Question

Calculate the price of a 6-month index call option with 1000 strike price using the following information.

Current index level	1,083
Index dividend yield	1% per annum
Risk-free rate	4% per annum
6-m index put option price w/ 1000 K	$34.94

Round the the nearest 2 decimal points. For example, if your answer is $123.456, then enter "123.46"

Answer 1

Price of six - month index call option:

Given:

Current index level = 1083

Exercise price = 1000

Index dividend yield = 1% per annum

Risk free rate = 4% per annum

Now we can calculate the fair future price of call option by continuous compounding method. The formula is as under:

Fair future price = Current market price x (1 + r)n

Since dividend yield is 1% per annum, yield for six months will be 0.5%

Risk free rate is 4% per annum, hence risk free rate for 6 months = 2%

Current market price = 1083 x 1.005

Current market price = 1088.42

Now putting the values into formula, we have:

Fair future price = 1088.42 x (1 + 0.02)

Fair future price = 1110.19

Hence, fair future price for six months is 1110.19.