Last week we began a series on the Greeks. These are the variables that describe how option prices are expected to change, in response to certain forces. Today we’ll continue with that subject.
There are exactly five forces that, collectively, are assumed to completely account for all option price changes. Each of these forces acts separately from the others. Each of them acts in one of two directions – it can either push upward or downward on a given option’s price.
Besides direction, each of the five forces has a specific magnitude. Those magnitudes are the values given by the Greeks.
At any time, three out of these five forces might be pushing an option’s price upward, with the remaining two pushing it downward; or there might be five down and zero up; or any other combination of upward- and downward-pushing forces. But the count of ups vs downs is not in itself definitive. It is quite possible that there could be four forces pushing downward on an option’s price and only one pushing upward, and that the option’s price would go still up. This could happen if the magnitude of the one upward-pushing force was greater than the magnitudes of the four downward-pushing forces combined.
The educated option trader understands the meaning of the Greeks, and has a big edge over traders who do not. In these short articles I can’t give you all the tools to exploit the Greeks to maximum advantage, but I can give you the broad outlines.
Here is a brief summary of the Delta, the first of the Greeks we discussed (last week):
Greek name: Delta
Force acting on option price: Actual movement of underlying stock price
Unit of measure: Pennies per share of option price change for a one-point increase in underlying price (multiply by 100 to get the amount of price change per option contract)
Sign: Positive for calls, negative for puts
Notes: Options which are far out of the money have the minimum possible Delta value of zero. Options which are far in the money have the maximum possible Delta value, which is +1 for calls or -1 for puts. The absolute value of Delta can never exceed 1.0. If it did, then an option’s price could move faster than its underlying stock. That would give rise to an opportunity for risk-free profits. A Delta value of zero indicates that the option is worthless, and that the next one-point change in the price of the underlying would not alter that – i.e. that the option is far out of the money.
So much for Delta, for now. Next, let’s discuss what is usually the next-most-important of the Greeks after Delta. That one is Vega. As you may know, Vega is not actually a Greek letter. Why the developers of the option pricing model decided to use the name Vega for this purpose is not entirely clear. If you are a math purist who insists on Greek letter names for variables, you can use its alternate name, Kappa. But no one will know what you are talking about, since you will be the only one.
Whatever you choose to call it, Vega/Kappa measures the magnitude of the expected change in an option’s price due, given an increase in market expectations of future underlying price moves. Wow. That’s a mouthful of stacked abstractions. Let’s break it down.
First, let’s just say plainly that the options of fast-moving stocks are worth more than the options of slow-moving stocks. Take stocks A and B. Both stocks are currently trading at $100 per share.
Stock A moves, on average, within a range equal to 50% of its price in a year. We would say that it has a historical volatility of 50%. If the coming year were typical, we would expect Stock A to move in a range $50 wide (50% of $100), with that range centered on its current $100 price. In other words, we would expect that a year from now, the price of Stock A would most likely be between $75 and $125.
Stock B, on the other hand, has a history of moving within a range equal to only 10% of its price in a year – a historical volatility of 10%. In a typical year, we would expect Stock B to move in a range $10 wide, centered on its current $100 price. We would expect that a year from now, the price of Stock B would most likely be between $95 and $105.
So a year from now when the options expire, Stock A might be anywhere within a wide range between $75 and $125. Stock B will probably be in a much narrower range, between $95 and $105. Consider an option that will only pay off if the stock exceed $120 a year from now. Clearly this would be a bad bet for stock B, but a pretty good bet for stock A. For stock A, a $20 move is all in a typical year’s work. A $120 option on it would be much more valuable than on stock B, which is very unlikely to make a move that big.
OK. High-volatility stocks have expensive options, while low-volatility stocks have cheaper options, all else being equal. But what if an individual stock’s volatility changes? A new product line, a major acquisition, or a change in the company’s competitive position might suddenly make a stock much more (or less) volatile. Volatility itself is not static. As you can well imagine, a stock that is more volatile this year than last year will have more expensive options now than formerly, at any stock price. It is sort of as if non-volatile Stock B became volatile stock A.
So far so good. A change in volatility of a stock logically leads to a change in the value of its options. Increasing volatility will make the options (both calls and puts) more expensive, and decreasing volatility will make them cheaper.
Now for one more step. The amount of volatility that is reflected in the price at which any option currently trades, is not solely based on how fast the stock has actually moved in the past (its historical volatility). Instead, it is based on expected future volatility, also called implied volatility. If option traders expect a stock to move faster in the future than it has in the past, then they will pay more for the options (both puts and calls) now. This will be true whether the stock has yet actually begun to move faster or not. How much more the traders will pay is given by the variable Vega.
Note that the expectations for future volatility have no effect on the amount of intrinsic value in an option. Intrinsic value is determined solely by the relationship between the underlying price and the option’s strike price. The one and only thing that can change an option’s intrinsic value is actual movement in the underlying price. Therefore changes in implied volatility only affect the non-intrinsic-value portion of an option’s price – its extrinsic value, also referred to as time value. That being the case, we would expect options that have a large amount of time value to be more effected by changes in implied volatility, than options with a small amount of time value. This is in fact the case.
So far, here is our summary scorecard for Vega.
Greek name: Vega
Force acting on option price: Market expectations of underlying stock’s future volatility (aka Implied Volatility).
Unit of measure: Pennies per share of option price change for a one-percentage point increase in implied volatility (multiply by 100 for the price change per option contract)
Sign: Positive for calls and puts. Increasing volatility makes both option types more expensive.
Notes: Options which are at the money have more time value than options which are either in the money or out of the money. At the money options therefore have the highest Vega values. As the underlying price moves, an option’s moneyness changes, which changes the amount of time value in the option; therefore the option’s Vega changes as well. Options that expire further in the future have higher Vega values than those that expire sooner, because those more distant options have more time value. The passage of time causes Vega values to decrease.
That’s all the space we have today. Next week we’ll continue our examination of the Greeks.
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