If you're dealing with those kind of wings, its probably best to eschew explicitly calcing the theta decay (unless you're capturing the daily steepening of the skew) - you'll probably finding your model telling you it quickly becomes worthless, while in reality it'll keep a bid. I'd say to just look at the current weeklies that have the same time to maturity that you're interested in. Ie, if you're selling the 1m 5d put, and want to know its value in 1 week, look at where the 3 week 5d put is pricing. As with everything, its imperfect, but probably the simplest, most robust means.
I have to come back to , essentially, the same issue looking at it from a more theoretical perspective. What is hard for me to understand is why the price of a same delta option varies with time. Why does the price of a 0,05 delta 1 month to expitarion have to be different than a 0,05 delta 1 week to expiration? I guess that time value is already incorporated in the value of the delta, so I would expect that same deltas mean same prices. Also delta shows, though not completely accurately, the possibility of the option expiring ITM. So, does it make sense to have equal deltas but different corresponding prices? Off course it does, but there is something I am missing here...
because one has more time until expiration. You might note, that to get the same delta AND price from a 1 month and a 1 week till expiry (same underlying) you either have to have massive volatility differences or a strike difference. (maybe a dividend but lets not go there) The alternative could be that you have an ATM in different expiry dates, with the same delta, different implied vols and similar prices.....but then the gamma will be radically different. Time value is incorporated into the price, the delta is a derivative of the price and how it moves. delta is about the change in prices.....its not really representative of the actual prices. Your 2nd sentence is wrong. yes - it makes perfect sense - you clearly are not understanding what delta is or have some unique situation. Can you show an example of where you have the same delta options, same type (put or call), different expires and the same price? Using way OTM options will be similar in price as they are all relatively small in price, but its unlikely to have the same deltas.
Yes... This is exactly the issue. There is a 'time decay' in delta and that reflects into the price. It is totally a mathematical issue. I just cannot grasp the whole idea from a theoretical standpoint...
in laymans terms from a theoretical reasoning why - delta will increase to 1, or decrease to 0 over time based on weather or not it is ITM, OTM. Everything else being kept equal. This is simply because they have less optionality over time.....hence they either behave more like the underlying when ITM, or if OTM naturally the delta has less effect as they lose the optionality. (well picked up by Doobs789 as I read multiple different questions being asked.)
I 'll give an example so that I make sure we are on the same page here. - 1920 May s&p Call, delta 0,08 , price 1.50 - 1960 May s&p Call, delta 0,08 , price 2.50 So, there is a $1 premium holding the 0,08 Delta June call relative to the May call.
I am assuming your 2nd option there is meant to be June???? (otherwise it makes no sense) So its a 1960 June call? If so - then things are not equal - you have different strikes. This seems perfectly normal. Is your question - despite being different strikes, and despite being different expiries, given they have the same deltas, why dont they have the same price?
Yes it is June... And yes.. The question is this exactly. I would expect same deltas to have equal prices, but they haven't. I am trying to figure out why
Delta is not the "probability" of being in the money. And being in the money isn't the only criteria to think about with the option. You also need to think about how deep in the money you can be. Today, right now, both have the same sensitivity to a small change in spot. But over time and spot ranges, their sensitivities (gamma, gamma of gamma, etc.) will differ. The June option should be worth more because there is more time and hence a wider distribution of possible in the money scenarios.