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What do you mean, buy flat and sell flat?
Flat buying and flat selling refers to the deterministic relationship between call options and put options under the same conditions of no arbitrage and no dividend payment in the complete financial market.

As a financial tool, apartment purchase and apartment sale have the same exercise price and expiration date. The price of put right and call right must be the same. If not, there is room for arbitrage.

If one portfolio consists of stocks and put options (S+Vp), and the other portfolio consists of zero coupon bond/pure discounted bonds (or bank deposits) and call options (K+Vc), then the returns of the two portfolios are the same.

Extended data:

Call option and put option have the same exercise price and expiration date; The maturity date of zero coupon bond/pure discount bonds or bank deposits should also coincide with the maturity date of options. The parity relationship of call options can be applied to options that the buyer of options can only exercise on the expiration date, that is, they can't exercise in advance and can only exercise on the expiration date.

At a certain time in the future (expiration date), the option holder has the right to buy/sell the agreed amount of currency from the option seller at the pre-agreed exchange rate (transaction price) and pay the electricity fee for purchasing this right.

Baidu Encyclopedia-Parity Relationship of Trading Rights