Last week I wrote a back-to-basics article about the nature of options. I noted that the causes of the change in the value of an option include: changes in price of the underlying asset, the passage of time, and changes in market expectations of volatility. Today we’ll expand on that.
Each of those three separate forces can be estimated, and each has a measure with a Greek letter as its name. Those measures, or “Greeks,” tell us how an option’s price should respond to each type of change. Since every option contract is a zero-sum proposition between the option buyer and the option seller, any change that puts money into the pocket of one of them, takes that same amount of money out of the pocket of the other.
Let’s use a concrete example for our explanation from here on.
As of the date of this writing, September 18, 2013, the SPY exchange-traded fund closed at $173.05, a new all-time record high. Markets were giddy with the news that the Fed was not going to stop buying Treasury bonds any time soon. Other equity indexes also made new highs. Gold had its biggest one-day gain in years. Bond prices soared. It seemed that the only thing dropping was retail gasoline prices. A good time was had by all.
Imagine the reactions of two investors, Rosie and Thorne.
Rosie loves breakouts. Her strategy is to buy whenever a new high is made. She learned to trade four years ago and she’s been trading this way the whole time. She’s done very well. Economic numbers are coming in pretty well. The fed is putting more rum in the punch bowl. There is no resistance overhead, since the market has never traded this high. Since SPY’s previous high at 171 has been cleared, she’s looking forward to another up leg, and she’s looking to add to the bullish positions that have worked so well.
Thorne, on the other hand, is always suspicious of upward movement. He looks for any opportunity to bet on prices reversing to the down side. He loves to be short. This has cost him some money over the last few years, as markets have moved relentlessly higher. But he learned to trade in 1999, and remembers the crashes of 2000 and 2008 vividly. He notes that the debt ceiling talks are coming soon. Geopolitical crises await all over the word. The Fed meets again in six weeks. He is sure that the current folly will be short-lived.
Both traders eye the SPY October 173 call options, whose current price is about $1.87. Rosie contemplates buying these options as a way to get control of this $173 asset for less than two bucks. If SPY goes up strongly, as she expects, those options will shoot up too. If SPY goes up less than 5%, to $181 in the next few weeks (and how could it not?), those 173 calls will be worth $8.00. She will more than quadruple her money. She slaps down her $187 and buys a call.
Meanwhile, Thorne believes that Rosie (whom he doesn’t know personally, but whom he is sure is out there somewhere) and her pals are delusional. Thorne believes that SPY will drop from here, and will be far below $173 tomorrow, and lower still in a few weeks. He eagerly hits the Sell to Open button, taking in $187 in credit into his account for selling those same 173 calls.
Thorne and Rosie are now on opposite sides of their bet. What happens now?
The Greeks tell us how the option price will react.
First, how will a change in the price of SPY affect each of them?
That is shown by the property of the option called the Delta. The Greeks are shown on the option chain for each option. For our November 173 calls, Delta was .54. The Delta of an option represents the percentage of the next 1-point change in the underlying price that the option will experience as a result of that change. A Delta value of .54 indicates that for the next $1.00 change in the price of SPY, this option will change by 54% of $1.00, or $.54. This applies whether the underlying price change is up or down. The call option’s price will move in the same direction that SPY does.
If SPY goes up another dollar, to $173.05, the call option’s value will increase by $.54, from $1.87 to ($1.87 + $.54) = $2.41. At that point, Rosie could take her profit, if she wished, by selling to close the call option at the new $2.41 value.
If Rosie were to choose to do this, Thorne would not be affected, even though he sold the same option that Rosie originally bought. As I mentioned last time, the option clearing house (the Options Clearing Corporation, OCC) interposes itself between every buyer-seller pair. Rosie bought the option and Thorne sold it. But technically Rosie bought from the OCC and Thorne sold to the OCC. So Rosie’s later sale doesn’t affect Thorne’s deal. He is still short the option.
Fine. So let’s say Rosie does this and is now out of the picture. Where does Thorne stand? The call he sold short is now worth $.54 more than when he sold it. His position shows an open loss of $.54 – the same amount that Rosie made. His loss is still a paper loss – an unrealized loss – for now.
Note that the delta of this call is not fixed at 54%. Delta describes its reaction only to the next $1.00 of price change in SPY. For any further change, Delta will be different.
This brings up the next aspect of Delta: it also represents the approximate probability of the option’s finishing in the money. In this case, that means the approximate probability (which is calculated based on SPY’s past volatility) that SPY will be above $173 at the expiration in October. Now that SPY has moved up, that probability is higher than it was. It has $1.00 less to move now in order to make that happen. The new Delta value then will be about .64.
How do we know what the new Delta will be after a price change in the SPY?
Because of another of the Greeks, called Gamma. We’ll talk more about that, and the rest of the Greeks, next week.
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