If the Greeks of options pricing are Greek to you, some of the Options 101 articles might prove challenging. Many articles also include charts that also show us how options prices will change under certain conditions. The profit-and-loss charts show what the Greeks tell us.
However, newer subscribers or those who haven't previously familiarized themselves with the Greeks of options pricing might like basic articles for reference. Two weeks ago, the Options 101 article discussed theta, and last week's article built on that discussion. This week, it's time to discuss theta, another of the two best-known of the Greeks.
Just as delta describes how much an option's value might change with a price change, theta describes how much the value might change with the passage of time.
One Long At-the-Money NDX Put, 22 Days to Expiration:
We see from the pull-down menu under the chart that the theta of this position is -54.66 (or -0.5466 if your quote source does not automatically apply the 100 multiplier). This put theoretically loses $54.66 in value for each day that passes.
Delta can be positive or negative, and so can theta. We remember that, with delta, the delta is positive for calls and negative for puts. Is that why theta is negative in this case, because it's for a long put?
No. All long single options that you purchase, whether calls or puts, will be negative theta. Whether we know much about the Greeks of options pricing or not, we know that the value of our options decays with the passage of time if price and other factors stay the time. The negative theta reflects that decay with the passage of time.
If we sell an option, the theta will be positive, and that time-related decay will benefit the trader who sold the option.
Same Put Strike, Same Time to Expiration, This Time Selling the Put:
We see from the pull-down menu that this time, the position has a positive theta of +54.66. If the SPX were to stay in the same place and implied volatilities and interest rates were to stay the same, this position would theoretically gain $54.66 in value for each day that passed.
That brings up another topic. Delta changes as time passes. Does theta? Instincts and experience certainly tells us that it will.
Same Sold Put Option, Time Rolled Forward Five Days:
Theta is now +62.25 for this sold option, if no other factors have changed. The absolute value of the theta will grow larger as expiration approaches.
Many readers will be familiar with this aspect of theta-related changes in an option's price, with the absolute value of the theta growing more rapidly in the last 30 days before expiration. The put that might have been valued at $25.10 twenty-two days before expiration would be worth only $1640 strike - $1638.17 current price = $1.83 at expiration if the SPX were to somehow sit at 1638.17 for that entire 22 days and then settle there on settlement Friday. The trader who sold that option and who was brave enough to hold it into option expiration (not me) would have been accumulating more and more unrealized profits as time sped toward expiration. Of course, the trader who had bought that option would have been experiencing larger and larger losses with each day that passed.
Traders should be aware, however, that option decay is not the same for puts and calls and for in-the-money, at-the-money, and out-of-the-money options. There might also be difference in equity options and those related to commodities. Out-of-the-money puts on equities, for example, sometimes hold onto their value a little better than out-of-the-money calls, due to their use to hedge against an Armageddon loss and other factors. Out-of-the-money calls on commodity-related plays might, too, because of their use to hedge against a sharp rise in commodity prices.
Options away from the strike price tend to lose money at a faster rate as their time to expiration moves from sixty days to thirty days than do at-the-money options. That's one reason that James Bittman, author of Trading Options as a Professional suggests that those who employ strategies that involve selling more premium than they're buying (i.e., iron condors) might do better to open their trades about sixty days before expiration and close them at thirty rather than to open them at thirty days and close them near expiration.
What about changes in implied volatility? Let's go back to our example of a sold put, sold twenty-two days before expiration. Let's lower the implied volatility a bit.
Sold Near-the-Money Put, Implied Volatility Rolled Lower:
The pull-down menu now shows that the original +54.66 theta for the position has now been reduced to +40.06. It's as if lowering the implied volatility moved the expiration further away. Raising it acts the opposite: it raises the absolute value of theta, as if expiration had moved closer.
Complex options positions can be either negative theta (debit call or put spreads, for example) or positive theta (most butterflies, calendars and iron condors, for example). What would happen to theta, however, if price ran way outside a butterfly's tent? Maybe that's a discussion for another time.
This is, of course, only a basic look at theta. It hopefully serves to point out some aspects you might investigate more fully. Bittman, a CBOE instructor, devotes a whole chapter to theta and other discussions in chapters on implied volatilities and complex trades. Bittman's book makes a decent if sometimes stodgy reference book, and the CBOE and the educational arm of the OIC, optionseducation.org, offer free online classes, too. Don't rely on books alone, however. Use a simulator available through your charting program, freeware such as OptionsOracle, your brokerage or even CBOE's free tools to test the effects of the passage of time and changes in the underlying's price and volatility. Start building your own sense of what happens with your preferred trade, and how quickly decay helps or hurts your profit-and-loss line.