A Brief Description of Option Price Movements

by Jay Pestrichelli on March 22nd, 2012

Not too long ago someone asked me to explain how deep In-the-money (ITM) options creates similar exposure to long/short stock despite the significantly lower amount of cash. I know he’s a frequent reader of this blog so I thought he’d appreciate a more detailed answer of how option price movements relate to movements in the underlying stock or index.

Lets focus on ITM calls and a do a little review of what that is. An ITM call is long call position that has a strike price lower than the current market price. Take for example the SPX (S&P 500), which is currently trading around 1395. Any long call with a strike lower than 1395, like 1375 or 1350 or 1300, etc., is considered ITM. Specifically speaking, there is no concrete definition for what a “deep” ITM call is, but suffice it to say, it means it’s far away from the market. In the previous examples, the 1350 or 1300 would be considered to be deep ITM. Some may consider the 1375 as deep ITM, but we don’t.

The benchmark we use at Buy and Hedge for defining ‘deep’ is when the time value is a noticeably smaller part of the overall premium. You may recall that option premiums (or prices) are composed of two portions; the intrinsic value and the extrinsic value. The intrinsic value is the mathematical difference of the strike and the current market price. For our SPX example above, the 1300 call would have \$95 of intrinsic value (1395 – 1300). The rest of the value is considered extrinsic or time value.

So if the premium of the 1300 call is \$125, the extrinsic would be \$30 (\$125 - \$90). It’s worth noting two points here: First, the deeper the options go, the smaller the extrinsic value and the larger the intrinsic value. Second, as the option nears expiration, the extrinsic value also shrinks and eventually goes to \$0.

This dynamic is what creates a performance that is very close to being long stock. There is a measurement known as delta that measures the rate of change between the option price and underlying stock price. For those of you that enjoyed calculus, you’ll recognize this rate of change as the first derivative.

Delta measures what happens to the price of an option as the underlying moves in price. Usually this is expressed in percentage points. So an option with a 0.50 delta means that if the underlying moves \$1, then the option will only move 50¢. Delta can also be negative, as it is with long puts. A move up in the stock will drive down a long put price. In the example we gave above, the SEP 1300 SPX call has a delta of about .075.

Being long a call means you are bullish and you profit as the underlying moves up. This is because the intrinsic value rises dollar for dollar. You could say that the intrinsic has a delta of 1 (100%) when a call is ITM. However the price does not go up \$1. In our example above a move of 10 in the SPX to 1405 would only result in the option price going up by \$7.5.

By a little deductive reasoning, we can determine that the extrinsic value declined by \$2.5 and would have gone from \$30 to \$27.5. This illustrates that as the option goes deeper in the money, the extrinsic value gets smaller.

Now that the extrinsic is smaller, the next time it moves up, we capture more and this is also reflected in the delta.

Eventually, the extrinsic goes to zero if the option is deep enough ITM and the time to expiration is reduced. Right now, the 1050 SPX calls have just about no extrinsic value in them and hence they have a Delta of 1.

On the flip side as the option gets less and less ITM, the extrinsic gains money but the intrinsic looses. This is why a \$1 lost in the underlying doesn’t result in a dollar loss in the position. The intrinsic loses \$1, but the extrinsic gains a little.

A side benefit of this delta-dynamic is that the volatility of the portfolio is reduced regardless of which direction it moves. And we know reducing volatility is always a good thing.

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