In your part about modeling the likelihood of an OTM spy option goes ITM, you are assuming SPY follows a normal distribution. I think this is where the disconnect comes from with the positive expected value because that underlying assumption probably is not correct.
Also, 0.02 is the bid price. You won't get filled buying that option for 0.02, rather the asking price of 0.03. Although the difference is small, it's 50% more expensive than in your calculation. While "last" does say 0.02, it could be someone selling a call at the bid so it's not a safe assumption you can buy this option for 0.02
Maybe it would be a good idea to do some more research on stock price distributions on my part. Are you aware of anything that might let us put together a stock price distribution more accurately?
Regarding the bid price, you are right that most likely you would not be able to get filled at the bid. The way I look at it is somewhat twofold.
1. It is unlikely that you get filled, but if you place tens or hundreds of orders like this the probability of one them getting filled is higher, and you only really need one to get filled anyway.
2. Even if you did not purchase at the bid price, I think it would be a somewhat trivial difference. The option is 50% more expensive, however, the idea is that these options should run hundreds of percent. That is unlikely, but again, if we have just one of these we can pay for our losses and then some.
Opinion-
In your part about modeling the likelihood of an OTM spy option goes ITM, you are assuming SPY follows a normal distribution. I think this is where the disconnect comes from with the positive expected value because that underlying assumption probably is not correct.
Also, 0.02 is the bid price. You won't get filled buying that option for 0.02, rather the asking price of 0.03. Although the difference is small, it's 50% more expensive than in your calculation. While "last" does say 0.02, it could be someone selling a call at the bid so it's not a safe assumption you can buy this option for 0.02
Thanks for commenting Michael!
Maybe it would be a good idea to do some more research on stock price distributions on my part. Are you aware of anything that might let us put together a stock price distribution more accurately?
Regarding the bid price, you are right that most likely you would not be able to get filled at the bid. The way I look at it is somewhat twofold.
1. It is unlikely that you get filled, but if you place tens or hundreds of orders like this the probability of one them getting filled is higher, and you only really need one to get filled anyway.
2. Even if you did not purchase at the bid price, I think it would be a somewhat trivial difference. The option is 50% more expensive, however, the idea is that these options should run hundreds of percent. That is unlikely, but again, if we have just one of these we can pay for our losses and then some.