For this question, I suggest that you copy tab 10.20 in the lectures_03_04.xlsx file on the course site into a new Excel file. You may, of course, use any other tool if you so desire. Set the parameters of the 3-period (forward) binomial tree to s = 100, K = 95, r = 0.05, T = 3, 0 = 0.3, and 8 = 0.03. First consider a European put option with those characteristics. In a second copy of this Excel tab (or other tool), consider the American put option with the same characteristics. (a) Comparing both 3-period trees, draw the 3-period tree that describes the evolution of the value of a (b) portfolio II which is long one unit of the American put and short one unit of the European put. What does this portfolio represent? -rh e After a single down move (i.e. when Sn = d So), does the following equation: IT= E="" E [p*Tidu + (1 p*)Irdd], describe the value of the portfolio? (Note that Ild is the value of the portfolio when Sn = d So, and II die and Idd are the two possible values of II, at 1 = 2h.) What is the rationale? c) Is Idd related similarly to Iddu and I7ddd? Why? d) What is the A of II at time 0? What is the financial intuition behind the sign of this A? (For potential partial marks, explain how you computed the A.) (e) Let IIo be the initial value of the portfolio with o = 0.30. Compute the corresponding value It when o is instead 31%, and V = (II; -110)/0.01. How should we interpret V? What the financial intuition behind its sign? For this question, I suggest that you copy tab 10.20 in the lectures_03_04.xlsx file on the course site into a new Excel file. You may, of course, use any other tool if you so desire. Set the parameters of the 3-period (forward) binomial tree to s = 100, K = 95, r = 0.05, T = 3, 0 = 0.3, and 8 = 0.03. First consider a European put option with those characteristics. In a second copy of this Excel tab (or other tool), consider the American put option with the same characteristics. (a) Comparing both 3-period trees, draw the 3-period tree that describes the evolution of the value of a (b) portfolio II which is long one unit of the American put and short one unit of the European put. What does this portfolio represent? -rh e After a single down move (i.e. when Sn = d So), does the following equation: IT= E="" E [p*Tidu + (1 p*)Irdd], describe the value of the portfolio? (Note that Ild is the value of the portfolio when Sn = d So, and II die and Idd are the two possible values of II, at 1 = 2h.) What is the rationale? c) Is Idd related similarly to Iddu and I7ddd? Why? d) What is the A of II at time 0? What is the financial intuition behind the sign of this A? (For potential partial marks, explain how you computed the A.) (e) Let IIo be the initial value of the portfolio with o = 0.30. Compute the corresponding value It when o is instead 31%, and V = (II; -110)/0.01. How should we interpret V? What the financial intuition behind its sign
