<t>In the pure BS setting, just hedging at discrete interval does a very good job and the drift is a second order problem. As soon as you enter the incomplete market realm with say stoch vol or jumps, things are much more complex. The big idea here is that pricing and hedging are no longer uniquely ...

<t>Alexei,I think you nailed it. The time effect in these Markov time homogeneous models (call it non stationary if you want) come indeed from the transitory path to some stable steady state. That is precisely the beauty of it. This steady state of course need not be stuck in one regime!The transito...

<t>Fermion,Warning: I'll be a bit provocative, just for the fun of it. The Finance Quant field is sadely poluted by physicists who come in Finance with one thing in mind: the world is stationary, there exists somewhere a magical Data Generating Process, they are going to find it, or at least approxi...

The current wisdom on the CBOE is the following:The index (say SP500) shows a declining smirk (a declining skew if you want) The individual stocks have higher implied vol with a smile pattern (larger on the extremes)

I see. You would then discount constant future payoff by the rate mu? Again, this lead to an abvious arbitrage.

A good reference is for instance a book called "Asset Pricing" by Cochrane, Princeton. Step 2: My point here is not about changing drift in time but comparing two situations with different constrant drifts. Try to think about it this way in terms of static comparison.

<t>QuoteOriginally posted by: OmarIn the absence of any hedging, I propose that the fair price of an option would be such that you to break even if you trade that option (under the same conditions) N times, in the limit N --> infinity. You end up being risk neutral, but only asymptotically. In the p...

<t>Omar,Yes, by assets I mean non-derivatives, an equity portfolio for instance.I cannot agree with the way you propose to price a European call in absence of a hedge. You propose to compute the price as the discounted expected payoff of the option in the historic (or objective or true) probability,...

<t>Quartet, you are right to worry about options and more genrally derivatives in a portfolio optimization framework. I expect this to be a growing field of investigation. So far, portfolio optimization has mostly looked at one period with a cross section of (possibly quite many) assets. It is tempt...

<t>As long as you use a bad model which fits hardly anything and you know it, it is indeed tempting to try to tweak and adjust your formula in order to fit the market. You may for instance do some bucketing, or study the sensitivity of the prices of your model to changes in parameters, which are sup...

<t>I can identify two main drivers for the future of the profession.1- A relentless increase in computing power. This makes complex algorithms possible which were only available in theory a few years ago. This is true for the calibration of PDE, for Monte-Carlo simulations, for risk management probl...

<t>Yes, clearly yield curve derivatives must be used in the calibration, at least caps, floors, and swaptions. The point in modeling the short term process only is that you do not create arbitrage opportunity. You could come up with a nice three factors model to explain the yield curve for instance,...

<t>Working on it. Here is the idea, and why ITO33 is interested. The big thing in HJM kind of modeling is the ability to use the current yield curve as initial data point of the yield curve dynamics. The cost is a complex, path dependent dynamics of the short term rate, and painful Monte Carlo simul...

I think that you have it right. Another issue for you. Try to see what these risk neutral world theories say about hedging. Is the market complete or not ? You are right that the foundation for this analysis is a bit curious.

<t>QuoteNewNumberTwo -<i> the price of the security is also the value of its perfect hedge. This is the Black-Scholes ideal world.</i>Completeness does <u>not</u> require log normal returns which is (IMO) the key to the issues we have with local vols, apparent skewness, unstable parameters etc.Your ...