Explain put–call parity is a model-independent relationship

Question

Illustrates that the put–call parity is a model-independent relationship.

Answer 1

Calls and puts with similar strike and expiration should have similar implied volatility. The attractiveness of put–call parity is that this is a model-independent relationship. In order to value a call on its own we require a model for the stock price, within particular its volatility. Very similar is true for valuing a put. Expect to value a portfolio having a long call and a short put, it may vice versa, no model is required. This model-independent relationship is few and far between in finance.