The Put-Call Parity theorem states that a long position in a call option and a short position in a put option with the same strike price will have the same valu...
The Put-Call Parity theorem states that a long position in a call option and a short position in a put option with the same strike price will have the same value at expiration. This theorem applies regardless of the underlying asset's price movement.
To illustrate this theorem, consider the following scenarios:
Call option: If the underlying asset's price rises above the strike price, the call option will expire worthless, and the long position will be worth the strike price minus the option's premium. Conversely, if the underlying price falls below the strike price, the call option will expire exercised and will be worth the premium paid for it.
Put option: Similarly, a short position in a put option will expire worthless if the underlying price rises above the strike price, and the short position will be worth the strike price minus the premium paid for it.
Therefore, the net value of both options will be equal and equal to the value of the underlying asset at expiration. This theorem provides a theoretical framework for understanding how options can be used to hedge or speculate on different price movements of an underlying asset