CIR随机利率模型下强路径依赖期权定价问题

发布时间：2018-05-29 03:38

本文选题：亚式期权 + 回望期权　；参考：《西南财经大学》2012年硕士论文

【摘要】：强路径有关期权在期权到期日的收益不仅依赖于当天标的资产的价格,而且依赖于在整个(或部分)有效期内期权标的资产价格历程。主要有依赖于价格的平均值的亚式期权和依赖于价格最大(小)值的回望期权。由于亚式期权具有强路径依赖性,所以其风险要小于标准期权,那么,价格也要低于标准期权。同样回望期权的收益对标的资产在期权有效期内价格演化的依赖也非常强,这类期权的收益高,相应的价格十分昂贵。由于这类期权的强路径依赖性,其定价问题也变得相当复杂。在以前的期权定价问题研究中,通常假定利率为常数,这样就可以使得问题变得相对较为简单。然而,在期权定价问题中市场是不稳定的,即便是短期利率也是不断发生变化的。那么,通常在期权定价时利率在期权有效期内不变这一假定,就不能够满足实际运用中的需要。因此,在研究期权定价时就可以考虑加入利率不确定性这一因素。本文在CIR随机利率模型下,建立了具有浮动敲定价格亚式期权以及回望期权的定价模型；同时,在考虑期权定价问题时加入了标的股票资产支付红利以及可提前执行这两种因素。并利用有限差分法给出了相应模型的数值解。最后分别给出实例,利用MATLAB编程求出其数值解。本文所提出的CIR随机利率模型下亚式期权和回望期权定价模型更符合实际。
[Abstract]:The yield of the option on the maturity of the option depends not only on the price of the underlying asset on that day, but also on the price process of the underlying asset during the whole (or part) period of validity of the option. There are mainly Asian options which depend on the average value of the price and the lookback options which depend on the maximum (small) value of the price. Because Asian option has strong path dependence, its risk is smaller than standard option, so the price is lower than standard option. The return of the option is also very dependent on the price evolution of the underlying asset during the period of validity of the option. The return of this kind of option is high and the corresponding price is very expensive. Because of the strong path dependence of this kind of option, the pricing problem becomes quite complicated. In previous studies of option pricing, the interest rate is usually assumed to be constant, which makes the problem relatively simple. However, the market is unstable in options pricing, and even short-term interest rates are constantly changing. Therefore, the assumption that the interest rate will not change during the term of the option when the option is priced can not meet the needs of practical application. Therefore, interest rate uncertainty can be taken into account when studying option pricing. In this paper, under the CIR stochastic interest rate model, we establish the pricing model of Asian option with floating strike price and the option of looking back, and at the same time, When considering option pricing, two factors are added: dividend payment of underlying stock assets and early execution. The numerical solution of the model is given by the finite difference method. Finally, examples are given and the numerical solution is obtained by MATLAB programming. In this paper, the pricing model of Asian option and lookback option under CIR stochastic interest rate model is more practical.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.9;F224

【参考文献】