随机利率下时间期权定价模型研究

发布时间：2018-03-26 16:39

本文选题：时间期权　切入点：随机利率　出处：《西南财经大学》2013年硕士论文

【摘要】：时间期权是OTC市场中奇异期权的一种。相比固定到期日的普通期权,它的到期日是随机的,这个随机到期日依赖于已经累积标的资产收益率的方差。当累积的方差等于预先设定的目标方差时,该期权自动到期,该时间为时间期权的到期日；当累积的方差小于预先设定的目标方差时,该期权不会被执行。当波动率增加时,时间期权的到期日会变短；当波动率减少时,时间期权的到期日会被自动延长。在以前的研究中,假定无风险利率是常数,忽略掉了无风险利率变动的风险。事实上,当无风险利率变动时,会影响标的资产的价格波动率,从而影响时间期权的到期日及价需格。因此要要考虑无风险利率在随机的情况下,利率与标的资产累计波动率的相关性。本篇论文对Vasicek模型下的时间期权进行定价研究。在假定利率是随机的情况下,使用鞅方法和随机分析等数学工具给出时间期权的定价公式。该公式的获得为进一步理解和应用时间期权起到非常重要的作用。
[Abstract]:Time option is a kind of strange option in OTC market. Compared with the ordinary option with fixed maturity date, its maturity date is random. The random maturity date depends on the variance of the accumulated return on the underlying asset. When the accumulated variance is equal to the predetermined target variance, the option automatically expires, which is the maturity date of the time option; When the accumulated variance is less than the predetermined target variance, the option will not be executed. When the volatility increases, the maturity date of the time option will become shorter; when the volatility decreases, the maturity date of the time option will be automatically extended. In previous studies, it was assumed that the risk-free interest rate was constant, ignoring the risk of risk-free interest rate changes. In fact, when the risk-free interest rate changed, it affected the price volatility of the underlying asset. Therefore, it is necessary to consider the correlation between the interest rate and the accumulated volatility of the underlying asset in the case of random risk free interest rate. This paper studies the pricing of time options in Vasicek model. Under the assumption that the interest rate is stochastic, The pricing formula of time option is given by means of martingale method and stochastic analysis, which plays an important role in further understanding and application of time option.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224

【共引文献】