【作者】 杨春；

【导师】 王健；

【作者基本信息】 湘潭大学 ， 基础数学， 2001， 硕士

【摘要】 近年来，随着金融市场的逐步发展与完善，投资者在追求投资回报与规避投资风险之间的矛盾日趋明显。越来越多的投资者希望通过期权投资策略进行套期保值。其中如何确定期权交易价格成为了关键性问题。1973年，F. Black & M. scholes 发表了题为《期权定价与法人义务》的文章，成功求解了欧式期权定价问题。由此，如何构造合理的期权模型来模拟市场中的运作成为金融数学领域研究的主流。因此，本文研究的主要问题是在Black-Scholes模型上，对模型进行一般化。并针对外汇期权的定价模型进行了求解，论证了相应的期权投资策略在实际运用中的意义和作用。本文内容如下：第一章：主要介绍了本课题来源、目的、国内外研究现状和我们所作研究的理论依据、研究方案和拟解决的问题和意义。第二章：根据侯振挺等［２］提出的Markov骨架过程，我们定义了一类特殊的马氏骨架过程，并建立和求解了交易货币价格服从此类特殊过程的欧式外汇期权定价模型。此模型与Black-scholes模型的根本区别在于：本模型中的标的资产价格不是一般的连续随机过程，而是一类特殊的马氏骨架过程。它考虑了标的资产的价格在时间上连续，而空间上连续和离散的变化。因此，较好的解释了由非经济因素带来的证券价格的异常跳跃。第三章：应用上述模型对实际案例进行分析。在墨西哥银行外汇储备案例中，我们提出中央银行通过构造一类卖出美元的期权进行外汇储备从而达到减小对外汇市场冲击的目的的可能性。给出了估计该类期权价格和分析使用概率的一类方法。并对决定该期权价格的各参数变动时相应的期权价格的灵敏度进行分析。第四章: 总结与展望更多还原

【Abstract】 In the recent years, with the development and consummation of the financial market, the investors’ contradiction between the expected return rate and the risk becomes more and more intense. Investors expect to avoid the financial risk by the option investments’ strategy, and then achieve the tuition of hedging. So how to price the option becomes the key problem. In 1973, F. Black & M. Scholes had published the famous paper —《Option Pricing and The Corporate liability》in which they had successfully solved the pricing problem of European option. So how to simulate the actual operate in financial market via the reasonable option model become the study’s mean-stream in the area of financial mathematics. So the main problem we have studied in the paper is how to generalize the Black-Scholes pricing model. And then we have solved the pricing model of foreign exchange option and demonstrated the meaning and the effect of the option investment strategy too.The context as follows: Chapter 1: At first, we have introduced the origin and the purpose of the problem, and the present conditions of the research work, which had been done by foreigners or compatriots. Then we have discussed about the theoretical basis, the research method of our work and the content and the meaning about the problems that we have solved. Chapter 2: On the basis of Markov skeleton process that proposed by Zhenting Hou [1], we have defined a kind of special Markov Skeleton Process. And we have established and solved the model of European foreign exchange option in which the foreign exchange price process obeys the special Markov framework process. The essential difference <WP=5>between the Black-Scholes model and ours is that the underlying asset price process is not a general continuous stochastic process in our model, but a special Markov Skeleton Process. It has taken into account that the underlying assets price process, which is continuous about time but has continuous and discrete changes in space. So our model can explain the abnormal jump of security price affected by uneconomical factors very well. Chapter 3: We have analyzed the actual instance on the basis of the pricing model of foreign exchange option that we have established in chapter 2. We propose the probability of acquiring foreign exchange on the exchange market, while taking care to avoid generating pressure on the exchange rate and to avoid sending signs that could be erroneously interpreted by the financial markets. And then we have given a method that how to price the option and analysis the probability of using the options. At last we have analyzed the sensitivity of the option price when the parameters that contribute to the determination of its price are changing. Chapter 4: Conclusion and Prospects.更多还原