Υπολογισμοί φραγμάτων για την προσέγγιση των αξιών ασιατικών δικαιωμάτων
The aim of this thesis is to give upper and lower bounds for the value of an arithmetic Asian call or put option not only in continuous but also in discrete time. Moreover, the calculations will be made for the exercise price of option, either constant or floating, as percentage on the value of share. The value of such an option is calculated by using the arithmetic average of the stock prices for a specific time period up to the expiry of the option. For the calculation of lower bounds the notions of the conditional average price and comonotonic dangers will be used. For the calculation of the upper bounds a methodology that is used in the Actuarial Science for the finding of bounds of stop loss premiums, for sums of dependent random variables, will be followed. These methods (that are relatively simple) lead to accurate analytic bounds that can be calculated. Comparisons of these bounds will also be made with the approximate prices of the asian options that can be found via the approach of distribution of the average of the stock prices for a period of specific number of days up to the expiry of Asian option.