## Options Education

### Demystifying Options: Explaining Put/Call Parity

A Primer on Put/Call Parity & How to Use It
This week, we review what are known as the put/call parity rules. If you know one rule - and you remember your high school algebra - you can quickly master all the rules. Mastery of these rules gives you a lot more flexibility when planning your option strategies.

Are Puts Cheaper than Calls?
(Here's a hint: Theyíre not.)

Look at most option prices in which the stock price is close to the strike price. You are likely to see that put premiums are lower than call premiums. Are puts cheaper than calls?

In fact, the time premiums of puts and calls at the same strike price (and the same expiration) are theoretically (and for practical purposes) the same. Why then do call premiums usually appear to be higher?

The answer is that with the stock equal to the strike, the calls are often in-the-money and the puts are out-of-the-money. This is because the real price of the underlying is the stockís future delivery price, which is determined by the stockís dividend and the going interest rate as well as by the stock price.

If the interest rate is higher than the dividend rate (as it usually is) then the stockís future delivery price will be higher than its current price.

Breaking It Down
If you are a market maker and you need to buy the stock (and lock in a price) for one-year delivery (for a call you are writing), you need to borrow the funds (at the one-year interest rate) to buy the stock.

This increases your effective price of the stock. However, you also get to collect the dividends (if any) on the stock. This will reduce your price. Thus, if the current stock price is \$100, the one-year interest rate is 6% and the dividend rate is 1% p.a., then the real cost of the stock for a one-year option is \$105.

Most simply, the price for future delivery of the stock is:
• Stock Price + Interest - Dividend.

In our upcoming example, we price one-year calls and puts using a standard Black-Scholes model with the stock at \$100, the interest rate at 6% and the dividend rate at 1%.

At the \$100 strike price, the call premium is higher than the put premium. At the \$105 strike price (equal to the future delivery price), the call and put premiums are exactly equal.

You will also notice that when you use the \$105 future delivery price as your underlying, rather than the \$100 current stock price, all the calculated time premiums of puts and calls for each strike price are equal...

Posted By: Value Line
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Lawrence D. Cavanagh is Editor (and Senior Analyst) of The Value Line Daily Options Survey. The Value Line Daily Options Survey offers evaluations and rankings on virtually the entire universe of regularly listed equity and ETF options, using the Value Line common stock ranks and proprietary volatility forecasting methodology. Before joining Value Line in 1991, Mr. Cavanagh was an options strategist for Capital Market Technologies (subsidiary of Elders Finance), helping design long-term synthetic foreign currency and gold option hedges. Before that, he was Director of Foreign Currency Options for the Chicago Board Options Exchange. Other work experience includes Dean Witter Reynolds (VP, Senior Currency Analyst), European American Bank (Director of Currency Forecasting) and the Federal Reserve Bank of New York (Assistant Economist).

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