An Efficient Algorithm to Price Lookback Options With Multinomial-Lattices Model

• Main Authors: Po-tsang Chen, 陳柏蒼
• Other Authors: Wen-i Chuang
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/27885579940173997862

碩士 === 國立臺灣科技大學 === 財務金融研究所 === 97 === For the valuation of lookback option, this study intends to establish an one-state variable multinomial lattices model to evaluate lookback option based on the notions of changing numeraire in Cheuk and Vorst (1997) and the tree model in Ritchken and Trevor (1999). With the framework of one-state variable multinomial lattices model, the results of continues-sampled lookback option prices can converge to efficiently the closed-form solution derived by Conze and Viswanathan (1991). The results of discrete-sampled lookback option prices can correctly approach the results of the Monte Carlo estimation and the closed-form solution derived by Heynen and Kat (1995). For the valuation of the continues-sampled lookback options, this model can generate more accurate results with the increase of number of multinomial lattices’ branches and the number of time steps, but there is still small bias between our results and the closed-form solution. For the valuation of the discrete-sampled lookback options, the more frequently is the observation number, this model can obtain correct result more fast and accurately. The results with one-state variable multinomial lattices model can not only approach the results of Monte Carlo estimation fast, but also are always within 95% confidence interval. In addition, this model can have better efficiency than the numerical implementation of the closed-form solution in Heynen and Kat (1995) for pricing discrete-sampled lookback options. Consequently, one-state variable multinomial lattices model of this study can generate more accurate results in real life.