I can not get the same Put price as the right answer does

Course Name: Options Trading Strategies In Python: Intermediate, Section No: 7, Unit No: 3, Unit type: Quiz

The first problem I see in solution is there is missing So in the formula, i.e., the correct one should be p = c + Xe-rt - So. In correct answer, the part -So is missing.
Anyway, I cannot get to the correct answer, which is 7.68. Moreover, considering that ATM call price is 60, how come the calculated Put price should be 7.68? It would make a spread of 52.32.

Oh, I read the formula in Solution incorrectly. The formula in Solution is actually right:

p = c + Xe-rt - So

So, the instruction reads:

Suppose the stock Infosys is trading at INR 900. A one-year ATM call on Infosys is priced at INR 60. If the interest rate is 6%, what should be the price of one year ATM put on Infosys.

Which gives the following :

p = 60 + 900 / (1+0.06)^1 - 900 = 60 + 849.05 - 900 = 9.05 ← but this is obviously wrong.

Where am I making a mistake?





 

Hello Tomas,



I see you didn't exactly use the formula for the discount factor which is e^(-rt). 

The approach you have taken is suited for discrete compounding of the interest rate. In such cases, you can use 1/(1 + r)^t as the discount factor. 



For options, interest rates are compounded continuously, as opposed to discrete compounding, where interest is compounded at fixed intervals. The formula for continuous compounding is based on exponential growth and results in a larger discount factor than discrete compounding, as the interest is compounded more frequently.



For step-by-step calculation of the solution to the quiz question, please refer to this response to your previous query here.



I hope this helps!!

Cheers Varun for your help. Appreciated.