The Closed–Form Approach to the Valuation and Greeks of Discrete Asian Options

• Main Authors: Yu-Chen Fan, 范育誠
• Other Authors: Yuh-Dauh Lyuu
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/66614964760464795894

碩士 === 國立臺灣大學 === 財務金融學研究所 === 97 === There are two types of discrete Asian options, fixed-strike and floating-strike. We focus on the fixed-strike type because the floating-strike type can be calculated through the symmetric property. To derive the closed-form solution to the option price and Greeks, we use the shifted log-normal distribution to match the moments of the arithmetic average value. Furthermore, we find a closed-form solution to the parameters which is new in the literature so that pricing and hedging are faster to execute than before. In the end, we compare three moment matching methods (based on shifted log-normal, log-normal and reciprocal gamma distribution) and Monte Carlo simulation as benchmark. Numerical results show our approach gives results very close to those by Monte Carlo simulation.