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Then what's wrong with my proof?

Initially I was, but I thought you were saying more generally that put call parity falls apart under incomplete markets. In any event, it seems natural that it does hold up considering real markets are incomplete.

It's interesting how confused everyone is about the price distribution as opposed to the returns distribution(admittedly, at first glance I made this mistake too). No one has even given you a correct answer yet. Under Black-Scholes assumptions the price distribution is certainly not symmetric...

Martinghoul, I don't see the issue with market completeness. Although there may be many possible risk neutral measures, the fair price for a derivative will still be discounted risk neutral expectation under one of these measures. Thus, as long as one chooses the same measure for the put and...

No need for snide remarks about whether or not I understood your last post. I clearly stated that option prices are risk neutral expectations in my prior post. This is equivalent to saying options are priced *as if* the underlying grows at the risk free rate. You initially said, "BS...

The difference between "expected value of the option" and arbitrage free price is quite simple. This is because the arbitrage free price IS the "expected value of the option", just with different probabilities, the risk neutral ones. I didn't read your last post(Rex) because it looks...

Not true. There is no such assumption about mu. Black Scholes model under the physical measure(the real world dynamics of the stock) is quite simply dS/S=(mu)dt + (sigma)dW You are both confusing real world and risk neutral probabilities.

There are no issues here, BS does not assume stocks grow at the risk free rate. Stocks are free to grow as they please, the point is that true growth rates are actually irrelevant from a no arbitrage pricing perspective. This is a fairly common misconception I think.

Perhaps we are thinking of different ways to derive the put call parity relation, but I was referring to the most elementary MBA level argument where one literally assumes that you can put 10 dollars at the bank and have it come out at 10(1+r) a year later. How is the possibility of default...

To be clear, you seem to be referring to the physical(or true) probabilities here. That is fortunately not something you need to know to price an option. The only thing you need to know about physical probabilities is which events have probability zero. For the purpose of pricing, you need...

You are right that put call parity doesn't follow from the validity of the risk free rate, it follows from no arbitrage. However, the argument does hinge pretty heavily on the existence of some form of safe investment of capital. If the economy were in a truly horrible state at which there...

Let me start by noting that I really don't understand what you are doing. You started by saying you were running a Markowitz optimization, then you said you were calculating probabilities of winning. Thats fairly inconsistent. There are two inputs to a markowitz optimization, a vector of...

Of course there are flaws in options pricing, and there always will be. The reason is that in order to price an option(or any derivative for that matter), one has to start with a model for the underlying. Truth be told, no one really knows what the right model is or even if a "right" model...

This should be fairly easy to do in R.

Why not? Speed issues? Or are they just not well known?

Actually, this is an options forum. Would assume that anyone trading options tracks at the very minimum implied volatilities and the greeks, and was simply curious if everyone still does this within a BS framework. No claim was made that you need Jump Diffusion to make money. Thank you for...

bump

pretty sure you can do this in R then export to spreadsheet if you wish...if you don't program in R, its pretty easy to learn(very similar to matlab if you know how to program in that)

Just look up the multidimensional taylor formula.

So...should i take that as a no? Everybody still using diffusion/jump diffusion then?