双因子跳跃—扩散随机波动率模型在实物期权的运用

发布时间：2018-06-23 17:06

本文选题：隐含波动率 + 实物期权　；参考：《西南财经大学》2014年硕士论文

【摘要】：房地产是国民经济稳定发展是关系到民生的重要支柱。但是,因为房地产开发周期长,高投入,大的价格波动的特性,使得房地产行业正面临着巨大的不确定性,存在着巨大的风险。房地产市场不确定呼唤科学的投资理念的发展,因此,使房地产投资在一个不确定的环境的理论研究具有重要的意义。房地产投资的主体是各房地产开发商,他们做房地产开发和投资的科学决策,对是否市场风险的显著影响,但会影响房地产行业的健康发展国民经济的持续稳定发展。本文主要得到以下结果：第一,我们建立了双因子跳跃-扩散随机波动率模型,随机波动率服从一个的随机过程。在求解欧式期权定价公式中,引入了价外指数,考虑到了标的资产的隐含波动率,通过对隐含波动率泰勒级数展开,得到了一个线性的渐进表达式,并具有很好的计算速度和精确度。第二,把双因子跳跃-扩散随机波动率模型创新性应用到房地产项目中,更加有效的对项目具体价值进行评估。为决策者提供了一个更加精确的数字。本文内容安排：第一部分为绪论,介绍房地产业对国民经济的增长贡献主要包括3个方面：(1)作为投资的组成,房地产开发投资对GDP增长具有直接贡献；(2)房地产带动关联产业对GDP增长具有间接贡献；(3)房地产开发投资通过对消费的拉动,引起GDP增长。影响商品房价格的风险因素有很多,诸如制度因素、政策因素、人口因素、技术因素、经济因素、国际因素、心理因素、灾害因素等等。这些具体的因素又可以从不同角度分为不同的类型。并对每一种因素加以具体分析。简述内容框架与研究方法。第二部分为基本知识,包括期权、实物期权、随机分析、维纳过程、伊藤引理的简单介绍,以及Black-Scholes-Merton公式的证明。第三部分为处理双因子跳跃-扩散随机波动率模型。第四部分为考虑隐含波动率的处理。第五部分对渐进表达式的证明。第六部分双因子跳跃-扩散随机波动率模型在实物期权中的实际运用。第七部分为总结与展望。
[Abstract]:Real estate is a stable development of the national economy is an important pillar related to the people's livelihood. However, because of the characteristics of long period of real estate development, high investment and large price fluctuation, the real estate industry is facing great uncertainty and great risks. The uncertainty of real estate market calls for the development of scientific investment concept. Therefore, it is of great significance to study the theory of real estate investment in an uncertain environment. The main body of real estate investment is the real estate developers, who make scientific decisions on real estate development and investment, which have a significant impact on the market risk, but will affect the healthy development of the real estate industry and the sustained and stable development of the national economy. In this paper, the following results are obtained: first, we establish a two-factor hopping diffusion stochastic volatility model, which is followed by a stochastic process. In the solution of European option pricing formula, the extravalency index is introduced. Considering the implied volatility of underlying assets, a linear asymptotic expression is obtained by the Taylor series expansion of implied volatility. And has the very good computation speed and the accuracy. Secondly, the double factor jump-diffusion stochastic volatility model is applied to the real estate project to evaluate the specific value of the project more effectively. It provides a more accurate number for decision makers. The first part is introduction, which introduces the contribution of real estate industry to the growth of national economy in three aspects: (1) as the composition of investment, investment in real estate development has direct contribution to GDP growth; (2) the real estate drive related industries have indirect contribution to GDP growth; (3) the real estate development investment leads to GDP growth by stimulating consumption. There are many risk factors affecting the price of commercial housing, such as institutional factors, policy factors, population factors, technical factors, economic factors, international factors, psychological factors, disaster factors and so on. These specific factors can be divided into different types from different angles. And to each kind of factor carries on the concrete analysis. This paper briefly introduces the content framework and research methods. The second part is the basic knowledge, including options, real options, stochastic analysis, Wiener process, Ito Lemma, and the proof of Black-Scholes-Merton formula. The third part deals with the double-factor jump-diffusion stochastic volatility model. The fourth part is dealing with implicit volatility. The fifth part proves the asymptotic expression. The sixth part is the practical application of double-factor jump-diffusion stochastic volatility model in real options. The seventh part is the summary and prospect.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F299.23

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