# Options – More Links in the Chain

The week before last we discussed who the option market makers are and last week we went over the Option Chain. To recap, the option chain is the list of put and call options that are available to trade on a given stock or exchange-traded fund. Today we’ll finish that discussion.

Besides the elements we discussed before, the chain gives us information about what will move each option’s price and how much. Collectively, these variables are called the Greeks because they have been named with Greek letters.

Here is a more complete option chain, now with the Greeks displayed as they normally are:

Notice the new columns labeled Delta, Theta, Vega and Gamma. Each one of these numbers shows how an option’s price will be affected when a particular thing happens.

First a quick description is in order of the main factors that change option prices. These are:

- Actual price change in the underlying stock. This is measured by the Greek called Delta.
- Changes in market expectations of future price change in the stock. Measured by Vega.
- The passage of time. Measured by Theta.

First, the movement in the underlying stock: The stock’s price is constantly changing as different numbers of investors ebb and flow on both the buy side and the sell side. At any given moment a certain number of shares are being bid for at the current price by potential buyers; while a certain number of shares are being offered by potential sellers at that price. If the bids outnumber the offers, then the stock price must move up, as the unsuccessful bidders are forced to pay higher prices after all the shares available at the original price have been sold. If, on the other hand, the offers outnumber the bids then the reverse happens. The unsuccessful sellers must accept lower prices to get rid of their shares after all the bids at the original price have been filled, and so the stock’s price must move down.

As the stock price fluctuates, the value of every option changes as well. Call options represent the right to buy the stock at a fixed price (the strike price). The higher the stock price is the more of a bargain that fixed price is. And so, as stock prices go up call values go up. And as stock prices go down call prices go down.

The reverse is true for Put options. Each of them represents the right to sell the stock at a fixed price. If the price of the stock goes lower, then that right to sell at a fixed price becomes the right to sell at an above-market price. The lower the stock goes the farther above the market price that put’s strike price is and, therefore, the more valuable the put is. As stock prices go down, put prices go up and vice versa.

The Delta is the variable that tells us just how much a given option’s price will change for the next small increment of stock price change. For example, in the top left quadrant of the option chain above, we see that the Call option at the 170 strike price has a Bid of $2.37 and an Ask of $2.40. Looking left to the column labeled Delta, we find a value of .5223. This means that if the underlying asset, IBM stock, rises by $1.00 from its current price of $170.22 to $171.22, then the value of this call option will increase by $.5223 per share. Stock up $1 = option up $.52. It also works in reverse; stock down $1 = option down $.52. That .5223 value is the percentage of the stock price change that the option will experience.

Notice that following across to the right in the option chain, we see that the Delta of the Put at the 170 strike is a negative number, -.4775. That means that if IBM goes up by a dollar, the value of this put will go down by $.48. And if IBM goes down by a dollar, the value of the put will go up by $.48.

We can use this information to estimate our risk and reward on an option trade. It helps us answer the question: if the stock does what I think it will, how much will my option position make?

Another of the Greeks shown above is Vega. While Delta measures the change in an option value for an actual change in stock price, Vega measures the effect of changes in expectations of the rate of change in future stock price movement – in other words, changes in implied volatility.

The quick explanation of Vega is that if option buyers change their opinion of how fast the stock’s price will move, that will change their valuation of every option. If they expect the stock to move faster, they will be willing to pay more for every option (both puts and calls). If they expect the stock to slow down, then they will be willing to pay less for any put or call. Less speedy movement of the stock means that the amount of value that an option can gain by stock price movement is less, and so that change in expectation is instantly reflected in the options’ prices. Vega tells us what the magnitude of this effect will be.

In our chain above, our June 170 call option has an Implied Volatility reading of 16.49%, and a value in the Vega column of .1385. According to the Black-Scholes option pricing formula, the Implied volatility reading of .1649 means that buyers of this option are expecting IBM to move in such a way that a year from now it should be in a range that is plus or minus 16.49% from its current price.

The Vega reading of .1385 means that if option buyers change their expectation of the rate of change in IBM stock, such that they now believe that its range could be plus or minus 17.49% instead of 16.49% (a one percentage point change in implied volatility) then this option will increase in value by 13.85 cents per share. A one percentage point increase in implied volatility equals a $.14 increase in the option value. And a one percentage point decrease in implied volatility equals a $.14 decrease in the option’s value.

We use Vega to help us estimate what will happen to our option position when expectations change. If expectations are overblown (shown by an unusually high reading for implied volatility), then most likely those expectations will decrease so that implied volatility returns to a more normal level. Vega tells how much that will affect our position.

Last for this week is Theta. This one shows us how fast an option loses value due purely to the passage of time. Almost every option loses a part of its value every day. This is because with every passing day, there is less time for the stock price to move. Since each option makes more money the farther the stock moves, its potential profits decline day by day as the scope for movement decreases.

Theta shows us how much value the option will lose in the next day, separately from the effects of stock price and expectations. Our June 170 call has a Theta value of -.0751. This means that tomorrow at this time the option will be worth $.08 less per share than it is no due to time decay alone. This effect will be added to the effects, if any, of stock price change and changes in expectations that have happened between now and then. The net effect on the option price will be the sum of the effects measured by Delta, Vega, and Theta.

Fortunately for us as option traders, there are software tools that make these calculations for us helping us to see visually how our option position is likely to do. That will be the subject for a later article.

Now you know the meaning of most of the columns in the Option Chain.

Understanding the Greeks is key to successful option trading. I’ve just scratched the surface here. For the full story, contact your local center about our Professional Options Course.

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