The parity formula comes from the principle of no arbitrage.
Construct two investment portfolios.
Call option C, exercise price K, expiration time T. Cash account ke (-rt), interest rate R, the option just becomes K when it expires.
Put option P, exercise price K, expiration time T, underlying stock, current price S0.
Look at the situation of these two portfolios at maturity.
Stock price St is greater than K: portfolio 1, exercise call option C, spend cash account K, buy the underlying stock portfolio 2 with ST's share price, give up put option and hold the stock with ST's share price.
If the stock price St is less than k: portfolio 1, give up exercising the call option, hold cash K. portfolio 2, exercise the put option, sell the underlying stock and get cash K.
Share price equals K: neither option can be exercised, portfolio 1 cash K, and portfolio 2 share price equals K.
As can be seen from the above discussion, no matter how the stock price changes, the value of the two portfolios at maturity must be equal, so their present value must also be equal. According to the no-arbitrage principle, two portfolios with equal value must have the same price. So we can get c+ke (-rt) = p+s0.
If you are asking how to calculate the discount factor of continuous compound interest, it is like this: suppose 1 yuan, and the annual interest rate is 100%. If simple interest is calculated, 1 *( 1+ 1) will be obtained after one year, and 1 *( 1) will be obtained if interest is calculated every six months. If the interest is calculated n times a year, the sum of the due principal and interest is1* (1+1/n) N. When n approaches infinity, that is, the interest is calculated continuously, and this function will converge to an irrational number, that is, E. For specific mathematical proof, see the solution of this schoolmaster:/question/36204067.