以Dirichlet Lattice模型評價回顧型選擇權

Abstract

對於回顧型選擇權的評價，本篇研究是利用 Kuan and Webber (2003a)所提出的 Dirichlet lattice method。此項方法使用 Brownian motion的conditional hitting time distribution來調整二元樹估價法中股價波動的機率。在這方法之中，可以估計股價在兩次觀察期之間所可能達到的最大值與對應的機率，使評價的準確度能大幅提升。在連續觀察時間情況下本研究之評價模型能快速精確的逼近 Conze and Viswanathan (1991)推導的回顧型選擇權封閉解，並且可以用遠少於現有方法的切割期數得到更加精確的結果。這些優點使本方法成為現有方法的重要補充。

For the valuation of lookback option, this study extend the Dirichlet lattice method suggested by Kuan and Webber (2003a). Kuan and Webber (2003a) describe a Dirichlet lattice method using the conditional hitting time distribution of the underlying asset price. In this method, the possible maximum stock prices and corresponding probabilities are estimated in every time step between observations, resulting in significant improvement in accuracy. With the framework of one-state variable binomial lattice model, the result of continues-sampled lookback option prices can converge to efficiently the closed-form solution derived by Conze and Viswanathan (1991). Compared to CRR model, this method can get more accurate result with much fewer time steps. All these merits make the method an important addition to the existing tools.