Personally, I think the best way to tackle this kind of question is to draw payoff diagrams. So I'd do that for the basic fee, a call option and a special option. These are my "jigsaw" pieces. Then I'd draw a pyoff diagram for the proposed new fee (with different gradient slopes, separated by discontinuities at S1=S0 and S1=U). Then I'd fit the jigsaw pieces inside this one. I know that some people prefer to work algebraically though - it's your choice which you use in the exam. What do others think?
Well, to be honest initially I found it easier to write out the payoff function and then fill in the blanks, but after seeing the graph, I have a greater understanding of the situation. So I guess it depends on your strengths as a student.
