不完全信息下期权定价研究

发布时间：2018-01-10 12:18

本文关键词：不完全信息下期权定价研究　出处：《浙江理工大学》2013年硕士论文　论文类型：学位论文

【摘要】：实物期权理论在风险投资领域占有重要地位,也是学术界研究的热点问题之一。然而,由于数据的偏差、缺失、波动,人们认知能力的有限,以及信息发布者的刻意隐瞒,投资者能够获得的信息往往是不完全的。这就对建立在完全信息假设下的传统风险项目评估方法提出了严峻的挑战。因此,研究不完全信息下的实物期权定价问题更加具有意义和价值。本文研究了不完全信息下的实物期权定价问题,研究工作主要从以下两个方面展开：针对项目投资过程中有现金流产生的情况,研究资产价值θt服从随机波动率时的实物期权定价。本文用投资过程中产生的可观测的现金流ξt来衡量不完全信息,并将其描述为一个均值回复过程。通过非线性滤波理论将信息模型加入到不可观测的资产价值模型中,得到θt的条件估计的随机表达式。这样便将不断更新的信息随时反映到了风险项目的估值过程中,使得评估结果更加可靠。再借助于Ito引理得到实物期权价格满足的偏微分方程,分析定价方程成立的初边值条件(根据实际背景得到),然后用有限差分方法进行数值求解。通过分析数值结果提出科学合理的投资决策方案。针对投资周期较长且投资前期不会产生现金流的情况,研究资产价值服从跳跃CIR情形下的实物期权定价。考虑到实际投资过程中同时存在着“正常的”(normal)和“稀有的”(abnormal)信息,本文在连续Cox-Ingersoll-Ross(CIR)模型的基础上加上离散的Poisson跳跃过程来描述资产价值的随机变动,用Bellman方程和Ito引理推导出定价方程。再将混合方程的状态空间离散化得到Markov-chain,在此基础上分析资产价值的状态转移情况。通过分析最优投资阈值及期权价格,并和跳-扩散模型作比较,阐述跳跃CIR模型的潜在优势。最后,本文分析了某房地产公司的投资案例,结果有力地说明了本文所研究的模型的合理性和优越性。
[Abstract]:The real option theory occupies an important position in the field of venture capital, is also one of the hot topics of academic research. However, due to the deviation of data, lack of volatility, people's limited cognitive ability, and deliberately concealed information publisher, investors can obtain the information is often incomplete. This poses a severe challenge to assess traditional methods of risk of project based on complete information assumption. Therefore, the research of real option pricing under incomplete information is more significant and valuable.
This paper studies the pricing of real options under incomplete information. The research work is mainly carried out from the following two aspects:
According to the condition of cash flow generated in the process of investment, the research of asset value is t to real option pricing with stochastic volatility. The incomplete information to measure the observable cash flow. This paper used t in the investment process, and describes it as a mean reverting process. Through nonlinear filter theory the information model added to the asset value model can not be observed in the expression of T by random theta estimation. This condition will continue to update the information at any time to reflect the valuation process risk of the project, which makes the evaluation more reliable. In the Ito lemma to obtain a partial differential equation satisfied by the real option price, analysis the boundary conditions established pricing equation (according to actual background), and then use the finite difference method. The numerical solution of scientific and rational investment decisions are proposed through the analysis of the numerical results.
Cash flow situation due to the long investment cycle and the investment will study the value of the assets subject to real option pricing under jump CIR. Considering the actual investment "also exist in the process of normal" (normal) and "rare" (abnormal), Cox-Ingersoll-Ross (CIR) based on the continuous random variable model based on the discrete Poisson jump process to describe the value of the assets, using the Bellman equation and the Ito lemma to deduce the pricing equation. The state space discretization and then mixed equations were obtained by Markov-chain, based on the analysis of the state transition of the asset value. Through the analysis of the optimal investment threshold and option prices, and a jump diffusion model for comparison, the potential advantages of the jump CIR model.
Finally, this paper analyzes the investment case of a Real Estate Company, and results in a powerful explanation of the rationality and superiority of the model studied in this paper.

【学位授予单位】：浙江理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.91;O211.6

【共引文献】