Question

Suppose the exchange rate is $1.03/C$. Let r $ = 7%, r C$ = 3%, u = 1.28, d = 0.83, and T = 1.5. Using a 2-step binomial tree, calculate the value of a $1.10-strike European put option on the Canadian dollar. Option D is correct, but how? Can you provide solution for Excel? formulas and steps or actual excel work sheet please?

Answers: a. $0.1049 b. $0.1229 c. $0.1302 d. $0.1106 e. $0.1166

Answer 1

We will not be able to upload any excel file. However, I have produced my excel model below so that you understand the mathematics and your end looking at the excel formula. I am laying down step by step explanation to help you understand and do it at your end:

As a first step, please see the inputs and two outputs, t and p (risk neutral probability) at the left top corner. Yellow colored cells contain the calculated value. Adjacent cell in blue color contains the formula used to get the value in yellow colored cell.

Second step: Please see the tree diagram. This is how exchange rate evolves over the two periods. Please don't get into calculation at this stage. Just examine the tree and see where the nodes are and where Suu, Cuu, Sud, Cud, Sdd, Cdd, Su, Cu, Sd, and Cd appear in the three.

Third step: Recall the following formula for calculation of each one of them.

• Suu = u² x S0; Cuu = max (Suu - K, 0)
• Sud = u x d x S0; Cud = max (Sud - K, 0);
• Sdd = d² x S0; Cdd = max (Sdd - K, 0)
• Cu = Cu = [p x Cuu + (1 - p) x Cud] x e^{-r$ x t}
• Cd = Cd = [p x Cud + (1 - p) x Cdd] x e^{-r$ x t}

Fifth step: Now start the calculation. Move from rightmost point Suu to leftmost point C0. Yellow cell contain the calculated value. Adjacent cell in blue color contains the formula used to get the value in yellow colored cell.

Sixth step: Move from right to left till the time you hit the value of C0 = 0.1106. That's your answer in option d.

I sincerely hope that you understand the formulation and excel formula. Please do let me know.

E A B C G H 50 So 51 rS 1.03 7 % 52 rCS 3% 53 u 1.28 t 0 t =1 t = 2 54 d 0.83 P 55 T 1.5 Suu 1.69G58 B53 56 n 2 57 K 1.10 Su Cuu MAX ( SB$ 57-156,0) 1.32 B53 B50 0.75 -B55/B56 58 t 0.44545(EXP((B51-B52) B58)-B54)/(B53-B54) 59 p Cu 0.00 (158 $B$59+164 (1-$B$59)*EXP(-$B$51*$B$58) 60 61 Sud 1.09 G58 B54 62 1 p so 1.03 -B60/B61 Cud 63 0.01EMAX($B$57-162,0) 64 Co P 65 (G60*$B$59+G69*(1-$B$59))*EXP(-$B$51 $B$58) 0.1106 66 Sd 1 p 0.85B50 B54 67 68 Cd 0.21 (164 $B$59+173 (1- $ B$59)) EXP(-$B$51$B$58) 69 Sdd 70 0.71 G67 B54 71 1 p 72 Cdd 0.39MAX($B$57-171,0) 73 en