What is Put-Call Parity & How Does it Work?

Put-call parity is a fundamental principle in options trading that establishes a relationship between call options, put options, the underlying asset, and the strike price. It essentially means that, in a market without inefficiencies, the prices of puts and calls with the same strike price and expiration should be interconnected in a specific way. This relationship helps traders assess whether the prices of options are consistent with one another and the underlying asset.

The underlying idea behind put-call parity is that a combination of a call and a put option, both with the same strike price and expiration, should have the same value as owning the underlying stock itself. This principle assumes that, under normal market conditions, there should be no price discrepancy between the options that could lead to an opportunity for risk-free profit. The put-call parity formula is typically represented as:

Call Price - Put Price = Stock Price - Strike Price

This equation enables traders to calculate any one of the four variables—call price, put price, stock price, or strike price—if they know the other three. For example, if you know the prices of the call and put options and the strike price, you can solve for the current price of the underlying stock.

Put-call parity works by linking the prices of call options, put options, the underlying asset, and the strike price through a specific relationship. At its core, the concept ensures that the price of a call option, together with the price of a put option, should align with the price of the underlying asset, adjusted for the strike price. This concept applies to multi-leg strategies as well. For example, a $5 wide short put spread paired with a $5 wide long call spread on the same strikes should amount to $5 all else equal.

The fundamental principle behind put-call parity is that a combination of a call and a put option with the same strike price and expiration date should be equal in value to owning the underlying stock, adjusted for the strike price.

This equation assumes that the options in question share the same strike price and expiration date. Using this formula, market participants can solve for any one of the four variables—call price, put price, stock price, or strike price—if the other three are known. 

Put-call parity helps traders understand market expectations. If there is a significant discrepancy between the theoretical and actual prices of options, it could indicate something unusual in the market, such as unexpected volatility, dividends, or liquidity issues. By applying put-call parity, traders ensure that they are not overpaying or underpricing options.

The put-call parity formula is a key concept that helps to link the prices of call and put options with the price of the underlying asset. 

It is typically expressed as: Call Price - Put Price = Stock Price - Strike Price. 

For situations involving dividends or longer-dated options, the formula may need slight adjustments to account for additional variables. 

This equation assumes that both the call and put options share the same strike price and expiration date. By applying this formula, traders can solve for any missing variable if the other three are known. For instance, if the prices of the call and put options are available, the formula can be used to calculate the fair value of the underlying stock, ensuring the options are correctly priced in relation to one another.

A hypothetical example can help reinforce the concept of put-call parity. 

Imagine you are analyzing stock XYZ, which is currently trading at $30.50. You are considering the at-the-money (ATM) $30 strike-price for a position, and want to assess the pricing of the call and put options for this strike price. You notice the $30-strike put option is trading for $1.10, and you want to determine what the price of the $30-strike call option should be based on put-call parity. This would be assessed using the put-call parity formula. 

When dividends are involved, put-call parity requires a slight adjustment to account for the fact that dividends lower the price of the underlying stock. Since dividends are paid out to shareholders, they cause a drop in the stock price once distributed, which, in turn, affects the pricing relationship between the call and put options.

For options on dividend-paying stocks, the expected dividend payment during the life of the options is subtracted from the standard put-call parity formula. This adjustment accounts for the stock price’s anticipated drop by the dividend amount on the ex-dividend date. The modified formula is: Call Price = Stock Price - Strike Price + Put Price - Dividend

This adjustment ensures the put-call parity formula accurately reflects the impact of dividend payouts on the stock price.

A hypothetical example can help reinforce the concept of put-call parity involving dividends.

Imagine you are analyzing stock XYZ, which is currently trading at $30.50. You are considering the at-the-money (ATM) $30 strike price for a position, and want to assess the pricing of the call and put options for this strike price. You notice that the $30-strike put option is trading for $1.10, and you want to determine what the price of the $30-strike call option should be based on put-call parity. Additionally, the stock is expected to pay a $0.30 dividend during the life of the options. To assess the pricing, you can use the modified put-call parity formula that accounts for dividends.

Put-call parity applies to both American and European options, but the ability to exercise American options early, especially around dividend payouts, adds complexity to the pricing relationship. European options are generally less complex, because they can only be exercised at expiration, making adjustments for dividends more straightforward.

For American options, if the stock pays a dividend before expiration, there's an additional consideration. Because American options allow for early exercise, a trader may choose to exercise the option just before the dividend is paid in order to capture the dividend. This potential for early exercise means that the intrinsic value of the American call option could be affected by the timing of the dividend.

• Put-call parity is a fundamental pricing relationship that links the prices of call options, put options, the strike price, and the underlying asset.

• The formula for put-call parity is: Call Price - Put Price = Stock Price - Strike Price

• This formula allows traders to calculate the price of one variable, given the others. 

• Implied volatility, time to expiration, interest rates, and dividends can all impact the price of options and may account for discrepancies between the put-call formula and the prices observed in the market. 

• If pricing discrepancies arise, further analysis may be needed to determine if they are caused by one (or more) of these factors.

• The formula for put-call parity with dividends is: Call Price = Stock Price - Strike Price + Put Price - Dividend. This formula accounts for the expected dividend payment, thus impacting the price of the underlying stock.

• American options have the flexibility of early exercise, especially around dividend dates, which can complicate the application of the put-call parity formula.