Assuming that the underlying securities have no income during the option duration, the parity relationship between call and put options is: the sum of the present value of the call option price and the exercise price is equal to the put option price plus the current price of the underlying securities (c+PV(X)=p+S). The sum of the present value of the call option price C and the exercise price K is equal to the put option price P plus the current price of the underlying securities S = KE (-RT): K multiplied by the -rT power of E is the present value of K, and the -rT power of E is the discount coefficient of continuous compound interest. The discount factor can also be expressed by exp(-rT).
According to the principle of no arbitrage, two portfolios are constructed.
1. Call option C, exercise price K, expiration time T. Cash account ke (-rt), interest rate R, when the option expires, it just becomes exercise price K.
2. Put option P, strike price K and maturity time T .. theme stocks, current price S. Look at the situation of these two portfolios at the maturity.
3. The stock price ST is greater than K: portfolio 1, exercise call option C, spend cash account K, buy the underlying stock, the stock price is St. Portfolio 2, give up the put option and hold the stock with the stock price of St.
4. The stock price St is less than k: portfolio 1, give up exercising call option, hold cash k ... Portfolio 2, exercise put option, sell the underlying stock and get cash k.
5. Stock price equals K: neither option can be exercised, the cash price of portfolio 1 is K, and the stock price of portfolio 2 is 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+c+ke (-rt) = p+s+S. Put it another way: c-p = s-ke (-rt).
Extended data
Settlement type
1. Stock settlement method
In stock trading, if investors want to buy a certain number of shares, they must pay all the fees immediately to get the shares. Once the stock price rises after buying the stock, investors must also sell the stock to get the spread profit. Therefore, the settlement requirement is that the transaction must be paid in cash immediately, and the profit and loss can only be realized if the subject matter is no longer held after the transaction. In the option market, the settlement method of stocks is very similar. ?
The basic requirement of stock settlement method is that the option fee must be paid in cash immediately. As long as the position is not hedged, the profit and loss cannot be realized. This settlement method is mainly used in the trading of stock options and stock index options, and the settlement procedures of option contracts are basically the same as those of basic assets.
2. Futures settlement method
The settlement method of futures is very similar to the settlement method of futures market, and it also adopts the daily settlement system. The futures market usually adopts this settlement method.
However, due to the high risk of futures settlement, many exchanges only use futures settlement in futures options trading, while stock settlement is still used in stock options and stock index options trading. In this way, the settlement procedures of option transactions can be greatly simplified, because the settlement procedures of options and their underlying assets are the same.
Baidu Encyclopedia-Options