双因素随机波动率跳扩散模型下复合期权定价

发布时间：2019-06-27 18:30

【摘要】：期权定价一直是金融数学、金融工程领域研究的核心问题之一.随着金融市场的快速发展,以及金融公司、投资者对复杂金融衍生工具的喜爱,许多金融机构不断推出新型衍生产品,因此新型期权(也称奇异型期权)就随之出现并得到了迅速发展.复合期权是最常见,应用最广泛的奇异期权中的一种.它是期权的期权,所以有两个到期日和两个执行价格.因为受到两个到期日的影响,与标准的期权相比,复合期权对波动率更加敏感,导致其价值的判断更加复杂.然而,在复杂多变的金融市场和发展时快时慢的经济环境下,传统的Black-Scholes模型,跳扩散模型以及单因素随机波动率模型已不再适用,因此,本文提出了在双因素随机波动率跳扩散模型下对复合期权进行研究.本文从多因素角度出发,全面考虑金融市场长期风险和短暂风险引起的波动以及经济发展时快时慢的特征,综合跳扩散模型和随机波动率模型的优点,建立双因素随机波动率跳扩散模型.在该模型下首先运用Feynman-Kac定理,Ito公式,多维随机变量的联合特征函数以及Fourier反变换等方法,推导出标准欧式复合期权定价公式.通过数值实例比较九类模型下复合期权价格随S0的异动情况,分析了短期、长期两种不同到期日的隐含波动率情况,以及短期、长期波动率的跳跃强度和相关系数对复合期权价格的影响,发现该模型能更好的捕捉隐含波动率期限结构的时变特征,短期、长期波动率的相关系数对复合期权价格都有正向的冲击,并且在短期波动率下复合期权价格波动比较剧烈,而在长期波动率下复合期权价格趋于更平稳状态.其次在本文模型下将单期复合期权推广到多期复合期权定价,运用多维随机变量的联合特征函数和多维傅里叶反变换方法,推导出多期复合期权定价公式.通过数值实例比较在Merton模型,SVIJ模型与本论文模型下多期复合期权的价格,分析了多期复合期权受短期波动率相关参数的影响,发现跳跃项的加入和双因素随机波动率的考虑对多期复合期权定价结果影响较大,并且短期波动率相关参数对多期复合期权价格会造成不同冲击.所以,在实际金融市场中,投资者不仅要关注长期波动率,更应该重视短期波动率及其相关参数引起的股价波动.在双因素随机波动率跳扩散模型下研究复合期权定价问题更适用于现实金融市场,为复合期权定价研究提供更为有力的理论依据和方法,同时也为风险管理者能做出更有效的判断提供了参考依据。
[Abstract]:Option pricing has always been one of the core issues in the field of financial mathematics and financial engineering. With the rapid development of financial markets and the love of financial companies and investors for complex financial derivatives, many financial institutions continue to launch new derivatives, so new options (also known as odd options) have emerged and developed rapidly. Compound option is one of the most common and widely used singular options. It is an option for an option, so there are two due dates and two execution prices. Because of the influence of two maturity dates, compared with the standard option, the compound option is more sensitive to volatility, which makes the judgment of its value more complex. However, in the complex and changeable financial market and the fast and slow economic environment, the traditional Black-Scholes model, jump diffusion model and single factor random volatility model are no longer applicable. Therefore, this paper proposes to study the compound option under the two factor random volatility jump diffusion model. From the point of view of many factors, this paper comprehensively considers the fluctuation caused by long-term risk and temporary risk in financial market and the characteristics of fast and slow economic development, and synthesizes the advantages of jump diffusion model and random volatility model, and establishes a two-factor random volatility jump diffusion model. Under this model, the standard European compound option pricing formula is derived by using Feynman-Kac theorem, Ito formula, joint eigenfunction of multidimensional random variables and Fourier inverse transformation. By comparing the variation of compound option price with S0 under nine kinds of models, this paper analyzes the implied volatility of two different maturity dates of short-term and long-term, and the influence of jump intensity and correlation coefficient of short-term and long-term volatility on the price of compound option. It is found that the model can better capture the time-varying characteristics of term structure of implied volatility. The correlation coefficient of long-term volatility has a positive impact on the price of composite options, and the price of composite options fluctuates violently under the short-term volatility, while the price of composite options tends to be more stable under the long-term volatility. Secondly, under the model of this paper, the single-period compound option is extended to the pricing of multi-period compound option, and the pricing formula of multi-period compound option is derived by using the joint characteristic function of multi-dimensional random variables and the method of multi-dimensional Fourier transform. Through the comparison of the prices of multi-period composite options under Merton model, SVIJ model and this model, this paper analyzes the influence of short-term volatility on the price of multi-period composite options. It is found that the addition of jump term and the consideration of two-factor random volatility have great influence on the pricing results of multi-period composite options, and the related parameters of short-term volatility will have different impacts on the price of multi-period composite options. Therefore, in the actual financial market, investors should not only pay attention to the long-term volatility, but also pay attention to the stock price volatility caused by the short-term volatility and its related parameters. The study of compound option pricing under the two-factor random volatility jump-diffusion model is more suitable for the real financial market, which provides a more powerful theoretical basis and method for the study of compound option pricing, and also provides a reference for risk managers to make more effective judgment.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F830.9;O211.6

【相似文献】