Numerical Evaluation of Dynamic Behavior of Ornstein–Uhlenbeck Processes Modified by Various Boundaries and its Application to Pricing Barrier Options
Numerical Evaluation of Dynamic Behavior of Ornstein–Uhlenbeck Processes Modified by Various Boundaries and its Application to Pricing Barrier Options
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DOI：
10.1007/s11009-009-9152-4
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发表时间：
2011-05
影响因子：
0.9
通讯作者：
Jun-ya Gotoh;Hui Jin;U. Sumita
中科院分区：
文献类型：
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作者：
Jun-ya Gotoh;Hui Jin;U. Sumita
在金融工程中，人们经常遇到障碍选项，即如果标的资产价值过高或过低，就采取合同中承诺的行动。为了计算相应的价格，有必要捕捉受边界修正的相关随机过程的动态行为。据作者所知，目前还没有可用的算法方法来以系统的方式反复计算这些价格。本文的目的是基于Sumita等人建立的Ehrenfest近似方法，开发计算算法来捕捉受各种边界修改的Ornstein-Uhlenbeck过程的动态行为（J Oper Res Soc jn 49:256 - 278,2006）。作为一个应用，我们评估了在时间τ m到期的看涨和卖出看涨期权的价格，并将执行价格写在时间met到期的贴现债券上，证明了所提出的计算算法的实用性、速度和准确性。
In financial engineering, one often encounters barrier options in which an action promised in the contract is taken if the underlying asset value becomes too high or too low. In order to compute the corresponding prices, it is necessary to capture the dynamic behavior of the associated stochastic process modified by boundaries. To the best knowledge of the authors, there is no algorithmic approach available to compute such prices repeatedly in a systematic manner. The purpose of this paper is to develop computational algorithms to capture the dynamic behavior of Ornstein-Uhlenbeck processes modified by various boundaries based on the Ehrenfest approximation approach established in Sumita et al. (J Oper Res Soc Jpn 49:256–278, 2006). As an application, we evaluate the prices of up-and-out call options maturing at timeτMwith strike priceKSwritten on a discount bond maturing at timeT, demonstrating the usefulness, speed and accuracy of the proposed computational algorithms.