Analytic approximations for Asian options
Date Issued
2009
Date
2009
Author(s)
Lo, Chien-Ling
Abstract
In this thesis we derive two analytic approximation formulas for floating strike Asian options and assume that assumptions underlying Black-Scholes (1973) model hold. In the literature, some researches use the second-order Taylor expansion to approximate the price of Asian options and they assume the Quadratic approximation is normally or chi-square distributed. In this thesis, we first derive the formula by improving the precision of the Taylor expansions. Next, we suggest that we even do not need to truncate the random variable via Taylor expansions, and the numerical results witness that our second formula is the most accurate approximation for selected values of the underlying parameters.dditionally, we derive the error upper bound for some formulas, and we also observe the rationality of all the assumptions by using the histogram Monte Carlo simulation. Finally, we leave all the troublesome calculations in Appendix.
Subjects
Asian option
analytic approximation
floating strike
Taylor expansion
Quadratic approximation
histogram simulation
Type
thesis
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