【作者】 杨崴；

【导师】 韩月才；

【作者基本信息】 吉林大学 ， 概率论与数理统计， 2018， 硕士

【摘要】 最近几年,目标波动率期权成为一种新的投资模式,需要参考波动率的变动情况.不同于纯波动率衍生品,这些新的产品依赖于与市场相关的资产及其未来的现实波动率作为调整因子.前人在给定波动率值时,单一因子的Heston波动率模型可以产生或者陡峭或者平缓的曲线,但是不能同时给出陡峭及平缓综合性的市场曲线.这样固定波动率值的单一因子模型具有很强的限制性.所以在求解目标波动率期权的定价公式时,考虑波动率与资产收益之间的相关系数是很有必要的.本文通过研究多因子随机波动率模型对目标波动率期权定价的影响,考虑了两个因子的Ornstein-Uhlenbeck过程来分析目标波动率期权.我们基于两个因子的Ornstein-Uhlenbeck过程,证实了资产收益和方差过程之间的相关系数并非常数,并给出了远期起始的目标波动率期权的定价公式及形式解.这些期权的定价公式可以让投机者考虑标的资产和现实波动率的情况来决定是否购入期权,更好的判断其价值.更多还原

【Abstract】 In recent years,the target volatility is a new kind of products.It’s different from pure volatility derivatives,the yield of it depends on the underlying assets and the realized variance.In equity options markets,the slope of the curve to a large extent depends on the level of volatility.Given the volatility,volatility of a single factor of Heston model can generate steep or flat curve,but cannot be given a steep and gentle curve of the market.Hence,this model has a strong restrictive.The payoff of target volatility options is a function of about the underlying asset and the reality volatility,and it is necessary to consider the correlation between the volatility of assets and profits.In this paper,we study the target volatility in option pricing,consider the two factors of Ornstein-Uhlenbeck process to analyze the target volatility options(TVO).Based on two factors of Ornstein-Uhlenbeck process,we presented to the forward-start TVO options pricing formula,and last,we solve the pricing problem with the Laplace transform and obtain a semi-closed form solution.The pricing formula of these options allows the speculator to take into account the underlying asset and the actual volatility to decide to buy the option or not,and it’s helpful to judge the value of the option.更多还原