【作者】 翟云飞；

【导师】 张曙光； 张强；

【作者基本信息】 中国科学技术大学 ， 金融工程， 2010， 博士

【摘要】 在本文中,我们研究当金融市场是随机波动率的非完全市场时,奇异期权(包括亚式期权,障碍期权和回望期权)的定价理论和风险管理理论。利用Dannis Yang提出的随机控制应用于期权定价的理论,我们导出在非完全市场上,奇异期权的定价也是与投资者持有头寸相关联的。在指数效用函数的假定下,我们得到决定奇异期权均衡价值的偏微分方程,随机控制理论同时也给出最优的交易策略。众所周知,前人基于无套利定价理论在随机波动率的市场上给出期权的价格中,含有一个未定的参数(λ)-marke price ofrisk,不同的市场假设下,λ有不同的表现形式,如Heston著名的工作就是在这个参数是波动率的线性函数的假设下做出的。基于我们随机控制动态推导的方法,我们发现λ是与投资者持有头寸和投资品种相关的。在投资者只持有欧式期权和只持有亚式期权的两种情况下,λ即使对相同的投资者也是不同的。遵循Dennis Yang的定义,我们称这个参数为personal price of risk on Asian option(或者Lookback option)。我们也讨论了当市场上包含所有金融期权产品,欧式期权和路径依赖的奇异期权,这些期权的定价是相互影响的。如,这时的欧式期权也会与回望期权的smdx(股票实现的最大值)有关,而不再是路径独立的。在研究这些期权的投资组合时,我们依然能够得到λ的显示表达式,它是与投资组合的各种期权的头寸相关,我们称之为"personal price of risk on Portfolio"。在得到各种奇异期权在非完全市场的定价方程后,我们发展了解这类定价方程的有效数值方法。在给出奇异期权理论性质的同时,我们给出了期权价格的数值解,验证了理论分析的正确性。最后,我们分析了最近市场上流行的累积期权(Knock Out Discount Accu-mulator),给出了在完全市场上基于风险中性的鞅测度框架下的期权定价公式,并分析了该类期权的一些套期保值参数。更多还原

【Abstract】 In this thesis, we study the exotic option Pricing theory and risk management theory under incomplete market, including, Asian options, Barrier options, Lookback options.Following Dennis Yang, we developed how to price exotic options with stochastic volatility in incomplete market. Under the exponential utility preference, we show that the fair price of exotic options is related to investor’s position holding. As well-known, based on the arbitrage pricing theory the PDE satisfied by the option price is derived with a undetermined parameter-market price of risk. Under different assumption, the market price of risk is also different. Based on the dynamic derivation methodology, we get an explicit expression for market price of risk, and we found that market price of risk is related to the position and the type of option contained in the portfolio. Fol-lowing Dennis Yang, we call it personal price of risk on Asian option(or Lookback option,and so on)We also discussed the portfolio optimization problem under stochastic volatility framework when the market consists all type of options, i.e. vanilla options and exotic options, we found that all options’ price is mutual dependence, i.e. the fair price of vanilla option is dependent on smax and never path-independence when the portfolio contain European option and Lookback options. Furthermore, we give the numerical result of option price, and verified the theoretical properties of options.Finally, we analysised the KODA option(Knock Out Discount Accumulator) which is popular in Hong Kong market recently. Under the risk-neutral martingale frame-work, we give an explicit formula for KODA option, and caculus some Hedging para-meters, like Delta and Gamma.更多还原