European calls, puts value with strike and expiration value

Question

Explain the relationship between the European calls, puts value with similar strike and expiration value.

Answer 1

C − P = S − Ke^−r(T−t)

This relationship, in among European calls (value C) and puts (value P) with similar strike (K) and expiration (T) valued at time t is an effect of a simple arbitrage argument. When you buy a call option, at similar time write a put and sell stock short.
When the stock is above the strike at expiration therefore you will have S − K by the call, 0 by the put and −S by the stock. A total sum of −K. If the stock is below the strike at expiration you will have 0 from the call, −S again from the stock, and −(K − S) from the short put. Again a total sum of −K. Therefore, whatever the stock price is at expiration such portfolio will all the times be worth −K, a guaranteed amount. Because this amount is guaranteed we can discount this back to the present. We should have C − P − S =−Ke^−r(T−t).

This is put–call parity.