忽略决策的灵活性而低估了项目的价值。针对这种不足,根据期权特性提出期权决策树评估方法．即把实物期权的思想嵌入到决策树中,从而使评估包括了项目投资的不确定性价值。期权决策树分析方法采用了BS期权定价公式以及McDonald和Siegel关于是否继续生产的期权定价公式,计算出了不同决策方案的价值。并进一步讨论了不确定性的价值大小以及对决策的影响。示例证明：期权决策树方法比传统的净现值方法更具有科学性、准确性和实用性。     

委托代理框架下实物期权最优投资策略研究

在非对称信息条件下，讨论实物期权定价及其投资优化问题。根据委托代理理论，提出实物期权投资者和经营者的价值模型，在实物期权经营者对于项目价值信息隐匿条件下，应用极大值原理推导出实物期权最优投资和转移价值的解，指出投资与项目价值、转移价值与项目价值间的关系，分析实物期权价值模型各参数对投资决策的影响作用。     

期权定价多元树的计算

树形结构法是期权定价的基本方法之一,其中二元树形法目前得到了广泛的应用．本文的主题是多元树形结构法,文中对其算法及构造进行了讨论,同时,还找出了二个新的五元树形结构模型和一个七元树形结构模型．与二元树形结构法相比,多元树形结构法能有更快的收敛速度和更高的计算精度,然而期权的内在收益函数(payoff function)的不光滑性会降低树形结构法的计算效率．本文讨论了克服这一缺陷的方法,最后文中对在定价计算中的效率问题进行了实证研究．     

基于GPU的最小二乘蒙特卡罗算法期权定价

期权是以金融产品作为行权品种的交易合约。随着期权交易规模和交易量的迅速增长,期权定价的计算量越来越大,在传统CPU平台上对期权进行定价变得越来越困难。图形处理器（GPU）平台的出现和发展为解决期权定价计算提供了解决方案。在GPU上使用最小二乘蒙特卡罗算法（Least Squares Monte Carlo,LSM）实现了对一维和四维美式期权定价计算：首先利用CURAND库产生大量随机数,然后并行化期权标的价格变化路径,最后对最小二乘法和贴现定价进行并行化。为提高GPU平台上LSM方法的计算效率,对整个过程进行了优化。实际测试结果表明,在CPU+GPU上实现一维和四维美式期权定价相对CPU平台的加速比最高分别达到20.275和47.538,且比其他文献的方法整体性能有较大的提升。     

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。     

随机波动率下的亚式期权定价问题在GPU集群上的实现

期权定价作为计算金融领域的核心问题之一,越来越受到关注.随着期权交易的规模和交易量的迅速增长,当前的期权定价平台越来越受到挑战,在尽可能短的时间内对期权进行定价变得越来越困难.传统的计算平台通常使用基于CPU的计算集群,而图形处理器(GPU)具有更高的浮点性能和访存带宽,在价格与功耗方面也优于CPU.尝试使用GPU集群来对具有随机波动率的亚式期权进行定价,同时使用带控制变量的MonteCarlo方法,减小模拟的方差.最终的测试结果表明GPU集群较CPU集群具有更多的优势,适合应用于期权定价领域.     

基于混合卡尔曼粒子滤波算法的期权定价方法

针对金融领域的期权定价问题,为提高粒子滤波算法对期权价格的估计精度,提出使用混合卡尔曼粒子滤波算法(MKPF)进行期权价格预测,该算法使用Unscented 卡尔曼滤波器和扩展卡尔曼滤波器作为混合建议分布产生重要采样密度.在某一时刻,每一个粒子首先经过Unscented卡尔曼滤波器更新得到一个状态估计值,然后以该估计值作为扩展卡尔曼滤波器的先验估计再次更新粒子,得到该时刻最终的估计值.实验中针对经典的Black-Scholes期权定价公式,使用包括MKPF算法在内的4种算法对期权价格进行预测,结果表明MKPF算法预测的期权价格与真实期权价格的误差最小,证明了MKPF算法在期权定价问题中的有效性.     

结合期权合约与现货市场的原材料采购风险管理

通过建立一个两时点的采购模型,研究在原材料价格波动下一个风险规避制造商的最优组合采购策略.制造商可利用期权合约购买原材料,或者从现货市场采购.研究结果表明,最优期权购买数量受到风险规避程度、期权费以及执行价格的影响.最优购买数量与决策者风险规避程度之间的关系受到期权定价影响;最优购买数量随着期权购买费或执行价格的增加而减少.最后,通过比较说明,采用组合采购策略可以提高制造商的均值-方差效用水平.     

A modified Black–Scholes pricing formula for European options with bounded underlying prices

In this paper, a modified Black–Scholes (B–S) model is proposed, based on a revised assumption that the range of the underlying price varies within a finite zone, rather than being allowed to vary in a semi-infinite zone as presented in the classical B–S theory. This is motivated by the fact that the underlying price of any option can never reach infinity in reality; a trader may use our new formula to adjust the option price that he/she is willing to long or short. To develop this modified option pricing formula, we assume that a trader has a view on the realistic price range of a particular asset and the log-returns follow a truncated normal distribution within this price range. After a closed-form pricing formula for European call options has been successfully derived, some numerical experiments are conducted. To further demonstrate the meaning of the proposed model, empirical studies are carried out to compare the pricing performance of our model and that of the B–S model with real market data.     

Real‐time waiting‐price trading interval in a heterogeneous options market: a Bernoulli distribution

Options pricing remains an open research question that is challenging for both theoreticians and practitioners. Unlike many classical binomial models that assume a “representative agent,” the model suggested herein considers two players who are heterogeneous with respect to their estimations of the distribution of the underlying asset price on expiration day, and with respect to their levels of willingness to make a transaction (eagerness level). A two‐player binomial model is developed to find the real‐time optimal option price in two stages. First, we determine a primary feasible pricing domain. We then find a narrower feasible domain, termed the “waiting‐price trading interval,” meaning the region within which the players may either wait for better offers (due to a change in market conditions or player beliefs), or make an immediate transaction. The suggested model is formulated by a nonlinear optimization problem and the optimal price is shown to be unique. We demonstrate that the counter player's eagerness level has a significant effect on the proposed optimal option price. Using empirical analysis, several known lattice‐based models for option pricing, such as CRR and Tian, are compared with the current model (herein, S‐H) in which the price offered by the model player takes into account the subjective beliefs of the opposing market player. The comparison shows significant advantages to the S‐H model in terms of the expected profit on expiration day.     

Modeling and Simulation of an Artificial Stock Option Market

Since their introduction in 1973, options have become an important and very popular financial instrument. However, despite much research performed on the subject, the effects of option trading on the underlying asset market are still debated. Both empirical and theoretical studies have failed to point out how price volatility and volumes of the underlying asset are affected. In this paper we present the first study on the effects of an option market related to an underlying stock market, using an artificial financial market based on heterogeneous agents. We modeled a realistic European option using two market models. The microstructure of the first model is kept as simple as possible, being composed only of random traders. The second model is more complex and realistic, involving the presence of various kinds of trading strategies (random, fundamentalist and chartist). We show that the introduction of options, in the proposed models, tends to decrease the volatility of the underlying stock price. Moreover, the traders’ wealth can be strongly affected by the use of option hedging.     

Improving option price forecasts with neural networks and support vector regressions

Options are important financial derivatives that allow investors to control their investment risks in the securities market. Determining the theoretical price for an option, or option pricing, is regarded as one of the most important issues in financial research; a number of parametric and nonparametric option pricing approaches have been presented. While the objective of option pricing is to find the current fair price, for decision making, in contrast, the forecasting activity has to accurately predict the future option price without advance knowledge of the underlying asset price. In this paper, a simple and effective nonparametric method of forecasting option prices based on neural networks (NNs) and support vector regressions (SVRs) is presented. We first modified the improved conventional option pricing methods, allowing them to forecast the option prices. Second, we employed the NNs and SVRs to further decrease the forecasting errors of the parametric methods. Since the conventional methods mimic the trends of movement of the real option prices, using these methods in a first stage allows the NNs and SVRs to concentrate their power in nonlinear curve approximation to further reduce the forecasting errors in a second stage. Finally, extensive experimental studies with data from the Hong Kong option market demonstrated the ability of NNs and SVRs to improve forecast accuracy.     

Numerical analysis for Spread option pricing model of markets with finite liquidity: first-order feedback model

In this paper, we discuss the numerical analysis and the pricing and hedging of European Spread options on correlated assets when, in contrast to the standard framework and consistent with a market with imperfect liquidity, the option trader's trading in the stock market has a direct impact on one of the stocks price. We consider a first-order feedback model which leads to a linear partial differential equation. The Peaceman–Rachford scheme is applied as an alternating direction implicit method to solve the equation numerically. We also discuss the stability and convergence of this numerical scheme. Finally, we provide a numerical analysis of the effect of the illiquidity in the underlying asset market on the replication of an European Spread option; compared to the Black–Scholes case, a trader generally buys less stock to replicate a call option.     

Fuzzy pricing of geometric Asian options and its algorithm

Owing to the fluctuations of the financial market, input data in the options pricing formula cannot be expected to be precise. This paper discusses the problem of pricing geometric Asian options under the fuzzy environment. We present the fuzzy price of the geometric Asian option under the assumption that the underlying stock price, the risk-free interest rate and the volatility are all fuzzy numbers. This assumption makes the financial investors to pick any geometric Asian option price with an acceptable belief degree. In order to obtain the belief degree, the interpolation search algorithm has been proposed. Some numerical examples are presented to illustrate the rationality and practicability of the model and the algorithm. Finally, an empirical study is performed based on the real data. The empirical study results indicate that the proposed fuzzy pricing model of geometric Asian option is a useful tool for modeling the imprecise problem in the real world.     

A stochastic approximation algorithm for option pricing model calibration with a switchable market

This paper is concerned with option pricing under a regime-switching model. The switching process takes two different modes, and the underlying stock price evolves in accordance with the two modes dictated by a continuous-time, finite-state Markov chain. At any given instance, the price follows either a geometric Brownian motion model or a mean-reversion model, depending on its market mode. Stochastic approximation/optimization algorithms are developed for model calibration. Convergence of the algorithm is proved; rate of convergence is also provided. Option market data are used to predict the future market mode.     

期权工具存在下的最优混合采购策略研究

原材料价格与需求不确定下,研究制造商混合期权合约、长期合约、现货采购的最优采购策略。利用期望效用模型建立了一个风险规避制造商的决策模型,并得到效用函数为二次效用函数下制造商的最优采购策略。研究结果表明,制造商最优采购量与风险规避度的关系取决于原材料期望价格与长期合约价格以及期权价格间的相对大小关系;当价格漂移率增加时,长期合约预定数量增加,期权购买量减小;当价格波动率或长期合约价格增加时,长期合约预定数量减少,期权购买量增加;采用混合采购策略可提高制造商的期望效用水平。     

Pricing Bermudan options under Merton jump-diffusion asset dynamics

In this paper, a recently developed regression-based option pricing method, the Stochastic Grid Bundling Method (SGBM), is considered for pricing multidimensional Bermudan options. We compare SGBM with a traditional regression-based pricing approach and present detailed insight in the application of SGBM, including how to configure it and how to reduce the uncertainty of its estimates by control variates. We consider the Merton jump-diffusion model, which performs better than the geometric Brownian motion in modelling the heavy-tailed features of asset price distributions. Our numerical tests show that SGBM with appropriate set-up works highly satisfactorily for pricing multidimensional options under jump-diffusion asset dynamics.