A share price is curently quoting ar Rs. 50. It is known at the end of six months it will be either 45 or 55. The risk free rate is 10% p.a. with continous compunding. what is value of six month European Put option with a strike price of Rs. 50.
Not able to solve (Answer given in scanner only).
Answer- Value of Put :- Rs. 1.16.
Firstly calculate risk neutral probability of making up move and down move. It is calculated as under:
(exp(r)-d)/(u-d) here r is risk free rate applicable for period under consideration, d is down price/initial price and u is up price/initial price. You need to use exponential function on any scientific calculator. Else it will be given in question paper.
in this case risk neutral up probability is 75.64%. so the same for down probability is 24.36%.
Here if price moves up value of put is zero but if it moves down it is Rs. 5. probability of down move is 24.36% so expected value is 1.218. we further discount this using risk free rate to arrive at the value of Rs. 1.16
u=55/50= 1.1,
d=45/50=0.90,
r for 6 months = 6/12 = 0.05
C1=0
C2=50-45=5
value of put = [u-1-r /u-d] [C2/1+r]
= [1.1 - 1 - 0.05/1.1 - 0.9] [5/1+0.05]
= [0.05/0.20] [4.76]
=1.19 [Minor difference of .03 to be ignored]
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