Monthly closing prices for stock XYZ:
Date : Stock Price
January 31, 2008: 105
February 29, 2008: 120
March 31, 2008: 115
April 30, 2008: 110
May 31, 2008: 115
June 30, 2008: 110
July 31, 2008: 100
August 31, 2008: 90
September 30, 2008: 105
October 31, 2008: 125
November 30, 2008: 110
December 31, 2008: 115
The following are one-year European options on stock XYZ. The options were issued on December 31, 2007.
(i) An arithmetic average Asian call option (the average is calculated based on monthly closing stock prices) with a strike of 100.
(ii) An up-and-out call option with a barrier of 125 and a strike of 120.
(iii) An up-and-in call option with a barrier of 120 and a strike of 110.
Calculate the difference in payoffs between the option with the largest payoff and the option with the smallest payoff.