QuoteOriginally posted by: numbersixNobody cares about the vanillas.Tell that to all the nobodies who trade them every day. I understand that modelling exotics is your major interest and once I've exhausted the still very rich world of vanillas and the price series I'll move into that too. But calling me and everyone else still finding plenty of interest in vanillas a "nobody" doesn't make us disappear. Quote"Local volatility": that is even worse than a out-dated concept. This is a "corrupt" concept.Then I guess the price series is a "corrupt" concept too, because it definitely exhibits a local volatility and tells us where the smile comes from.

QuoteOriginally posted by: FermionQuoteOriginally posted by: numbersixNobody cares about the vanillas.Tell that to all the nobodies who trade them every day. I understand that modelling exotics is your major interest and once I've exhausted the still very rich world of vanillas and the price series I'll move into that too. But calling me and everyone else still finding plenty of interest in vanillas a "nobody" doesn't make us disappear. Quote"Local volatility": that is even worse than a out-dated concept. This is a "corrupt" concept.Then I guess the price series is a "corrupt" concept too, because it definitely exhibits a local volatility and tells us where the smile comes from.What do you mean the price series exhibit a local volatility ?

QuoteOriginally posted by: madmaxWhat do you mean the price series exhibit a local volatility ?I've posted some info on this in various threads since January of this year. Do a search and you'll see as much as I am willing to disclose publicly. If it interests you, pm me.

Fermion,Let us first make sure the two of us are addressing the same issue.My concern is what (in numerous posts and articles and talks) I've been calling the "smile problem."To my mind, the vanillas do not pose a smile problem, and nobody - yes, nobody: sorry to invoke again that famous person, the one person really able to solve the smile problem - nobody needs a smile model to price the vanillas or trade them.You need a smile model to hedge the vanillas, or equivalently, to price (and hedge) the exotics.Sorry to say, I am a total disbeliever in times series, price series, or any way of mixing up history in the pricing of derivative instruments.Why? Big question there. A priori philosophical stance. How can a backward looking analysis help me value a forward looking instrument? I wish I could debate this with you, or for you. I'd rather dimiss the issue almost as spectacularly and enigmatically as in my previous post and say: "Nobody cares about the past."I believe only in the present (the present of presently traded prices, I mean) and in the future that the present trading strategies allow me to lock more or less.To know how to hedge the vanillas and / or price the exotics, I need present information about the smile dynamics. (Smile dynamics is tautologically forward looking.) This information is contained in the present prices of exotics. To calibrate my pricing and hedging to the present prices of exotics, or in other words the smile dynamics as presently predicted by the market, and to lock that predicition in a relative value trading strategy, this is where I need a smile model.No local volatility model, and even less so, no historical analysis of price series can be calibrated to the current prices of exotics. So much for your whole framework.Or are you telling me you need the price series, and the smile information that you say it contains, in order to predict the prices of vanillas? We are back to my point about the past predicting the future. Finally, a word about local volatility.True, local volatility can be interpreted as the expected local variance of the underlying in more general stochastic volatility models, or general models of underlying price dynamics.You can always ask the question, in any stochastic model: "Conditionally on the underlying trading at price S, at future time t, what would be its expected variance?" This, as shown by Gatheral among others, is the meaning of local volatility (the only relevant meaning, to my mind). And this expectation is directly linked to the present prices of vanillas through Dupire's formula, as shown by Gatheral in very general contexts.But this does not mean local volatility is everything. It means exactly it is nothing. Only the vanillas are determined by expected variance as seen from today. But you should expect the prices of exotic instruments (typically the barriers) to be precisely dependent on what gets erased in that expectation. On the difference of time scales between models, on the fine structure of the dynamics, on the conditional probability structure, etc. etc. Do you say all you care about are the vanillas? Then again, you won't need a smile model.

QuoteOriginally posted by: numbersixLet us first make sure the two of us are addressing the same issue.Good idea.QuoteMy concern is what (in numerous posts and articles and talks) I've been calling the "smile problem."To my mind, the vanillas do not pose a smile problem, and nobody - yes, nobody: sorry to invoke again that famous person, the one person really able to solve the smile problem - nobody needs a smile model to price the vanillas or trade them.You need a smile model to hedge the vanillas, or equivalently, to price (and hedge) the exotics.Well, somebody who traded vanillas without hedging might as well play poker. But however they choose to hedge, whether with exotics or not, the primary information they need is in the smile model, or, pretty much equivalently for vanillas, the greeks. I have not worked with exotics yet, and I haven't seen them traded on any of the regular exchanges here in the US, but I agree there is more hedging information available there. I just don't agree that vanillas tell you nothing or that you should ignore them, which was the substance of your original claim that "Nobody cares about the vanillas.".QuoteSorry to say, I am a total disbeliever in times series, price series, or any way of mixing up history in the pricing of derivative instruments.Why? Big question there. A priori philosophical stance. How can a backward looking analysis help me value a forward looking instrument? I wish I could debate this with you, or for you. I'd rather dimiss the issue almost as spectacularly and enigmatically as in my previous post and say: "Nobody cares about the past."This particular nobody does. "Those who ignore the past are condemned to repeat it."QuoteI believe only in the present (the present of presently traded prices, I mean)Let me invoke "nobody's" friend "anybody" as in "Anybody with half an eye can see that markets are non-Markovian".Quote and in the future that the present trading strategies allow me to lock more or less.To know how to hedge the vanillas and / or price the exotics, I need present information about the smile dynamics. (Smile dynamics is tautologically forward looking.)Anything that is "tautologically forward looking" is not sufficient to describe the full smile. This nobody knows how important it is to mix future uncertainty with knowledge gained from the past. Even your "regime-switching" model is fundamentally based on past knowledge of what types of regimes are known and this will always be the case even if all your parameters were to be calibrated purely by exotics. If you were purely forward looking, why would you even imagine there was a smile?Quote Or are you telling me you need the price series, and the smile information that you say it contains, in order to predict the prices of vanillas? We are back to my point about the past predicting the future. History gives us information about the static structure. The dynamics need to be calibrated. Some smile parameters are determined in some degree by history, others are not.QuoteFinally, a word about local volatility.True, local volatility can be interpreted as the expected local variance of the underlying in more general stochastic volatility models, or general models of underlying price dynamics.You can always ask the question, in any stochastic model: "Conditionally on the underlying trading at price S, at future time t, what would be its expected variance?" Back to your Markovian assumption again, I see. What makes you think volatility can depend only on S and t? You can't get a realistic smile dynamics that way -- which, in fact seems to be the point of your argument -- so you are plainly being self-contradictory here.QuoteOnly the vanillas are determined by expected variance as seen from today.That's a terrible way to go about things. How do you predict expected variance without a smile model? Since we know that vanilla markets smile, why would you even try?QuoteBut you should expect the prices of exotic instruments (typically the barriers) to be precisely dependent on what gets erased in that expectation. On the difference of time scales between models, on the fine structure of the dynamics, on the conditional probability structure, etc. etc. Sure. But why blind yourself to what history can tell you about this?QuoteDo you say all you care about are the vanillas?No. Just that there is so much information still to extract from the price series, vanillas and greeks. As it happens, I expect to be moving on to exotics very soon, once I find out more about how they are traded and how to get data.As long as you continue to caricature what I write in such ridiculously restrictive ways, you have no hope of understanding what I actually write.

Did you say "greeks"? What greeks?Non Markovian makes things only more complex. How do you calibrate non Markovian smile models, (for instance, interest rate models)?The predictive power of history breaks down even in the Markovian setting. How will it fare in non Markovian?Local volatility. You believe in it. I don't. You seem to want to reduce all smile models to local volatility. I wonder how the non Markovian escape route can help you there.(Read Gatheral, though).Caricature: for lack of space, for fun, and for tiring of repeating myself.

[Sorry, double posting error]

QuoteOriginally posted by: numbersixDid you say "greeks"? What greeks?Oh, I don't know. How about Aristotle, Plato and Socrates? Joking aside, I guess you French must have a different word for the sensitivities of traded instruments to changes in dependent variables. Or perhaps you think "Nobody" cares about them any more?QuoteNon Markovian makes things only more complex. How do you calibrate non Markovian smile models, (for instance, interest rate models)?Well, I haven't worked with interest rate models, since there are about 200,000 equity options in US markets to keep me occupied. And with those, the answer to your question is "more accurately".QuoteThe predictive power of history breaks down even in the Markovian setting. How will it fare in non Markovian?Better (in a non-Markovian world).QuoteLocal volatility. You believe in it. I don't. You seem to want to reduce all smile models to local volatility. Not necessarily. When I see it isn't sufficient, I'll move beyond it. I think William of Ockham had something to say about this.QuoteI wonder how the non Markovian escape route can help you there."Escape" is hardly the word for getting real.

Fermion:It would be advisable to ponder on risk and hedging in terms of information and decisionmaking rather than of history and volatility.

QuoteOriginally posted by: AristonFermion:It would be advisable to ponder on risk and hedging in terms of information and decisionmaking rather than of history and volatility.Well, I don't know about "rather than", but I guess it depends on what you mean by "information and decisionmaking" in this context. Perhaps you'd like to explain a little?

There is C++ source code associated with this thesis. Is it possiblefor the author to make the code available on the forum?

QuoteWell, I haven't worked with interest rate models, since there are about 200,000 equity options in US markets to keep me occupied. And with those, the answer to your question is "more accurately".QuoteBetter (in a non-Markovian world).Are you serious ?I see that you are doing a lot of talk, and playing the devil's advocate. If you are serious and so smart, why don't you stop talking and post some code for calibrating non-Markovian "more accurately", blablabla, and why not computing hedges.

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 approximate it some way.FORGET IT!Welcome to social (soft) sciences. Finance is and will remain the realm of non stationarities. The question is not "is it Markov or not", the true point is "is it stationary or not?". You wake up one morning, some new info on a company comes in, you reprice everything almost as if today was a new creation of the world. Much of the relevant info of today is not contained in the past prices, but is priced in the current option prices. Is is therefore interesting to decipher what today's prices mean, and it is almost always a waste of time to try and use the past to predict the future.And too bad for the billions invested in stat arbs...Well, let's be serious now. Yes, you can argue that there is some stationary components in the economy, what would be really foolish is to think that everything is non stationary. Pr Kurz from Stanford has shown that it takes very little in an equilibirum to introduce fatal non stationarities: all it takes is a few investors who believe that the world may not be entirely stationary...

QuoteOriginally posted by: madmaxAre you serious ?Yes. Why wouldn't I be?QuoteI see that you are doing a lot of talk, and playing the devil's advocate.That's not my intention. I thought that was NumberSix's job.My intention is:1. To discuss things that interest me in the hope of learning something new from others' points of view.2. To stimulate interest from others in mutually profitable ventures.Quote If you are serious and so smart, Well, I don't know about how smart I am. Sometimes I feel quite humble when faced with market data...Quotewhy don't you stop talking and post some code for calibrating non-Markovian "more accurately", blablabla, and why not computing hedges.Sorry. I have my reasons. I am willing to engage in general discussions with others who wish to do so in a civil way, but I am not willing to publicly disclose my IP or divert my attention from my current program. If you don't believe my claims, that is your prerogative. There's no law that says you have to agree with me and I have no desire to persuade you if you are reluctant. In fact, I wonder why you bother to comment at all if my ideas are such anathema to you.