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Ok, here is the scenario -

Trying to enter into long deep ITM call position with target of about 4 weeks and considering following cases

  1. Buy weekly call options and roll them into next week on the expiration day

  2. Buy calls expiring directly 1 month out

Now the goal is to minimize the extrinsic or time value paid per day and find out which case achieves that.

Looking at option chain with ATM IV values, I notice that IV is showing lower for one week vs one month. Off course, in real world the IV would not remain constant for every week cycle, But assuming theoretically it does not change -

Would #1 be cheaper on cost basis ? So basically, total time value spent 4 times could be less than time value spent just once ?

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Premium decay is non linear and speeds up as time passes. Therefore, for other than high delta options, the cost per day will be less for longer dated options. Simply determine the time premium and divide by the number of days until expiration.

If you're buying very high delta calls, the time premium won't matter much. Where you'll probably get ripped is the B/A slippage and commissions (if you're still paying them). Deep ITM options are usually illiquid with wider B/A spreads and buying weekly options and rolling them every week will be cost ineffective.

As a general rule, option sellers should sell nearer expirations in order to take advantage of the higher theta decay and option buyers should buy further expirations in order to avoid being penalized by theta decay.

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  • $\begingroup$ Thank you, precisely what I was trying to determine if time premium is linear assuming IV is same for different expirations. If I plot time premium on the option price calculated with Black-Scholes , the graph is almost linear in the short term at least. $\endgroup$ – John Smith Oct 2 '20 at 14:13
  • $\begingroup$ You're welcome. I added a theta decay graph to my answer. You can see how theta falls off the cliff toward expiration. $\endgroup$ – Bob Baerker Oct 2 '20 at 14:40
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Deep ITM options will not have much time value left and will experience very little time decay. They will trade like the stock as the delta will be very close to 1. All else being equal (same strikes) one week options will have faster time decay than one month options. However, one month options will have rapid time decay as well.

By using one week options, you will have roll risk in that implieds could pop and you may end up paying a little more (this could work for you as well). A one month position will be easier to manage and have lower transactions costs as you wouldn't have to transact as often. But you will not save much on time decay (if at all) if you are using deep ITM options--basically it makes no difference.

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  • $\begingroup$ Thank you, this is very helpful. $\endgroup$ – John Smith Oct 2 '20 at 14:07

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