多标的资产期权定价的Monte Carl模拟方法及其应用研究

鉴于一般的偏微分解析方法和传统数值方法处理高维期权定价问题存在很大困难,本文在单标的资产价格随机模型的基础上,推导了具相关性的多标的资产价格的随机过程公式,以此构造蒙特卡罗模拟高维欧式期权定价的随机模型,给出模拟算法,并分析了影响蒙特卡罗模拟效果的几个关键因素,模拟算例的结果显示模拟效果较好.     

蒙特卡罗模拟方法在期权定价中的应用

蒙特卡罗模拟作为金融衍生证券定价的一种有效的数值方法之一,近年来得到了不断的应用和发展。本文简要介绍了蒙特卡罗模拟在金融衍生证券定价的应用,评价了蒙特卡罗模拟的三个改进方向：基本方差减少技术、拟蒙特卡罗模拟、随机化的拟蒙特卡罗模拟,提出了利用超均匀序列Halton序列的拟蒙特卡罗模拟技术,以欧式看涨期权定价为例,比较了三种蒙特卡罗模拟结果。     

基于Copula GARCH的多资产期权定价

自从Black和Scholes在1976年开创性的提出了BS期权定价公式以来,期权定价理论得到了极大的发展,而在其后的研究中发展基于BS公式的隐含波动率对于执行价格具有类似微笑的曲线,其原因是标的资产的过程并不是BS公式所假设的几何布朗运动。Engle提出的ARCH模型和Bollerslev提出的GARCH模型能对标的资产的收益率序列进行很好的描述,因此将GARCH模型引入期权定价。在多资产期权定价研究当中,最为关键的是标的资产之间的依赖关系,关于依赖关系的最有力的就是Copula理论,而Copula的一大优势就是可以将边缘分布和联合分布分开,可以分别考虑边缘分布和数据的相关结构。本文设想将多元GARCH引入多资产期权定价中,但是一般的多元GARCH的系数过多而不易估计,另一方面模型的灵活程度较小,所以用一元的GARCH模型分别对各个标的资产的收益率序列进行建模,再用Copula将各个资产的分布联接起来,这便是Copula based MGARCH模型。接下来便可以通过Monte Carlo模拟对期权进行定价。     

基于Copula GARCH的多资产期权定价

自从Black和Scholes在1976年开创性的提出了BS期权定价公式以来,期权定价理论得到了极大的发展,而在其后的研究中发展基于BS公式的隐含波动率对于执行价格具有类似微笑的曲线,其原因是标的资产的过程并不是BS公式所假设的几何布朗运动。Engle提出的ARCH模型和Bollerslev提出的GARCH模型能对标的资产的收益率序列进行很好的描述,因此将GARCH模型引入期权定价。在多资产期权定价研究当中,最为关键的是标的资产之间的依赖关系,关于依赖关系的最有力的就是Copula理论,而Copula的一大优势就是可以将边缘分布和联合分布分开,可以分别考虑边缘分布和数据的相关结构。本文设想将多元GARCH引入多资产期权定价中,但是一般的多元GARCH的系数过多而不易估计,另一方面模型的灵活程度较小,所以用一元的GARCH模型分别对各个标的资产的收益率序列进行建模,再用Copula将各个资产的分布联接起来,这便是Copula based MGARCH模型。接下来便可以通过Monte Carlo模拟对期权进行定价。     

我国大陆地震巨灾价差期权定价研究

本文借鉴国内外相关研究结论,运用泊松分布对中国大陆地震发生频率进行拟合,并对其进行χ2检验,进一步构建模型对中国大陆地震巨灾价差期权进行蒙特卡罗模拟定价,对中国大陆地震价差期权价格的影响因素进行了实证检验,最后提出了推动中国大陆地震巨灾期权发展的建议。     

篮子期权定价的蒙特卡罗方法研究

篮子期权是多标的资产的一个投资组合期权,随着投资者对其投资组合分散化日益增长的要求,人们对这种投资组合期权的需求也不断增加.当维数不断增大时,运用蒙特卡罗模拟法来定价相对来说更可行.但是随着维数的增多,模拟的效率将大幅度下降,因此对模拟进行适当的改进是十分必要的.本文在给出篮子期权定价的蒙特卡罗模拟模型基础上,应用方差减少技术中的控制变量法进行改进,并以欧式看涨篮子期权为例,进行了模拟分析.     

亚式期权定价的模拟方法研究

由于算术平均价格亚式期权的定价没有解析公式，所以文章用Monte Carlo模拟方法通过Matlab软件编写程序对亚式期权进行了定价。发现在某些情况下，亚式期权的价值并不是国内外一些研究者所认为的低于相应的欧式期权的价值。     

资产评估中实物期权应用的探讨

实物期权是金融期权在实体经济领域应用的拓展,可用于资产价值的评估和投资策略的分析。《实物期权评估指导意见（试行）》的颁布,开辟了评估业务的新方法和新思路。与金融期权相比,实物期权中参数的选取更为复杂,实际应用时也受到更多的限制。另外,评估对象的复杂性导致评估时可能涉及多因素标的资产上的复合期权,而非普通单因素标的资产上的单个期权。本文在比较不同期权定价模型适用条件的基础上,对模型中重要影响因素和参数的确定,以及多重复合实物期权定价方法的应用进行了探讨。     

某种多资产期权的定价与研究北大核心CSSCI

本论文将引入一种期权,通过事先支付一定的成本,它能让投资者一段时期内获得多个标的资产中表现最好的那个超出执行金额的部分,这不仅能解决资金分配的问题,而且可以确保投资者不会在交易中因选择失误而悔恨不已。从本质上讲,该产品是一个欧式多资产期权,本文旨在从理论和实际操作两方面对其进行定价和研究。理论方面,本文会在假设资产收益率服从特定布朗运动的前提下,结合鞅论给出其定价公式。实操方面,本文会以蒙特卡洛模拟为基础,提出现实中对此类产品定价的方法。最后,为结合实际,本文会通过回测分析产品的特点和在避险方面的优势。     

Turbocharging Monte Carlo pricing for the rough Bergomi model

The rough Bergomi model, introduced by Bayer et al. [Quant. Finance, 2016, 16(6), 887–904], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially time-invariant, and are able to capture the term structure of skew observed in equity markets. In the absence of analytical European option pricing methods for the model, we focus on reducing the runtime-adjusted variance of Monte Carlo implied volatilities, thereby contributing to the model’s calibration by simulation. We employ a novel composition of variance reduction methods, immediately applicable to any conditionally log-normal stochastic volatility model. Assuming one targets implied volatility estimates with a given degree of confidence, thus calibration RMSE, the results we demonstrate equate to significant runtime reductions—roughly 20 times on average, across different correlation regimes.     

Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes

Lévy processes are popular models for stock price behavior since they allow to take into account jump risk and reproduce the implied volatility smile. In this paper, we focus on the tempered stable (also known as CGMY) processes, which form a flexible 6-parameter family of Lévy processes with infinite jump intensity. It is shown that under an appropriate equivalent probability measure a tempered stable process becomes a stable process whose increments can be simulated exactly. This provides a fast Monte Carlo algorithm for computing the expectation of any functional of tempered stable process. We use our method to price European options and compare the results to a recent approximate simulation method for tempered stable process by Madan and Yor (CGMY and Meixner Subordinators are absolutely continuous with respect to one sided stable subordinators, 2005).     

On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives

This paper analyses the robustness of Least-Squares Monte Carlo, a technique proposed by Longstaff and Schwartz (2001) for pricing American options. This method is based on least-squares regressions in which the explanatory variables are certain polynomial functions. We analyze the impact of different basis functions on option prices. Numerical results for American put options show that this approach is quite robust to the choice of basis functions. For more complex derivatives, this choice can slightly affect option prices. This revised version was published online in June 2006 with corrections to the Cover Date.     

Decision-making in incomplete markets with ambiguity—a case study of a gas field acquisition

We apply utility indifference pricing to solve a contingent claim problem, valuing a connected pair of gas fields where the underlying process is not standard Geometric Brownian Motion and the assumption of complete markets is not fulfilled. First, empirical data are often characterized by time-varying volatility and fat tails; therefore, we use Gaussian generalized autoregressive score (GAS) and GARCH models, extending them to Student’s t-GARCH and t-GAS. Second, an important risk (reservoir size) is not hedgeable. As a result, markets are incomplete which makes preference free pricing impossible and thus standard option pricing methodology inapplicable. Therefore, we parametrize the investor’s risk preference and use utility indifference pricing techniques. We use Least Squares Monte Carlo simulations as a dimension reduction technique in solving the resulting stochastic dynamic programming problems. Moreover, an investor often only has an approximate idea of the true probabilistic model underlying variables, making model ambiguity a relevant problem. We show empirically how model ambiguity affects project values, and importantly, how option values change as model ambiguity gets resolved in later phases of the projects. We show that traditional valuation approaches will consistently underestimate the value of project flexibility and in general lead to overly conservative investment decisions in the presence of time-dependent stochastic structures.     

The role of stochastic volatility and return jumps: reproducing volatility and higher moments in the KOSPI 200 returns dynamics

This paper investigates the role of stochastic volatility and return jumps in reproducing the volatility dynamics and the shape characteristics of the Korean Composite Stock Price Index (KOSPI) 200 returns distribution. Using efficient method of moments and reprojection analysis, we find that stochastic volatility models, both with and without return jumps, capture return dynamics surprisingly well. The stochastic volatility model without return jumps, however, cannot fully reproduce the conditional kurtosis implied by the data. Return jumps successfully complement this gap. We also find that return jumps are essential in capturing the volatility smirk effects observed in short-term options.

高科技上市公司内在价值评估：基于连续型实物期权模型的实证研究

高科技企业高度不确定性的特征决定其本身具有潜在的期权价值,所以,传统的评估方法难以客观地评估出高科技公司内在价值.针对高科技公司高度不确定性的特征,引入Schwarz的连续型实物期权模型,在对模型进行离散化处理后,利用蒙特卡洛模拟对中国软件开发板块的高科技上市公司进行价值评估,并由此对整个软件开发板块的高科技上市公司价值评估进行的实证.研究发现,实物期权模型能较好地对高科技企业进行价值评估.