A stock index currently sells for 100. One-year European put and call options are available on the stock index both with strike prices of 100. The market price (i.e. price at time 0) of the put and call options are 8.02295 and 15.71131 respectively. Compute the one-year continuoosly compounded interest rate?

In the given problem we need to compute one year Continous compounding interest rate.

Give Value of Put option =8.02295 ,Value of Call option = 15.7131 . While Strike Price = Spot price = $100 & t= 1year

Using Put Call Parity we get

Call + PV of Strike Price = Put + Spot Price .substituting the above values in the given formula to get

15.7131 + 100 * e^{- r * 1} = 8.02295 + 100 or

100 * e^-r = 108.02295 -15.7131 or

   e^-r = 92.30985 /100 = 0.923095 or

    e^-r = 0.9231 using Present value interest factor table we can get the value of r = 0.08 = 8%

Therefore Continous Compounding interest rate for 1 year = 8%