When I first encountered a positive model theta in IB, I thought there must be some mistake - theta is always negative right? I looked all around online but couldn't find a good explanation for this. So I ran my own analysis using Bjerksund-Stensland in C# (which was a good learning exercise). I plugged in the numbers and the model price aligns with the actual mid price. So far so good. I used the highlighted option (AGNC, exp 01/17/2020, strike 19) and I ran the model each day from now until expiration, and simulated a price drop on the ex-div dates of the current dividend. This is the "neutral case" which assumes no net price movement in the stock (other than from the dividend). The "actual" theta is -0.00431 to -0.00417 throughout the option life (IB and other brokers can't seem to separate this value out, but I wanted to know it), however the monthly dividend creates a "dividend effect" of 0.00533 per day (average). If you combine these together you get an annual gain of about 0.374 (vs. 3.20 option price) or about 11.7% (the stock's div yield is 12.7% currently). The option value is charted below as time passes from this simulation. I am aware the actual market prices in the dividend as it approaches so it would be smoother than this in reality, but it demonstrates the two forces of the dividend vs. time decay. As the call value at this strike is negligible (model = 0.00) I believe the the put's internal sort of "yield" is approximately the yield of the stock minus the risk free rate (I think that's expected by put-call parity). The IB provided theta value * 365 is about 9% over the cost of the option, so I think the true return is somewhere in between (probably a bit lower than the 11.7% I calculated, but over 10%). So, it makes sense in a highly leveraged portfolio (portfolio margin) at IB to use the option with the highest positive theta relative to the option price to hedge the long stock position. All parts of the hedge have a high positive return after accounting for IB margin borrowing costs.
Theta can go positive on long options. Deep ITM long european options in the presence of high interest rates or dividend yield can do this. Good on you for crafting a model. That's the way you do it.
These are american options. That's why people were telling me the theta can't be positive (that euro exceptional case doesn't apply). It's also why I had to implement an option model that's designed for american options. I haven't seen a broker that will run the option simulation over time, only spit out values at a point-in-time, which wasn't enough information to understand it.
It would have been helpful if you had included the price of the UL which was 16.20 at Wednes. close. You are assuming a constant share price less the div. each month. This + the div. factor gives the positive theta illusion. The declining share price also supports the put price. The 3.20 option price has .40 in TV wiggle room. You would collect (3x.16).48 in divs. This means that there is only room for a profit of (.48-.40) .08 or about 1/2% at expiry. Transaction costs reduce the yield. Furthermore, the OI is 44 and volume is 5. There's no liquidity. This means that getting the mid price would be highly improbable, given the assumption of static share price. You may have to pay more than mid, further reducing profitability.
The most important part is that there is no significant net time decay for the hedge. IB just reports these funky thetas in their model so I've tried to run my own model. I have been determining the discounted dividend value looking at time value for the deepest puts. Generally the puts I want are at -99 delta so it's about the same. Execution has more impact than the real time value accounting for div. I haven't had issues executing at or just below the mid luckily. My intent is to roll at 30 dte into 120 to 180 dte as needed. Spread is lower when selling them. I was hoping to model closer to exchange model but I can only approximate.