Question

A stock price is currently $50. It is known that at the end of two months it will be either $53 or $48. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a two-month European call option with a strike price of $49?

Answer 1

Strike price =	$49.00
Current Market price =	$50.00
Risk-free rate = 10% per annum or 0.10
Rate for 2 month 10*2/12 =	0.01666666667
Continuous compounding rate formula (e^0.0166667)= (r)^1/ 1 + (r)^2 / (2*1)  + (r)^3 / (3*2*1) + (r)^4 / (4*3*2*1)
(0.0166667)^1 /1 + ((0.0166667)^2 / (2*1) + ((0.0166667)^3 / (3*2*1) + ((0.0166667)^4 / (4^3*2*1)
0.01680633038
Value of call option = Strike price - Stock price (subject to 0)
Upside Stock price =	53
Value of call option = 53 - 49=	$4.00
Downside Stock price	48
Value of Call option = 48-49 =0
Call detlta = (VC at upper - VC at lower)/(Upper value - downside value)
(4-0) / (53-48)
0.80
Value of Call option = ( Current market price -Present value of downside value) * Call delta
present value of downside value = Downside value/(1+i)
48/(1+0.01680633)	47.20662978
So, VC = (50 - 47.2066297)*0.80
$2.23
So, value of call option is $2.23.