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# "Skews, Ranges, and Probabilities"

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"Skews, Ranges, and Probabilities"
By Lee Lowell

Let's finish off our subject of volatility "skew". For anyone just recently joining us, you can look at our past discussions on the OI website under the "Options 101" section. To recap, volatility "skew" is a characteristic of options where the implied volatility level is different for each option in the chain. Instead of all options trading at the same volatility (flat skew), each option has its own unique implied volatility which can be either higher or lower than its neighbor option. This is called a volatility "skew" and it can take several different shapes.

I want to discuss another strategy that takes advantage of the skew effect. It is the type of skew in which the OTM calls get increasingly cheaper on an implied volatility basis. We'll use the backspread as an example. In a backspread, the trader will sell an ITM call and buy two or more ATM or slightly OTM calls for a credit in the account. The backspread can be used after a stock has a pullback, but the trader is still bullish over the longer term. But if for some reason your prediction is wrong and the stock goes down, you still have the initial credit to soften the blow. Assume the scenario: IBM is trading at \$100/share. The June \$70 call is trading at \$35 with an implied volatility of 45% and the June \$100 call is trading at \$10 with an implied volatility of 40%. Let's sell 1 June \$70 call and buy 2 June \$100 calls for an initial credit of \$15. This gives us unlimited profit potential if IBM moves above our breakeven point of \$115 because we'll be longer 1 extra call option.

Now if these call options had a flat skew, our profit picture would look a little different. We'll keep the \$70 call as is, but move the \$100 call's implied volatility to the same level as the \$70 call. Now we have a flat skew where both options are trading at 45%. The \$70 call is still worth \$35 but now the \$100 call is worth \$13. If we initiate the same backspread, we'll start out with a credit of only \$9 this time and our breakeven has moved up to \$121. You can see how volatility skew can change your profit/loss scenarios. Like I've said previously, if you buy an option with lower implied volatility than the option you're selling, you start off with an advantage.

Basically, whenever you put on any options strategy, whether it is an outright buy or sell of a single call or put, or any complicated spread, just make sure you have an idea of what the volatility level is or what the skew looks like. Knowing your volatility levels and skews ensures you of starting with an advantage or disadvantage for your option position.

Not only can implied volatility give us an idea of whether options are relatively cheap or expensive according to past levels, but it can also act as a predictor of possible future movement of the underlying. When you're trying to figure out the probability of profit of your option position, it is the implied volatility that can help. Let's use IBM again. IBM is at \$100/share on March 1. You want to sell credit spreads to bring in some extra income to your account, but you need to have an idea of what range IBM might trade in over the next six months. Is there a way to figure that out? Yes.

Remember what implied volatility really represents? It's the market's best guess of the future movement of the underlying stock until expiration day. If IBM has a 35% implied volatility, that means that IBM should be trading in a range of +/- 35% from its stock price today over the next year. Well what if we want to find out what the range of IBM might be over the next 6 months, 6 weeks, 6 days, etc. Here's a formula for figuring that out. The implied volatility of 35% helps us figure out a 1 standard deviation move for IBM. This will give us a range for IBM that is 67% accurate. Here's what the formula looks like:

1 STD move = (IV) x (Underlying Price) x (Square root of DTE/ 365)

Let's put in some numbers:

IBM = \$100

IV (implied volatility) = 35%

DTE (days to exp.) = 180

365 = days in a year

STD (standard deviation)

1 STD = (35%) x (\$100) x (Square root of 180/365)

1 STD = (.35) x (\$100) x (.70)

1 STD = 24.5 (approx.)

Our result tells us that over the next 6 months, IBM should trade in a range of \$75.50 - \$124.50 with a 67% success rate. If we wanted to be sure with a 95% accuracy rate, then we just double the range to +/- 49 points. So if you were going to sell put or call credit spreads on IBM, use the 2 STD calculation to give yourself more margin for error. Now you know you should sell the \$150 calls or the \$50 puts as the short leg of your spread. This way you are 95% sure that IBM won't trade through your short option. Check your options chains to see if these strikes have enough premium to sell because they are quite a bit OTM. I would suggest not selling any spreads for less than \$0.75. It's just not worth it for that little amount. There's always an exception though. Just remember there's a 5% chance that IBM will go beyond the ranges we just figured out. And you must be aware of the changing implied volatility of IBM. You should probably re-calculate your ranges once a week to make sure your still comfortable with the spread. Always be prepared for the unpredictable.

Now don't just go out and haphazardly sell any credit spreads on any stock. You still need to take into consideration the relative level of volatility. Try to sell credit spreads when the stock's volatility is in its high end of the historical range. And look at the price trend of the stock too. If the stock is in an uptrend, you'll be better off selling put credit spreads. If the stock is in a downtrend, you should look to sell call credit spreads. If the stock is in a trading range, then you could sell put and call credit spreads at the same time on the same stock using the same month's expiration.

Let's do one more example with the following data:

EBAY = \$150

DTE = 35

IV = 75%

1 STD = (.75) x (\$150) x (sq. root 35/365)

1 STD = (112.5) x (.31)

1 STD = 35 points

EBAY should trade in a range of \$115-\$185 over the next 35 days with a 67% accuracy or \$80-\$220 with a 95% accuracy. So set your spreads accordingly.

So we've figured out our probabilities if we're selling the options. What about if we buy an option? What's our probability of the option being ITM by expiration? That's where the delta of the option comes into play. The delta of an option can tell us a few different things.

One, the probability of our option finishing ITM by expiration day. If you buy a call option with a .75 delta, this is telling you that the option has a 75% chance of being ITM by expiration. A delta of .25 indicates a 25% chance of our option finishing ITM. This doesn't mean that you will make money on your option even though it might be ITM by expiration. If you bought an IBM \$130 call at \$10 and IBM closes at \$132 on expiration day, you will have lost \$8 on your trade even though your option finished ITM. You really want your option to finish ITM by more than what your option cost you. In order for your \$130 call to be profitable, you need IBM to close above \$140 by expiration.

The delta also tells us the rate of change in the option price compared to the movement of the underlying. If your call option has a .75 delta, this means that for every \$1 move in the underlying (up or down), your option price should increase or decrease by \$.75. The last way to use the delta really affects floor traders more than anyone else. The delta number will tell you how many shares of stock to completely hedge against your option position. If you buy 100 call options with a .75 delta, this is equivalent to being long 7500 shares of stock. So you would need to sell 7500 shares of stock to be completely delta neutral. This really applies to floor traders who deal in large quantity of stock and options. They do this sort of hedging activities to lock in price discrepancies of the options. They will buy or sell large quantities of the options and then immediately offset their risk by simultaneously buying or selling the underlying security in the amount indicated by the delta.

That pretty much sums up what volatility skew is all about. We've also seen how to figure out the probable range of a stock over a certain amount of time, and the probability of an option position finishing ITM by expiration. As Forrest Gump once said, "That's all I have to say about that".

Good luck,
Lee Lowell

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