How to calculate discount factor

Options & Futures
1

Hello,

Could anybody shed a light on how to calculate discount factor (in bold) in following question?

(from Options Trading Strategies:Intermediate)



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?





Hint:

Use put-call parity equation to calculate the put price.

c + Xe-rt = p + So



c = call price

X = strike price

e-rt = discounting factor

p = put price

So = initial price of underlying



Solution:

p = c + Xe-rt

2

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



Anyway, I cannot get to the correct answer, which is 7.68. Moreover, the ATM call price is 60, how come the put price should be 7.68?



Any help appreciated.

3

Hello Tomas, 

The formula and the solution given in the quiz question are right. Let me explain to you how this is calculated. 



Discount factor is e^(-rt) where r = 0.06 (i.e. 6%) and t = 1 (1 year). So discount factor would be e^(-0.06) which is 0.94176 



The put-call parity equation is: 

c + X(Discount Factor) = p + So



Let's substitute the values



60 + 900(0.94176) = p + 900

907.584 = p+900

hence, p = 7.584 ≈ 7.58



I hope this helps!

4

Cheers Varun for the explanation, I found my mistake!