QuoteOriginally posted by: Traden4AlphaGood points, katastrofa.There's nothing wrong with banks losing billions as long as it's shareholders' money, not bond holders' or depositors' money. And the leverage problems weren't just at the banks. Home buyers over-leveraged, too. What's a mortgage with the <3% downpayment except a >33:1 leveraged purchase. Leveraged lender + leveraged borrower = disaster. The rule should be that if a bank wants to lend to a high-leverage home buyer, then the bank needs low leverage. And if a bank wants to be high-leverage, then it can only lend to low-leverage borrowers. Someone must hold enough equity in reserve to buffer the volatility. In the recent crisis, we had no one holding sufficient reserves.We have known this about leverage for a long, long time. Remember risk-weighted assets in the old, old days of Basel I? The issue is not knowing that too much leverage is bad; it is recognizing when there is too much leverage and having the power to act against it. In the most recent crisis, the regulators failed to see the leverage because it was hidden via off balance-sheet structures (CDOs). Or, where they did see it, they pretended that it didn't matter because things were different this time. Credit crises are systemic problems, not just problems with individual lenders/borrowers. You can't solve them just by fixing individual leverage limits: financial innovation will find a way round these, and you still haven't dealt with TBTF and related, global, problems.QuoteOne sticky challenge is making sure that financial firms' assets and liabilities have the right correlation. With CDOs, banks owned covered calls in real estate. These positions lose value in times of volatility. If a bank sells variance swaps, it's liabilities increase in times of volatility. Not good!I think this may be a terminally sticky challenge! Whenever you assume concrete, quantitative, things about asset correlations, you will tend to end up allowing risk-offsets for these correlations. This will, from an individually rational perspective, lead to increased leverage. The Murphy's Law nature of expectations-driven economic equilibrium is almost always going to mean that, collectively, this behaviour is going to increase your tail-risk, though things will look just fine while things are good. Which sows the seed for the next crisis. q.v. Great Moderation.

QuoteOriginally posted by: CaesariaQuoteOriginally posted by: PaulQuoteOriginally posted by: Caesaria Lets say that I am Goldman Sachs, and you want to buy a variance swap on a November future for Crude. You have a business need for this swap, ...What should I do, should I sell you that Nov Crude Variance Swap?Fantastic questions! The answer could consist of any or all of: Reduce volume, perhaps to zero; Statically hedge; Charge highest price you can get away with; Diversify; Make market in something as similar as possible; Play the odds, estimate standard deviations; Hope; Pray; Make sure your boss knows your concerns and ok's whatever you do. And probably many more. ....One of my favourite quotations of Keynes is "It is better to fail conventially than to succeed unconventionally."PMy client needs 3000 lots of a Crack Spread Option (or as I mentioned below, you can make it as exotic as you want), I can't reduce the volume since thats what he wants! How do I statically hedge this option, I have no idea, do tell me! Charge the highest price I can get away with". Then there would be an offer war between me and JP! I'll keep offering it 1 cent lower than JP until I think that the risk is too much to handle, if JP gives up at a point where my premium for hedge error is a 1.5 STD (rather than a 2 STD), should I bail and let JP handle the risk for a 1.6 STD hedge error? Or should I still go the Commodity Regulators and complain about JP charging an unusually low price for the Derivative, how low is too low? I like the quotation of Keynes, so what he basically says is that "The brilliant guy sitting in his lab, waiting to overcharge for his derivatives and never getting any business is better off than a large investment bank who charges 'competitive' rates and makes money until a bust? Since in the end, both their total profits 'at some point' will a.s. hit 0. Only that the unconventional guy was paid by his shareholders and finally lost all their money. And the conventional guy never made any money in the first place? Really now, if we do not believe in calibration, how can there be a derivatives market? You can't even arrive at a fair value, unless you have a structural model for the underlying! Should there be a crackdown? Or any other viable ideas for making markets on exotics?You want to take on the business if you think you can do it sensibly. The first question mightbe "do you think you really understand your client's market?". If the answer to this is "yes", then presumably somemodels have already been built that at least are a basis for exploring the hedgibility of the exotic in question. Calibrating them and testing a hedging plan would certainly be an important step. I agree with Paul that the ultimate answer might be, for a particular client request, to say "no, we are not interested, at least at this time".But, calibration would/should certainly play a role in arriving at a putative "no". So, rather than hating on calibration, more useful would be a discussion on how to use it properly.

Last edited by Alan on May 6th, 2011, 10:00 pm, edited 1 time in total.

QuoteOriginally posted by: Alan So, rather than hating on calibration, more useful would be a discussion on how to use it properly.Depends what you mean by calibration. Just move a bit away from classical calibration, for example: Ask first a) "How do I choose a model?" followed by b) "How do I choose parameters in my model?" Calibration tends to mean, in the finance context, something very precise i.e. taking a snapshot of the market at one point in time, and ignoring history completely. Which obviously means if there's something temporary going on in the prices then your model parameters will be odd. And remember that those model parameters are forward looking, you aren't supposed to change them.Now if we compare and contrast the option-pricing calibration with the spring example we quickly see the differences:Springs: You could start from first principles, looking at the electromagnetic forces between molecules, etc. etc. That would be a pain. And probably wildly inaccurate. Or since springs behave the same, time and time again, and you have a very good model (Hooke's law), you just say sod first principles let's cut to the chase and calibrate. And we double check that that's ok by recalibrating every now (using different weights!) and then finding that the parameter in the model never changes. Fantastic!Options: We could start from first principles and only look at the underlying, its time series for example. Problem is that's backward looking and how do we know the future will be like the past? It's not a spring. Ok, so let's take inspiration from Hooke and calibrate to a snapshot, that's forward looking. Problem is that the parameters are very unstable, immediately saying that the model is wrong. Again, it's not a spring. So you ought to throw it away. That's the problem we have. Classical exotic sellers go for pure calibration. Stat arb people go for the time series approach. (I'm just being black and white here.) It is possible to do something mid way that works for both. For example, why do people calibrate? It goes like this:1. I don't know the parameters, what can I do? 2. Look at traded contracts, what parameters are being used there?3. But what if those parameters then turn out to be wrong? (No one is naive enough to think they are stable.)4. Well, I can statically hedge with the same traded contracts to reduce my parameter risk.Why not cut out the middle bit and say the following: "My contract has so much gamma, and therefore model risk. If I want to reduce that model risk by reducing gamma by static hedging with traded contracts then how much is that traded gamma going to cost?" So you are valuing the gamma in your exotic and seeing the price of that gamma in the market. That's what you are really trying to do. And you don't have to calibrate to do that. And this also allows you to say, perfectly consistently, that this is the market price of gamma today. It may change. Do I want to buy it now? Should I wait until it gets cheaper? You don't have to lock in the market parameters, you can use any model you like to do this.Sorry, it's a complex subject. It's easier to explain more slowly in stages. The real problem is: 99.9999% of people are wedded to calibration; 99.5% don't know of other possibilities besides calibration; 85% don't really understand what the problems are with calibration and the rest don't care.P

Thanks, Paul -- that's helpful. Please elaborate on what you mean by"You don't have to lock in the market parameters, you can use any model you like to do this".Also, it would be very helpful if you can elaborate with the problem of hedging a barrier option with traded contracts, as this is something I have been focusing on lately.

That's a very interesting topic. At the moment I'm reading a review about superhedging by Davis Hobson. That's nice since you don't take care of the model but the superhedging price will be SO HUGE than no one will enter the contract.When you are pricing exotics by superreplication you are assuming that you are infinite risk averse (for any affine model you can be safe).Another approach to that is the utility based pricing (where you assume that you want to bear some risk).Modelling the market in PHYSICAL sense is in my view a nice idea. I have read a thesis about a guy who modelled the crude oil by a multi agents model based on economical argument and it fits very well the market. For me the real question is the link between the underlying price and the option one. Assuming only a link through their vols is maybe false.A lot of work and I'm very happy to see that some people working in banks begin to ask themselves those questions @Alan; if you are interesting into hedging a barrier option, I can send you a paper of Carr about semi static hedging (it's a static hedging which is rebalanced if the option knocks). Here a paper http://www.math.nyu.edu/financial_mathe ... -2.pdfHave a look at the theorem 5.5

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

Yes, thanks -- I know that paper. Carr and co-authors have generated a number of model-dependent static hedgesfor barriers. The last one I have seen is Carr & Nadtochiy. They all require continuity in crossing the barrier. That's why I asked Paul to elaborateon his approach to this problem --- as it seems to have a different flavor.

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

A lot of those Carr things try to match payoff using vanillas, which is daft because the point of exotics is that they aren't portfolios of vanillas!Do you know much about UVM? Or S(VM)^2 (as we seem to be now calling it)? And have you seen "A Note on Hedging: Restricted but Optimal Delta Hedging, Mean, Variance, Jumps, Stochastic Volatility, and Costs." (Hyungsok Ahn and PW)?I often use barrier options as examples: They can have delta and gamma changing sign, they have issues at triggereing, and they are weakly path dependent. So very interesting without being impossible.P

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

yes the main problem is always the model dependence. Static hedging is less model dependent I think than dynamic hedging but still it is. Super hedging is not model dependent (it only assume that your model is an affine one), but no one will buy the exotic you priced because the price will be huge.UVM is a bit in this case. To be competitive your vol bound have to be tigh and so it's VERY likely that you will have violation of your confidence interval.S(VM)² is a nice model. You assume a stochastic volatility and you price according to the mean variance framework with your aversion for risk. As for UVM the static hedging is directly fit on the market quotes.For my point of view, the main drawbacks of this model is :-you don't calibrate on the implied volatility surface (which is good) but you have to evaluate your parameters on the underlying historical data (example the drift and the vol vol) which can be very hard.-so when is the model not efficient enough? If your historical parameters evolve do you recalibrate (not in the implied vol but in the historical datas)? If I would be a quant, I would use for the pricing an uncertain stochastic volatility model (assuming as in S(VM)² a dynamic hedging in the underlying to minimize the variance of the portfolio) and then build an overall static hedge optimization (among all the vanillas available in the market) to minimize the best case. Then I would sell to this price. No market price of risk, no risk neutral measure and no risk aversion estimation. The price would be cheaper than a classical UVM and less risky than S(VM)².

So, of all the approaches mentioned in the last two posts (Carr's, UVM, etc,), which one best dealswith the underlying (say equities) jumping over the barrier and why?

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

There seems to be an emerging tendency in a finance to think of static hedges as superior, somehow, to dynamic ones. This has always bothered me.If this comes from true static replication (put on once, never change, payoffs guaranteed to be the same), that's fine (ignoring trivial issues like counterparty credit risk )But if your static hedges are model dependent, how are they necessarily going to be better than model-dependent dynamic hedges? What does one actually gain by being static? How is your static misspecification error going to be smaller than the dynamic one?

QuoteOriginally posted by: crmorcom But if your static hedges are model dependent, how are they necessarily going to be better than model-dependent dynamic hedges? What does one actually gain by being static? How is your static misspecification error going to be smaller than the dynamic one?In almost all cases the static hedge is an afterthought. In the sense that theoretically it doesn't help. So you are absolutely correct!!! But in practice it does help. Whereas all those models mentioned in my last post have a value/risk improvement in both theory and practice. I.e. static hedging is not an afterthought!@Alan...well, only one of those mentioned has 'jumps' in the paper title!P

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

@crmorcom,Well, you're right in principle. To relate this to my question, let's say all barrier static hedges assume a continuousprocess across the barrier and continuous monitoring. Then, in reality, let's say X% of the time the barrier is breached by a jump, due either to the nature of the monitoring or an underlying jump during a continuous monitoring period.Can a dynamic hedging strategy (based on a more realistic process decription that can jump) do better thanthe static hedges that assume continuity? I don't know -- hence my question before. @Paul,OK, will look for my answer in that one.

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

This is not unrelated to having a continuously monitored barrier but only hedging discretely, and that's covered in that paper too.P

QuoteOriginally posted by: frenchXS(VM)² is a nice model. You assume a stochastic volatility and you price according to the mean variance framework with your aversion for risk. As for UVM the static hedging is directly fit on the market quotes..Wait a minute, the assumptions are:(i) stochastic volatility, which doesn't describe the underlying when trying to price barriers(ii) mean variance framework, hahahaha(iii) your aversion to risk, which is quantified how?QuoteOriginally posted by: frenchX For my point of view, the main drawbacks of this model is :-you don't calibrate on the implied volatility surface (which is good) but you have to evaluate your parameters on the underlying historical data (example the drift and the vol vol) which can be very hard.What's the drift then? Or the vol of vol?How is estimating them any better than fitting a visible implied vol surface.You fit the traded option prices anyway, not the implied volatilities.QuoteOriginally posted by: frenchX If I would be a quant, I would use for the pricing an uncertain stochastic volatility model (assuming as in S(VM)² a dynamic hedging in the underlying to minimize the variance of the portfolio) and then build an overall static hedge optimization (among all the vanillas available in the market) to minimize the best case. Then I would sell to this price. No market price of risk, no risk neutral measure and no risk aversion estimation. The price would be cheaper than a classical UVM and less risky than S(VM)².I'd wager you still won't do any business, and your prices will be too slow.Besides, what model are you going to use for your static and dynamic hedging?Where will your parameters come from?To be honest this is all too vague without numbers.It's too easy to say you'll 'statically hedge' and act like that solves the problem.We need a test case of market values and see what calibration gives and what the alternatives come up with.

What I believe is that the best is a combination of the two (dynamic hedging for the underlying and static hedging with vanillas). Keep in mind that static hedges are not written in stone, you can rebalance them when you want. It's just the difference between greek matching and payoff matching. @Alan: I like very much the idea of Carr of semi static hedging: you build a static hedge that you will sell partially if the option knocks. For the hedging in the framework I though (UVM+S(VM)² ) it's really as written in my draft. There would be a drift term it's true but forget risk neutral arbitrage free because we are not dealing with pricing we are dealing with practical hedging. Moreover you can say that the underlying is a call option with 0 strike so you can easily add the underlyin g in the rebalanced static hedged.So what I would do Alan,-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.-I would check on long period how my parameters are stable and I will put corresponding uncertainties on them.-I will derive the best case/worst case PDE-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)If 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. At the question when should I rebalance my static hedge it's when the risk costs me more money than my cost of hedging and it can be evaluated with the daily PnL for the worst case.It'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.

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