Wrapping up my recent series on long call spreads (which starts here) got me thinking about the tight, not-always-understood relationship between options pricing, implied volatility and the trade's overall probability of success. Which factor comes first is a common chicken-or-egg dilemma among seasoned options traders -- but knowing that there's such a tight interrelationship isn't always obvious to newer traders. Let's explore what that interrelationship means to you as a trader. Read this first!
It's critical that we define our terms before moving forward. If you're not familiar with these concepts, I've included links to previous posts on my blog to get you started.
"Pricing" is probably the most obvious concept: what buyers are willing to pay and what sellers are willing to accept for an options contract. "Implied volatility", or IV, is a figure, derived from recent options prices, that captures what the marketplace is "implying" the volatility of the underlying security to be in the future. (I explained some of the factors behind options pricing and basics of IV in an earlier series, beginning here, called "Where Do Options Prices Come From?" I'd also strongly recommend that you take a look at part 5 of my series, 'Why Do We Care About Volatility?' It explains how you can use volatility to trade a credit spread and offers a perfect lead-in to the discussion on today's post.)
"Probability" of a trade's success refers to the chances your trade will earn one penny or more before expiration. (For simplicity's sake, we're not worrying about commissions or taxes in this calculation.) In many ways, it's the most "real world" of these three related concepts.
Simple Example
Let's start with a super-simple example. If you pay 2 dollars for a 5-point debit spread, you're essentially risking 2 to (hopefully) make 5, a trade with a 40% probability of making at least one penny (2 debit, divided by 5 point spread). If you'd paid 2.5 instead of 2, you'd have a 50% probability of success, and so on as you pay more in initial debit. Of course, if you pay less, that probability of success starts to sink. There's a mystery we're going to unravel -- or at least reveal -- in today's post: why is the price 2, exactly? And how does that price relate to IV and the trade's probability of success?
What's my probability of success? An example.
Let's move to a more concrete example, AAPL. As I write this AAPL is trading at 136.04 on8/30/07, so imagine we're putting on the following credit spread:
Apple @ 136.04
Buy AAPL Sept 07 150 Call @ 1.45
Sell AAPL Sept 07 145 Call @ 2.55
Net credit +1.10
Max gain = 1.10
Max loss = 5 - 1.10 or 3.90
Breakeven = 145 + 1.10 or 146.10
Our breakeven is the net credit plus the lower strike price, 145 + 1.10. The risk is pretty standard stuff so far, right? Now, let's check out the probability of success on this trade and make sure it's a move we can feel confident about. To do this, check out TradeKing's Probability Calculator (under the Tools menu). This tool offers a great, "math-lite" way to check probabilities for any trade you might be weighing.
(To enlarge this picture please click here.) Plug these numbers into the calculator, and you'll see there's approximately a 75.73% chance that the stock will stay below the breakeven of 146.10, i.e. in our profit-making zone.
But now let's look at the math from another, more common-sense angle. With this trade we're risking 3.90 (5 - 1.10 credit) to hopefully make 1.10 or basically the net credit received. The width of the spread is 5 points (145 strike - 150 strike).
5 - 1.10 = 3.90 risked on a 5 point wide spread
3.90/5 = 78% probability of success
But caveats aside, the larger principle should be clear: no matter which way you calculate the figures, your probability of success should be basically the same. And it's not just a fluke: all these symmetries tie back to those prices for each leg, +2.55 earned on the sold call, and 1.45 spent to buy the 150 call. Those numbers aren't nearly as arbitrary as they might at first seem. Higher or lower prices on those options start a domino-effect, impacting first implied volatility (which is derived from the options price). Then implied volatility is used in the calculation of the probability of a stock closing below or above the break-even point by the expiration date of the options.
If any one of those figures gets too far out of whack, the market will rush to correct the error. Imagine your eagerness if you could score a higher-probability trade than the going rate -- but those prices wouldn't last long, as traders like you would rush to take advantage and bring the calculations all back into sync with each other.
Next week I'll take this from another angle, a debit spread, and talk a bit more theory to illuminate the concept further. But hopefully you've had an "aha!" moment or two. Understanding that these three factors work in tandem is pretty key to how options work.
Regards,
Brian (OG)
[image: knotted rope by lady mohan on flickr]
Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options.
While implied volatility represents the consensus of the marketplace as to the future level of stock price volatility or probability of reaching a specific price point there is no guarantee that this forecast will be correct.
Any strategies discussed or securities mentioned, are strictly for illustrative and educational purposes only and are not to be construed as an endorsement, recommendation, or solicitation to buy or sell securities.
