I see what you mean, but it's not a mispricing. Once you take into account the cost of carry it works out even. On 140 strike the cost of carry is 140*0.0525*10/360=0.20, which is what the profit on the conversion is.
MTE, I don't understand what you meant. I thought the cost of carry is built into the option pricing model. I am using SPY (not a future). What I don't understand is why the IV for call is not the same as IV for put. Using the diagram that I posted, IV for Jan 140 call is 11.99, and for Jan 140 put is 10.92. TOS told me that both were computed using the mid of bid and ask. There is a discrepancy between TOS model and my own, I like to get your opinion to get it fixed as I might have some misunderstanding of the option theory. Can you illustrate what you meant the conversion profit using the following data (the data from my diagram)? SPY @ 141.13 Bid Ask IV Jan07 140 call 1.85 1.95 11.99 Jan07 140 put 0.50 0.60 10.92 [edit] I understand there is no arb profit in this case. Just don't understand why TOS shows different IV.
Ok, let's do the calculation (using the midpoints). Since the put is trading at lower IV it is presumably underpriced (the call being overpriced). So in order to arb that we sell a call at 1.9, buy a put at 0.55 and buy the stock at 141.13. This means that we sold the synthetic stock for 141.35 (140+1.90-0.55) and bought the actual stock at 141.13. So, we got a difference of 0.22. The cost of carry on the actual long stock, with 10 days to expiry and interest rate of 5.25%, is 0.20 (140*0.0525*10/360), which is almost exactly the same as the difference we locked in. So, as you can see, and as you have correctly pointed out, the cost of carry is built in to the option pricing (i.e. into the synthetic stock).
MTE, Thanks for the clarification. I don't understand why the IVs shown in TOS are different. Does it mean TOS's computation is wrong?
Just finished talking to TOS, it's not a model a problem. Looks like the market makers are bidding the calls slightly higher causing the IV to be higher. That is, the calls are bid parity, which puts the midpoint higher and thus causing the IV to be higher, but there is still no arb opportunity.
I talked to Scott from TOS too. They didn't look at the software and just gave me the quick and easy answer. I used the same data (spy = 141.13, call price = 1.9, and put price = 0.55) and entered in a BS model, the IV of the call is 11.25 and IV of the put is 11.26. I believe TOS software has a bug in it. You can try it yourself. My advice is don't use the impl_vol from TOS for your model. Thanks a lot for your clarification on the conversion calculation.
I put on a Mar debit spread (call) 1415/1425 and noticed over 10K contracts traded at those two strike points..while over on the put side no equivalent number of trades so the above explanation does seem to make sense.
Donna, The discrepancy occurs everyday in SPX. I accepted their excuse and didn't follow up on the investigation until today. Today I found out there was a big difference (around $500) in P&L between my own model and TOS software, and so I digged into it. I just entered the data into an option calculator, and it revealed that the IV calculated from TOS was wrong. Just by changing the model to use the option premium (instead of the IV), I fixed the problem. It is so easy to verify it, but I chose the easy way and accepted their excuse. I hope you all can verify it yourselves.
lindq: I agree that trading options introduces issues that straight futures (or stock) traders don't have to face. However, because you have so much more control over the structure of an options position than you do over a stock or futures portfolio, getting a consistent return from options trading is far more attainable (for the diligent trader) than for a trader that does not use options. Additionally, because you can control your risk so easily with options, an options trader never faces the possibility of "blowing-out" in a day or a week. This is not true for straight stock or futures traders. While options can be complicated, they are not hard. Conversely, the amount of fundamental analysis I see being done by futures traders appears to be limitless and never sufficient. They constantly complain about underreported production numbers or bad (meaning inaccurate) government reports. This is to say nothing of the technical analysis required to trade well. These things certainly impact an options trader. However, using sound options trading techniques is far more important than predicting the direction of a stock. As you may have guessed, I believe good stock or futures traders are magic while good options traders are simply utilizing highly repeatable techniques...kind of like the McDonalds of trading.