##### Level: Intermediate

Understand how 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”. Learn the importance of how dividends and interest rates affect underlying stocks when implementing options strategies.

## 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.

## 4 thoughts on “Understanding Put-Call Parity”

1. Dan M says:

You put an asterisk after the interest rate in the equation. I assume that’s because it is unknown? What interest rate is normally used?

1. Interactive Brokers says:

Hi Dan, thank you for commenting. The asterisk represents that you are supposed to multiply (1+ interest rate) by (days until expiration/365) when calculating forward value. Please see the video at 1 minute and 8 seconds for more information. We hope this helps clarify things.

2. Robert B says:

Webpage software has bug. I completed the quizzes on the first two lessons (Intro to Options and Vertical Call Spread) and the page DOES show completed for each of these two. But I completed the quiz for Understanding Put-Call Parity (with a score of 100%) and when I hit Submit, it shows 100% but NEVER saves my results and NEVER says Put-Call Parity lesson was completed. I tried the next lesson (Intro to Options – The Greeks) took quiz, says 100%, but won’t mark it as completed. Super frustrating.

1. Interactive Brokers says:

Hello Robert, thank you for reaching out. We could not replicate this situation internally. We would advise you to try the link on a different device and/or browser. We hope this solves the issue. If it persists, please contact Client Services: http://spr.ly/IBKR_ClientServicesCampus

##### Disclosure: Interactive Brokers

The analysis in this material is provided for information only and is not and should not be construed as an offer to sell or the solicitation of an offer to buy any security. To the extent that this material discusses general market activity, industry or sector trends or other broad-based economic or political conditions, it should not be construed as research or investment advice. To the extent that it includes references to specific securities, commodities, currencies, or other instruments, those references do not constitute a recommendation by IBKR to buy, sell or hold such investments. This material does not and is not intended to take into account the particular financial conditions, investment objectives or requirements of individual customers. Before acting on this material, you should consider whether it is suitable for your particular circumstances and, as necessary, seek professional advice.

The views and opinions expressed herein are those of the author and do not necessarily reflect the views of Interactive Brokers, its affiliates, or its employees.

Options involve risk and are not suitable for all investors. Multiple leg strategies, including spreads, will incur multiple commission charges. For more information read the “Characteristics and Risks of Standardized Options” also known as the options disclosure document (ODD) or visit ibkr.com/occ

##### Disclosure: Multiple Leg Strategies

Multiple leg strategies, including spreads and straddles, will incur multiple commission charges.