Numerical Methods for Pricing Path-Dependent Options

• Main Authors: Robin Draw, 卓啟翔
• Other Authors: Lyuu Yuh-Dauh
• Format: Others
• Language: en_US
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/53337066816800745803

碩士 === 國立臺灣大學 === 資訊工程學研究所 === 88 === With the rapid growth of the financial market, an increasingly large number of sophisticated options are traded in the over-the-counter market to meet clients'' needs. Path-dependent options are such sophisticated options. A reset option is a kind of path-dependent option that allows the exercise price to be reset when the price of the underlying asset ever hits the reset barrier during its life. A lookback option is another kind of path-dependent option whose payoff depends on the extreme of the underlying asset''s price over a certain period of time. In this thesis, we propose a combinatorial method to value European-style reset and lookback options by the use of the reflection principle. Under this method, we derive a linear-time algorithm to value reset options and a quadratic-time algorithm to value lookback options. Traditional methods take quadratic time to value reset options such as Ritchken''s trinomial tree algorithm and cubic time to value lookback options using backward induction. Although the combinatorial method is highly efficient in pricing European lookback options, it converges slowly. It also underestimates the analytical value. We propose an interpolation method to improve its convergence. We also price the American-style lookback options by the use of the interpolation method. The interpolation technique is found to work well for price approximations and is efficient. In this thesis, all programs run on a PC with Intel Pentium-$2$ $266$ CPU, $64$ MB DRAM, and Windows $98$ platform.