# Options parity theorem,

Understanding the Put Call Parity relationship can help you connect the value between a call option, a put option binary options zigzag strategy the stock.

When you see how these building blocks are connected, you will be able to create other synthetic positions using various option and stock combinations. The original formula provides the basis and we'll take a look later in the article how to account for American style stock options that pay dividends.

Forward and futures contracts Video transcript Voiceover: We've seen that the payoff diagram at option expiration for owning the stock plus a put on that stock at some strike price that this payoff diagram will look exactly the same as the payoff diagram as owning a call option on that stock at the same strike price as the put option plus a bond that's going to be worth the strike price at the time of expiration. One point of clarification and actually let me just draw that payoff diagram just so you know what it looks like. So, if this is the underlying stock price, stock price. And let's just do the payoff diagram when we look at the value of the portfolio or your holdings.

Put Call Parity Formula The formula supposes the existence of two portfolios that are of equal value at the expiration date of the options. The premise is that if the two portfolios have identical values at expiration then they must be worth the same value now.

If one portfolio was worth more than the other then traders would buy the undervalued asset and sell the overvalued asset until no further opportunity exists - also referred to as the "no arbitrage" principle. This therefore means that buying options parity theorem call and put at the same strike price with the same expiration date will have the same value as the stock price minus the strike price.

Given this, the payoff profile of each side will also be the same and we can see this with a synthetic long stock profile, which is long call and short put. Put Call Parity Example Let's look at some real world examples of put call parity to understand how prices fit together.

### Put and call options

Take a look at the option series below for MSFT. We'll see if we can back out the price of the call option given the prices of the other components.

- Put–call parity - Wikipedia
- Individuals trading options should familiarize themselves with a common options principle, known as put-call parity.
- Forward and futures contracts Video transcript If we want to get the upside of owning a stock while still mitigating the downside, in case the stock price goes down, we saw that we could buy a stock and an appropriate put option.

The last traded price of the call option in the market, however, is 1. Why is this?

- Put-call parity (video) | Khan Academy
- In the case of dividends, the modified formula can be derived in similar manner to above, but with the modification that one portfolio consists of going long a call, going short a put, and D T bonds that each pay 1 dollar at maturity T the bonds will be worth D t at time t ; the other portfolio is the same as before - long one share of stock, short K bonds that each pay 1 dollar at T.
- Put-call parity states that simultaneously holding a short European put and long European call of the same class will deliver the same return as holding one forward contract on the same underlying asset, with the same expiration, and a forward price equal to the option's strike price.

Well, as mentioned earlier, the basic formula we've used so far assumed European options on stocks that don't pay dividends.

But MSFT is a company that does pay dividends to its' stock holders and the options traded are of American style.

### How to create a watchlist for trading options -- Options Trading

So how can we account for dividends with put call parity? Put Call Parity with Dividends As we know stocks pay dividends and these dividends affect the future valuation of the stock as money is being taken out of the company and paid to its' shareholders.

Because options have an expiration date, we need to value the option not against the current price of the stock but against what the expected value will be at the expiration date. This is known as the forward price.

Andrew Hecht Updated March 24, Options are derivative instruments. One of the reasons that option trading and investing is so much fun is that is it like a game of chess. During the life of an option, there are so many opportunities that will enhance or destroy the value of a position. There are so many moving pieces in the puzzle of options trading. The nominal option prices move higher or lower as implied volatility can move up or down and supply and demand for options themselves will move option premiums.

Now going back to our MSFT example, let's apply dividends and interest rates and see if the market agrees with put call parity. First, we need to check if MSFT is paying a dividend prior to the expiration of the options. For Options parity theorem stocks we can find this information easily on Yahoo under "company events".

This arbitrage opportunity involves buying a put option and a share of the company and selling a call option.

Looking back we can see that the data shown on Yahoo confirms that the stock was adjusted on the 15th for a 0.