The Closed–Form Approach to the Valuation and Greeks of Discrete Asian Options
Date Issued
2009
Date
2009
Author(s)
Fan, Yu-Chen
Abstract
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.
Subjects
discrete Asian options
shifted log-normal distribution
Greeks
moment matching
closed-form solution
Type
thesis
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ntu-98-R96723063-1.pdf
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