Call-Put Parity for Dummies

Put--call parity is a static replication, and thus requires minimal assumptions, namely the existence of a forward contract. In the absence of traded forward contracts, the forward contract can be replaced (indeed, itself replicated) by the ability to buy the underlying asset and finance this by borrowing for fixed term (e.g., borrowing bonds), or conversely to lend (short) the underlying asset and loan the received money for term, in both cases yielding a self-financing portfolio. These assumptions do not require any transactions between the initial date and expiry, and are thus significantly weaker than those of the Black--Scholes model, which requires dynamic replication and continual transaction in the underlying. Replication assumes one can enter into derivative transactions, which requires leverage (and capital costs to back this), and buying and selling entails transaction costs, notably the bid-ask spread. The relationship thus only holds exactly in an ideal frictionless market with unlimited liquidity. However, real world markets may be sufficiently liquid that the relationship is close to exact, most significantly FX markets in major currencies or major stock indices, in the absence of market turbulence. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg https://www.amazon.com/MIND-MATH-Learn-Math-Fun-ebook/dp/B017QEIF18

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