The put-call parity shows the relationship between European call options and put options. This concept is important to understand in options pricing. The put-call parity shows that the prices of these options as well as the price of the underlying asset must all be consistent with one another. This holds true for puts and calls that have the same underlying asset, strike price, and expiration date. The put-call parity states that a portfolio holding a long position on a call option and a short position on a put option of the same underlying asset with an identical strike price and expiration should be equal to a portfolio holding a long position of the underlying asset and a short position of the strike price. This equation can be rearranged and interpreted in a number of different ways. By solving for a single variable, you can create what is referred to as the synthetic portfolio. For example, using the put-call parity equation we can solve for just a long position of the call option. This relationship shows that it should be equal to a portfolio holding a long position on the underlying asset, a long position on the put, and a short position on the strike price. This portfolio is referred to as the synthetic call option. In this put-call parity calculator, you can see how each component is calculated and how they are related to each other. By entering the values and leaving one of either the put option price, call option price, or spot price of the asset blank, this calculator will show you what that price should be according to the put-call parity relationship. If a put option, call option, or spot price of the underlying asset is not equal to the portfolio which consists of its corresponding synthetic version then this indicates a potential opportunity for arbitrage.
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