Aarush (Delhi) (1566 Points)
22 May 2012A 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.
Shubhankar Limaye
(B.Com.)
(174 Points)
Replied 23 May 2012
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
CMA CS Mohammed Isaq
(M)
(47 Points)
Replied 23 May 2012
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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