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"
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.
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