Pricing Moving-Average-Lookback Options

• Main Authors: Chih-Hao Kao, 高志豪
• Other Authors: Yuh-Dauh Lyuu
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/21107546771208443477

碩士 === 國立臺灣大學 === 財務金融學研究所 === 90 === This thesis investigates computational methods for pricing complex path-dependent derivative securities, especially geometric- and arithmetic-moving-average-lookback options. The latter security was first issued by Polaris Securities in 1999. Our methodology can be easily modified to price similarly structured options issued by other securities firms. The moving-average-lookback option is a call option struck at the minimum moving average of underlying asset price. We consider both geometric averaging and the much harder arithmetic averaging used by Polaris. The pricing results show that our algorithms on the CRR model converge quickly to the correct value. We also find that the price difference between geometric averaging and arithmetic averaging is slight. As it takes much less time to price the geometric-moving-average version, it serves as a good approximation to the arithmetic-moving-average version. The least-squares simulation, introduced by Longstaff and Schwartz (2001), can be applied to price American-style moving-average-lookback options. Compared with our algorithms, the least-squares approach systematically undervalues the options. When applied to the two arithmetic-moving-average-lookback options issued by Polaris Securities in 1999, our algorithm prices them almost exactly. The numerical delta and gamma of the options are also investigated.