[mosta]

when you pose a scenario: stock is going down, what does that do to the value of the stock/call/put--you have to allow that stock and call and put are essentially equivalent, a priori. any one of them can be replicated by the others. these equivalency relationships supercede your outlook in the underlying's market, because they provide *riskless* trading opportunities if they get out of line. if you jack the puts by a dollar, arbitrageurs will take the free dollar all day, and you will be synthetically getting short the stock--"great", you think stock's going down--but doing it at one dollar below market. if you want to get short, why give away a dollar in the process?

I know this is just repeating. I do see how there is an intellectual dissonance between the asymmetry in stock distribution and the symmetry in options of opposite delta. I think the points are 1. option arbitrage relations are independent of underlying distribution (jason would be the authority on this, not me) and 2. the real value in the option is its convexity, its gamma-theta-vega. you can make the delta whatever you want. as far as convexity goes, call and put hvae the same. therefore they are the same option.

I've read through all of jason's posts and I followed them completely until his proofs on the asymmetry of up and down strikes. as I studied hull on my own (crash course), when I looked back I realized I didn't fully comprehend all the steps separately, and distinguish which steps relied on geeomtric brownian motion, which depended on the continuous dynamic hedge, which depended on stock price distributions, etc. it didn't matter at work, but I want to go back to that on my own time. I like to refer to the dynamic hedging strategy and I know it doesn't all depend on that. but I find that very comprehensible.

but I think I'm correct thta you don't need any math or distributions or dynamic hedges to see that long a call and short a put on the same strike is equivalent to a foward in the underlying (there is a qualification for risk of stock closing exactly at strike on expiration and there being ambiguity over whether either or both options will be exercised, but forget that...). a forward is just like the underlying (plus basis), so long call, short put is called synthetic stock. once you have that you have

+stock = +call -put
-call = -put -stock
etc etc etc

these relatoinship control, because arbitrage trading opportunities dominate.