Are There Flaws In Options Pricing?

[VGSSD]

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 necessarily assumes that the underlying asset grows on average at the risk free rate.", which is incorrect.

Quote from rew:

Well, each sigma also defines a new expected value for the options, and guessing what the future volatility will be is not much easier than guessing mu.

I'm interested to hear what other people have to say about this, but my understanding is that estimates for mu are far noisier than estimates for sigma.

Nonetheless, your main point seems valid, I'll have to think about it a bit more.

 

[rew]

Quote from VGSSD:

This is equivalent to saying options are priced *as if* the underlying grows at the risk free rate. You initially said, "BS necessarily assumes that the underlying asset grows on average at the risk free rate.", which is incorrect.

I agree that my initial statement was badly stated and misleading.

 

[VGSSD]

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 the call one can still get the put-call parity relation just by calculating


Call - Put

= E[exp(-rT)(S-K)^(+)] - E[exp(-rT)(K-S)^(+)]

= E[exp(-rT)S] - E[exp(-rT)K]

= S(0) -exp(-rT)K (using risk neutrality)

with respect to whatever measure Q you choose to price with. I don't see why uniqueness of Q matters.

 

[Martinghoul]

I thought we were discussing replicating portfolios?

 

[VGSSD]

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.

 

[Martinghoul]

Quote from VGSSD:
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.

Actually, it doesn't... The Collector (Espen Haug) has talked a lot about the violations of put-call parity that do occur in very incomplete mkts. In general, it's a very robust principle, indeed, but you can easily imagine it breaking down.

 

[VGSSD]

Then what's wrong with my proof?

 

[nitro]

Quote from Martinghoul:

There are all sorts of flaws, including the use of the "risk-free rate" shortcut. In reality, as mentioned above, it should always be based on the marginal funding rate, rather than some particular mkt rate. There are all sorts of other drawbacks, but they don't invalidate the theory.

I strongly disagree with this notion. We always backed out rates from Eurodollar futures.

 

[Martinghoul]

Quote from nitro:
I strongly disagree with this notion. We always backed out rates from Eurodollar futures.

Well, you should come to me to do some wonderful trades, amico... I make you nice prices.

In seriousness, mate, don't get me started on the subject. I can talk about why using LIBOR rates is wrong for a long long time.

 

[spec77]

Quote from Martinghoul:

Well, you should come to me to do some wonderful trades, amico... I make you nice prices.

In seriousness, mate, don't get me started on the subject. I can talk about why using LIBOR rates is wrong for a long long time.

how about OIS ?