Understanding Put-Call Parity

Study Notes:

As you go through the examples that follow, you may notice that certain strategies use different mixes of products yet have similar risk/reward structures.

This is because the prices of puts and calls are inextricably linked to each other and the price of the underlying stock through an equation known as “Put/Call Parity”.

The equation states:

Call Price + Strike Price = Forward value of Stock Price + Put Price

It is important to use the forward value of the stock, which is adjusted for interest rates and dividends, rather than strictly the current price of the stock. We can calculate the forward value this way:

Forward value = (Current value) x (1 + interest rate * days until expiration/365) – dividends

In a low rate environment, the forward value of a stock that pays no dividends is roughly equal to the current value. If interest rates are high, or a stock is hard to borrow, or the stock pays a dividend during the life of the option, the forward value may differ meaningfully from the current stock price.

When we examine the Put/Call Parity formula, simple algebra allows us to demonstrate how different structures have similar payoffs. For example:

Call Price = (Forward Value – Strike Price) + Put Price

This shows that the value of a call is the same as being short the stock and long a put. You will notice that those payoff graphs look quite similar. As you go through the study guide, keep this equation in mind when you see other similar looking graphs.

If we structure the equation this way, we see that a long call and short put with the same strike and expiration creates a synthetic future:

Forward value = Strike Price + Call Price – Put Price

As we saw above, the difference between the forward value and the current value of a stock is a function of interest rates and dividends. Because options prices are based on the forward value of the underlying product, it is crucial that options investors consider the effect of dividends and interest rates when implementing their strategies.