TinMan,(i) What do you mean by "which doesn't describe the underlying when trying to price barriers"?(ii) It just gives you an average value given all the things vol could do in the future and a standard deviation of that value. Seems harmless to me! What is really weird is thinking there's one value for something when you don't know the model or the parameters in the model! Only in quant finance!(iii) Outside finance one does this all the time! Ok, not 'quantified' but certainly a risk/reward tradeoff. The problem is that in quant finance we've been spoiled since 1973 to think that a) we never need to worry about drift and b) we don't have to worry about risk aversion. Prior to 1973 people were happy with those two concepts! Historical parameters are going to be more stable than calibrated ones! So with my cynic's hat on I'd say that risk management ought to prefer it! (The reason they don't is that they don't understand that recalibrating negates the whole calibration exercise!!)P

QuoteHistorical parameters are going to be more stable than calibrated ones!This is usually just because, in estimating parameter stability historically, you are almost always using overlapping data sets. If you try estimating, say, SVJ, on non-overlapping data sets you find very unstable parameters, unless you incorporate some seriously restrictive priors.Suppose you had estimated mortgage backed default rates from historical experience. You would be very bankrupt by now.

I should have put the 'cynic' bit earlier in the paragraph!! But the serious point is that it's still much harder to show that historical parameters are wrong. But with calibration you just need to calibrate once, go play golf, come back and recalibrate...and bingo calibration unstable.And I'm not saying that implied values don't appear in any parameter estimation. Let me just add, to clarify my position, that my goal is to do better than other models and not to expect perfection. The above is an example of this: You can't criticize the stability of historical parameters when you are trying to justify calibration.And I love that reference to mortgage-backed securities, again that's a sticky wicket for you not me! P

Last edited by Paul on May 8th, 2011, 10:00 pm, edited 1 time in total.

QuoteOriginally posted by: PaulTinMan,(i) What do you mean by "which doesn't describe the underlying when trying to price barriers"?I mean the underlying jumps and may gap through the barrier, a stochastic vol model without jumps won't give you that behaviour.QuoteOriginally posted by: Paul(ii) It just gives you an average value given all the things vol could do in the future and a standard deviation of that value. Seems harmless to me! A standard deviation of a continuous path, still won't value the barrier appropriately.A confidence interval around something fundamentally wrong is of no use to me.QuoteOriginally posted by: PaulWhat is really weird is thinking there's one value for something when you don't know the model or the parameters in the model! Only in quant finance! Straw man, and it's not much better to give a range if the range is too wide to be useful.QuoteOriginally posted by: Paul(iii) Outside finance one does this all the time! Ok, not 'quantified' but certainly a risk/reward tradeoff. The problem is that in quant finance we've been spoiled since 1973 to think that a) we never need to worry about drift and b) we don't have to worry about risk aversion. Prior to 1973 people were happy with those two concepts! They weren't happy with them, which is why they contrived to get rid of themQuoteOriginally posted by: PaulHistorical parameters are going to be more stable than calibrated ones! So with my cynic's hat on I'd say that risk management ought to prefer it! (The reason they don't is that they don't understand that recalibrating negates the whole calibration exercise!!) So what's the drift of the S&P 500?If take ten different time windows will I get the same answer?

It might be a sticky wicket for me if I were defending calibration: I am not. The mortgage mess was a crisis borne of overconfidence in worldviews and models. The fallout applied to calibration instability and to things which had always been true turning out not to be. Historical estimation was no defence.My point - and we've had most of this discussion before - is that the useful discussion is not "calibration vs historical estimation" but "how should one intelligently use mis-specified models".

QuoteOriginally posted by: frenchX -I would design a SVJ (stochastic volatility+jump in the underlying). The model will not be calibrated on the implied volatility surface but rather parametrized on the underlying historical prices.How many parameters? Heston with jumps has 8 I think.QuoteOriginally posted by: frenchX-I would check on long period how my parameters are stable and I will put corresponding uncertainties on them.What if they're not stable?How wide will your price range be with uncertainties on 8 parameters?QuoteOriginally posted by: frenchX-I will optimize some static hedges (vanillas+underlying) with goal of minimizing a risk coherent measure for the worst case (example minimizing the expected shortfall or simpler first the variance)Don't you need the PDF to calculate expected shortfall?And why does the risk measure need to be 'coherent'?QuoteOriginally posted by: frenchXIf you have to hedge a up and out barrier option which is close to the barrier, the model will thanks to the drift term and the jump term automatically give you the best hedge transaction costs adjusted.Assuming your model and parameters are correct. What if they're not?QuoteOriginally posted by: frenchXIt's a very hard mathematical problem and it involves high dimensional nonlinear optimization, it's true. But I believe it's really one of the most effective way.What is your belief based on, is it experience?

QuoteOriginally posted by: crmorcomMy point - and we've had most of this discussion before - is that the useful discussion is not "calibration vs historical estimation" but "how should one intelligently use mis-specified models".Yes -- I asked in a related thread for people in MFE programs to post if their course work includeddiscussions of "best practices" case studies. There were no MFE responses (although Paul did respond on his CQF program).Another useful discussion topic is: how to improve your models and how to know when your model is embarrassingly wrong.

Last edited by Alan on May 8th, 2011, 10:00 pm, edited 1 time in total.

@Tinman:-so there should be : drift, long term vol, vol mean reversion, vol vol, correlation, mean jump size, variance of jump size and jump rate (so it's eight you are right).the longer the expiration of the option, the more unstable the parameters would be and the more critical the model error will impact your PnL. Imagine a 1Y maturity option. You have a 5 years historical data span. What I would do is to estimate the parameters at different time windows (example one month lag). You would have a set of paramters from which you can deduce confidence interval. You have a lot of small uncertainties (8) but on a given parametric form (heston model+normal jump) so I think that the price will still be lower than classical UVM with wide bounded vol.A measure need to be risk coherent to imply diversification. I don't remember the article title but there was an article which showed than VaR is not risk coherent and so you can have agregate risk (the optimal portfolio when you are multi asset under VaR is not well diversified). You are totally right you need the PDF for the expect shortfall (that's why it's harder than the variance). Nevertheless, you can use Foker Planck equation backward and you can optimize your initial boundary (the payoff exotic+hedges) to obtain the best expected shortfall. It's quite hard because derivation a Fokker Planck equation under uncertainty is not trivial. For the variance it's easier you just look at how the uncertainty impact your daily PnL.Concerning the correctness of the parameters. It's the most important question. I don't have a clear anwer about that. What I would do is to check at my daily PnL and to separate that into explained model PnL+unexplained one. If my model only explain a few percent of my PnL then I would be worried ! Once ago I had the stupid idea (got a lot ) about a self evolving model which autocalibrate to reduce the unexplained part of the daily PnL. That's very naive but at the moment I don't have a clear idea about when to recalibrate. Concerning my experience in finance I can say that I'm by far the less experienced guy of this forum. But calibration problems are not only face by traders, in plasma physics it's a very common topic and so beliefs are mostly based on what I have read in the finance literature and my experience as a physicist.Actually I would enjoy VERY MUCH to try my idea and to backtest it.

QuoteOriginally posted by: frenchX@Tinman:-so there should be : drift, long term vol, vol mean reversion, vol vol, correlation, mean jump size, variance of jump size and jump rate (so it's eight you are right).[\q]So given that we can get S&P data back 50 years or more, what are those parameters for the S&P?Does 8 parameters seem sensible to you? Seems like overfitting to me.QuoteOriginally posted by: frenchX Imagine a 1Y maturity option. You have a 5 years historical data span. What I would do is to estimate the parameters at different time windows (example one month lag). You would have a set of paramters from which you can deduce confidence interval. What happens when a big market move falls out of your time window?So after 1992 for instance your model wouldn't take account of 1997.QuoteOriginally posted by: frenchX You have a lot of small uncertainties (8) but on a given parametric form (heston model+normal jump) so I think that the price will still be lower than classical UVM with wide bounded vol.Heston is garbage with calibration. I doubt it would be much better with historical data.QuoteOriginally posted by: frenchX A measure need to be risk coherent to imply diversification. I don't remember the article title but there was an article which showed than VaR is not risk coherent and so you can have agregate risk (the optimal portfolio when you are multi asset under VaR is not well diversified). There's more to coherence than diversification. It doesn't take into account liquidity risk for example.QuoteOriginally posted by: frenchXYou are totally right you need the PDF for the expect shortfall (that's why it's harder than the variance). Nevertheless, you can use Foker Planck equation backward and you can optimize your initial boundary (the payoff exotic+hedges) to obtain the best expected shortfall. It's quite hard because derivation a Fokker Planck equation under uncertainty is not trivial. For the variance it's easier you just look at how the uncertainty impact your daily PnL.But this is supposed to be an improvement on calibration, all I can see are problems.QuoteOriginally posted by: frenchX Concerning the correctness of the parameters. It's the most important question. I don't have a clear anwer about that. What I would do is to check at my daily PnL and to separate that into explained model PnL+unexplained one. If my model only explain a few percent of my PnL then I would be worried ! Any calibrated model will have a high explanatory value for your P&L, for a while anyway.QuoteOriginally posted by: frenchX Concerning my experience in finance I can say that I'm by far the less experienced guy of this forum. But calibration problems are not only face by traders, in plasma physics it's a very common topic and so beliefs are mostly based on what I have read in the finance literature and my experience as a physicist.That's physics though, this is social science.QuoteOriginally posted by: frenchX Actually I would enjoy VERY MUCH to try my idea and to backtest it.Just download the data and value a barrier option.

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I think the problems go right back fundamentally to David Hume as people have discussed time and time again on these forums. Basically quant finance is not a science, just a more numerical part of economics which has got itself a bit stuck in a rut and forgotten to be widely read about economics.Paul's point about Hooke's law and some such parameter calibration in finance is not the problem in and of itself, it is just a very nice illustration of why all financial models are deeply flawed philosophically. One simply cannot defend calibration because it is logically inconsistent as Paul points out - you have disproved your own model's parameters by having to recalibrate it. If you have to do this under all market conditions without reliable known boundaries of applicability then you have disproved your model.However, does it matter if all quant finance is philosophically flawed? What is the problem we are trying to solve? Hooke's Law (although perhaps not really a Law any more, not like conservation of energy etc) attempted to solve the problem of the observed relationship between the extension of the spring and the mass on the end. Hence it is a scientific question with easily reproducible experiments with which to falsify the "Law" within the use cases defined as part of the "Law" in and of itself. In finance, as the original poster poses by the question, we are actually not trying to write a "Law" which can be testable in and of itself. Actually, our boss has told us that a client wishes to enter into some kind of crazy OTC exotic contract and we wish to fill the client's order whilst minimising the bank's risk, then take them out to the rugby and get drunk together and pat each other on the back. We hope that following on from this deal that any / either / all the following things may or may not be true in order of importance 0.) We made our boss happy and we can always leave or get bailed out if it all goes horribly wrong1.) We made a fat margin and fooled the client into being happy2.) The client is good for the cash if it all goes wrong; and they are a good sport / laugh if they lose their money / we go out drinking3.) Our model was vaguely something which with good luck will turn out not to be horribly wrong in the time period of the deal4.) We manage to do some kind of combination of static and dynamic hedging in liquid markets which remain open, with entities which are good for their money, or they get bailed out if it all goes horribly wrong5.) If we got it wrong, everyone else got it wrong, or there is some kind of fall guy, or we are all the fall guy and therefore don?t feel bad if we all have to pitch in foraging for berries together in the central reservation of the M25.Here is where I am really cynical about quant finance, and so best to pose a positive question: Paul et al, if you don't like calibration (or implying parameters from the market) what do you suggest? Some form of eigenvector analysis to find principal components instead of blind Gauss distribution models with no proof of central limit? Some kind of trained classifier, for example used in computer vision? I noticed talk of Fisher's Linear Discriminant Analysis elsewhere (was it referring to Fisher describing the separation between distributions of two classes to be the ratio of the variance of the classes?) ...I think it needs to start with economic thinking, not mathematical: what I would like to see is some mathematical models for derivatives contract valuations based on more than just Gene Fama, taking Keynes and others into account explicitly in the model's original assumptions?. But then that is another story ?

Last edited by TitanPartners on May 8th, 2011, 10:00 pm, edited 1 time in total.

Oh god no, let's not get into philosophy, these threads always turn into a treatise on bloody philosophy.That lets people off the hook too easily.I mean, we all know this isn't science and we all know there aren't any laws.But we all have jobs to do, and some alternatives have been put forward below,I've read enough threads where someone says they would hedge with this or optimise over that, but without numbers it's all flannel.

QuoteOne simply cannot defend calibration because it is logically inconsistent as Paul points out - you have disproved your own model's parameters by having to recalibrate itIt is only logically inconsistent if you expect your model to be a perfect fit. This is the case with ALL attempts to fit an incorrect model. In economics, no sane person ever expects their model to be perfect. Paul's reduction ad absurdam is a non sequitur. As TinMan says,QuoteI mean, we all know this isn't science and we all know there aren't any laws.But just because there aren't absolute laws doesn't mean that partial ones aren't useful. You just have to be careful not to generalize inappropriately. But this is as true in the negative as in the positive...

I still don't think we are all that far away from each other. From my perspective a problem I have is that people keep reading things into what I write that aren't really there! There are very few things people have said in this thread that I disagree with.How many of you have PWOQF2? If I could just suggest some reading from that then we could make some progress here, maybe even come up with something better than before.P

There are a lot of interesting comments here. Falling into deep philoshophy is not my type and I'm only interesting into practical application (for this topic at least). It's not a question to ask if the model is realist or not, it won't be. We all agree here that there isn't a hidden law in the market. I agree with Tinman that we could talk for weeks what we need is a quantitative comparison. I also distinguish a model for pricing to a model for hedging. For me it's two different thing and a model can be very good at one and very bad at the other. I will try to catch some datas (the historical price are not that hard but the implied vols are trickier to obtain) to backtest the model.A thing that always puzzled me is : where is the economy and the finance in quantitative finance (at least for derivative pricing) ? Will you price exactly with same procedure an option on Apple and an option in a small cap tiny unknown firm ?I think that quantitative finance=Maths+finance+economy+psychology+sociology and that's why I find it VERY interesting. People are always focused on one point (risk neutral stuff for the math part, behavioural finance for the psycho social one, limits of arbitrage for the accounting, finance, economic one) but I have never seen an attempt (put your guns down I said ATTEMPT I know it's very hard) to try to link these facets.I have seen only ONE paper which tried to combine derivative pricing with behavioural finance for example. To focus back on implied vol calibration vs historical parameter estimation, it's not a good fight. The best would be not the extract info from one or the other but to extract the maximum information from the both. For example, the link between the realized vol and the implied one is for me less than obvious. I suspect than the implied vol contains far much more information than just the future expectation of the realized vol perceived by the market. It's also funny in finance to see that there is technical analysis (trading signals and so on), fundamental analysis (financial ratios and accounting stuff) and quantitative finance (finance math) and there aren't many cross use of them in the derivative world. Surprising to me. In my case, the best thing one can do is to know his weapon (which weaknesses have your model, what would be the impact and so on ). @Paul: I have started learning finance with your books. If I would have started with the books about risk neutral change of measure and martingale pricing, I wouldn't be here. It's a very weird way of introducing quantitative finance and it's VERY discouraging for students. The portfolio building concept as in your books (or the lectures of Gatheral) are the best for learning

Last edited by frenchX on May 8th, 2011, 10:00 pm, edited 1 time in total.

QuoteOriginally posted by: PaulI still don't think we are all that far away from each other. From my perspective a problem I have is that people keep reading things into what I write that aren't really there! There are very few things people have said in this thread that I disagree with.How many of you have PWOQF2? If I could just suggest some reading from that then we could make some progress here, maybe even come up with something better than before.PI have it, but I need a copy of "A note on hedging: restricted but optimal delta hedging ..."as you referred me to that.Thanks,

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