Consider the following binomial tree. The numbers in squares are stock prices. T

Question

Consider the following binomial tree. The numbers in squares are stock prices.

The numbers in circles will be option prices (# numbers are the exercise numbers to answer your calculation).

Today, the stock is at 100 and can go up and down over the next week, and then again up and down from there. We are pricing a call struck at 110. Quiz 13 Q6-14.PNG

Use the computed q to sweep back through the tree to fill the call values in circles. For #7-#9 use the option terms, then for nodes #10-#12 use the resursive formula: C = q Cu + (1-q) Cd. Ignore interest

1) Compute the probability of the up-step: q = ______

2) What answer corresponds with the field labeled #7-#12 above?

#7 Call Value =

#8   Call Value =

#9    Call Value =

#10 Call Value =

#11   Call Value =

#12   Call Value =

3) Today, the delta (hedge ratio) is   =

4)  Interpret the delta. If you sell a call option on one hundred shares, the delta hedge will require you to buy _______________ shares of stock (how many?).

Explanation / Answer

Given S= 100, K=110

u = Su/S = 110/100 = 1.1

d = Sd/S = 90/100 = 0.9

q =(S-Sd)/(Su-Sd) = (100-90)/(110-90) = 0.5

#7 Payoff = Max (0, St-K) = Max(0, 120-110) = 10

#8 Payoff = Max (0, St-K) = Max(0, 100-110) = 0

#9 Payoff = Max (0, St-K) = Max(0, 80-110) = 0

#10 C= qCu + (1-q) Cd = 0.5*10+0.5*0 = 5

#11 C= qCu+(1-q)Cd = 0.5*0+0.5*0 = 0

#12 C= qCu+(1-q)Cd = 0.5*5+0.5*0 = 2.5

3) delta = (Cu-Cd) / (Su-Sd) = (5-0)/(110-90)= 5/20 = 0.25

4) if i sell call option of 100 share, we will require 0.25*100 = 25 shares to be bought for delta hedge

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