# The Put-Call Parity

Put-call parity is a fundamental concept in options trading that describes the relationship between the price of a call option and the price of a put option on the same underlying asset with the same strike price and expiration date. Put-call parity is based on the principle of arbitrage, which states that if two assets have the same value, they should have the same price.

To understand put-call parity, let's consider an example. Suppose you are interested in buying a call option on a stock that is currently trading at $50 per share. The call option has a strike price of $55 and an expiration date three months from now. At the same time, another investor is interested in buying a put option on the same stock with the same strike price and expiration date. The put option is currently priced at $4.

According to put-call parity, there must be an arbitrage-free relationship between the price of the call option and the price of the put option. This means that if the call option and the put option are not priced correctly relative to each other, there is an opportunity for arbitrage.

The put-call parity equation is as follows:

Call Price - Put Price = Stock Price - Strike Price / (1 + Risk-Free Interest Rate) ^ Time to Expiration

Using this equation, we can determine whether the prices of the call option and the put option are consistent with each other.

In the example above, the call option is priced at $2.50, which means that if we plug the values into the put-call parity equation, we get:

$2.50 - $4 = $50 - $55 / (1 + r) ^ 3

Solving for the risk-free interest rate, we get:

r = 3.7%

This means that the risk-free interest rate would have to be 3.7% for the prices of the call option and the put option to be consistent with each other, given the stock price, strike price, and time to expiration.

Put-call parity is an important concept for options traders because it can help them identify opportunities for arbitrage. If the prices of the call option and the put option do not follow the put-call parity equation, there may be an opportunity to profit by buying one option and selling the other.

In summary, put-call parity is a fundamental concept in options trading that describes the relationship between the price of a call option and the price of a put option on the same underlying asset with the same strike price and expiration date. Put-call parity is based on the principle of arbitrage and can help traders identify opportunities for profit. By understanding put-call parity, options traders can make more informed trading decisions and manage their risk more effectively.

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