Setting all these differential equations and models and theories aside, all it comes down to is designing positions to make profit. I have perused various threads on this forum; most recently, the DITM (guts) thread. I have long been wondering: Is it possible to capture every market move with an option strategy? There is no need to prove that the market moves up and down. In the case of DITM guts (assume delta close to unity), if the market moves up, the call makes money; and when the market moves down, the put makes money. Unfortunately, the other option will lose just as much money; the loss is aggravated by bid/ask spread and commission. Is it possible to have opposing positions similar to the calls and puts in guts, but with the except that when one makes money, the other does not lose money or loses very little? (This is my previous post about "direction-biased delta.") If we can do this, then we are in good position to capture every market moves. Since this can mean serious windfall profit, somehow I feel it is not possible, or that arbitrage will arise. Can someone prove it is not mathematically possible ?