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摘要翻译：
时间相关的双障碍期权是一种衍生证券，如果在时间间隔$[0,t]$期间没有碰到连续的时间相关障碍$B_\PM:[0,t]\到\RR_+$中的任何一个，则在到期时交付终端值$\phi(S_T)$。利用概率方法，我们得到了一类广泛的支付函数$\phi$、障碍函数$b\pm$和线性扩散$(S_t)_{t\in[0,t]}$的障碍期权价格分解为相应的欧式期权价格减去障碍溢价的分解。我们证明了障碍溢价可以表示为沿障碍$b_\pm$的积分和，即期权的delta$\delta_\pm:[0,t]\到在障碍处的rr$之间的积分和，并且这对函数$(\delta_+,\delta_-)$求解第一类Volterra积分方程组。在常双势垒情况下，给出了该系统的半解析解，并简要讨论了含时情况下的数值算法。
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英文标题：
《Local time and the pricing of time-dependent barrier options》
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作者：
Aleksandar Mijatovic
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
A time-dependent double-barrier option is a derivative security that delivers the terminal value $\phi(S_T)$ at expiry $T$ if neither of the continuous time-dependent barriers $b_\pm:[0,T]\to \RR_+$ have been hit during the time interval $[0,T]$. Using a probabilistic approach we obtain a decomposition of the barrier option price into the corresponding European option price minus the barrier premium for a wide class of payoff functions $\phi$, barrier functions $b_\pm$ and linear diffusions $(S_t)_{t\in[0,T]}$. We show that the barrier premium can be expressed as a sum of integrals along the barriers $b_\pm$ of the option's deltas $\Delta_\pm:[0,T]\to\RR$ at the barriers and that the pair of functions $(\Delta_+,\Delta_-)$ solves a system of Volterra integral equations of the first kind. We find a semi-analytic solution for this system in the case of constant double barriers and briefly discus a numerical algorithm for the time-dependent case.
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PDF链接：
https://arxiv.org/pdf/0809.1747
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