# Are there comprehensive analyses of theta decay in weekly options?

Are there comprehensive analyses of how much theta a weekly options loses in a day, per day?

I know what the shape of theta decay looks like, in theory, where the decay towards zero happens more rapidly the closer you get to expiration.

But with weeklies, an example question would be: do they lose 20% by first Friday (with the weekend theta decay getting priced in by market close), or is it 30%? 10%?

Assume the option is at the money, or 1 strike out of the money. This is the area where the extrinsic value will be greatest.

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While the time decay on the time value component of an option does not depend on how much the option is in the money, theta is the change in total option value not just the time value due to the passage of time. Time decay is higher for options that are out of the money assuming volatility and the risk free rate are held constant. This is because a greater proportion of the full option value is intrinsic value for an option that is in the money. An option that is out of the money has a greater proportion of its value in the time value of the option so the time decay will have a greater impact. If you don't want to work through the Black-Scholes model, you can also use the GBSCharacteristics function in the fOptions package within the R programming language to test for various input combinations.

The fundamental model of small changes in the derivative increasing to larger changes in the derivative as time to expiration decreases is true in all cases. What changes is the convexity. As volatility increases and all else is held constant, the change in the rate of time decay increases. Another way to look at it: as volatility approaches 0, the graph will approach a straight line but the top left portion will always have smaller changes than the bottom right.

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yes, assume at the money or 1 strike out of the money where the extrinsic value is greatest. – CQM Dec 3 '11 at 23:33
I'm not sure what you mean by extrinsic value. If you mean "intrinsic value" it would be maximized when the stock price is highest compared to the exercise price for a call and the opposite for a put. This would be considered in the money not at the money or out of the money. If you're referring to when the time value is greatest, that would be when the option is out of the money and would have a greater time decay. Assuming we hold constant time to expiration, the risk free rate, and strike price such that a call option is at the money, time decay increases with volatility. – ProbablePattern Dec 4 '11 at 3:08
extrinsic value is everything that is not intrinsic value... so theta, volatility. – CQM Dec 4 '11 at 3:47
My last comment on the time value would apply. – ProbablePattern Dec 4 '11 at 13:06
Theta decay doesn't depend on the in the moneyness – DKM Dec 9 '11 at 18:03

Theta decay doesn't depend on the in the moneyness. A 70 delta call and a 30 delta call have very close theta decay at any given moment. They are slightly different because of skew with 70 delta put having slightly bigger theta. Theta is the decay of extrinsic value.

In practical trading, you can assume your decay distribution (using your graph is fine) using a fair volatility but nobody can say for sure what the theta decay distribution ought to be. To answer that question isn't all that useful anyway. In practical trading and in the weeklies, decays are slower than the theoretical because people still have bids out there to close their position or the asymmetry of buys and sells. (People don't really want to sell pennies/nickels unless they're long already).

And theta really depends on the stock events because for a weekly on monday and an announcement is coming out on friday, there'll be almost no decay until friday. It becomes more of a break even play since you don't expect to scalp your long gamma.

Think about theta as the token to play the gamma game, with so few days left it becomes a break even game since these options will have smaller and smaller deltas.

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Can you elaborate why you say that theta decay does not depend on moneyness? For a deep ITM our OTM option, theta is close to minimal...hence obviously the decay is also going to be minimal. Theta and hence decay is highest for ATM as CQM suggests. Is it not correct? – Victor123 Feb 25 '15 at 18:05