You are a trader and user of a model. One of the parameters of the model, say a correlation, is set very high: 95%, instead of a more realistic 30%. Imagine a deal is done. Market making gives you a value of 100, but instead should be 150 (you have hidden value due to the higher correlation). You hedge with the greeks given by the model with high (and wrong) correlation. Is the hidden value going to be maintained in the future, or it may be lost? .

Well, I'm assuming somebody bought from you if you are market making around a 100.... doesn't sound that smart to me, but let's say you were (somehow) able to actually buy 100s.It now totally depends on your hedging... should you decide to hedge with parameters of 0.95, and it turns out that realized correlation is much lower, you will certainly lose. How much? well depends on your dV/dRho, doesn't it? Of course there are sampling issues, etc. so you theoretically could end up making money or lose little, but then you're not really market making, your trading corr.Does this help?

3 points:- Sorry, I wrote too quick. I wanted to say marked-to-market instead of market making. - What is dV/dRho, variation of Vega wrt Rho? - I could not understand your opinion? Would we lose money or not? (at least theoretically)

At least theoretically you ask?Well the answer to that is: Theoretically, it depends. Of course you could lose money. What kind of question is that?dV is the derivative with respect to the value of your position, dRho (rho is also used as the greek letter for corr).The point is, if you're setting your corr too high, hopefully bringing down the value of the position (so you can have hidden reserves, which most likely will not be appreciated by risk management), you're most likely going to be underhedged on some leg (because you're assuming that corr is high), so should the corr turn out to be lower and markets move around as well, and you hedge like you would hedge if you had the correct parameters, you will most likely lose money. You're essentially trading realized corr.Hope this helps.

Perico, think of dV/dRho as Correlation Vega.

I agree mostly with you, but wanted to know the opinion of this forum. One simplistic argument: I think of the problem as if a have, for example, a call option in my book. I mark-to-market only 75% of it, giving value 75 for example. Therefore 25 is kept hidden. This corresponds to one quarter of an option which is not going to be hedged. Therefore, it may win or lose value (loses theta, but it may win in direction, volatility,..). Do you agree?

No, I don't agree. That's very simple option math.Say you got an ATM option, you mismark your vol from 35% to 25%, bringing about a 25% reduction in the value.Your delta is not going to change much (maybe by 0.01) and your vega ain't gonna change much. So, in this case, you're hedged fine.However, your gamma and theta are going to be reduced by 25% as well, so should you decide to try to capture vol based on that, your not going to be able to pay for your "real" theta...So, do we have a wannabe rogue trader in the making here or what?

If you buy call and pay 30 vol but hedge/manage the position at 50 vol, you will make more money in the event that your prediction is correct (realized vol ends up being 50) but you will lose money if realised comes in at 40 (or I shoudl say make less than you would have had you managed the position at 30 vol) The higher your taregt or hedging vol is, the less you will be delta hedging so if the stock makes lots of little moves bakc and forth you will capture less of them (although you shoudl do better in a trending marekt) If the market makes big moves and you are hedging at a low vol, you will miss alot of the move by delta hedging too much. There is no "right" way to do this. The question is, are you smarter than the market? Probably not. The market is charging 30 vol, you should probably use 30 vol to calculate your greeks. If you are on a different vol form the market as you move away form strike your mkt to mkt is going to start getting ugly as you are on a vastly different delta than the rest of the mkt. i think the practice at most places is to use market derived imputs as much as possible for hedging and pricing. The idea being that markets are pretty efficient.

Perico asks a very old but very tricky question. Basically he asks if ones must manage the book with IV or HV. When I began, my boss said " you check the prices, you calculate IV, you put it in the soft and you manage all the staff with that" I asked "What about HV ?" He answered "Market is right, forget about HV". This is wrong. To answer Perico question, it depends on what you are doing. Basically, I'd distinguish 2 different jobs : market-making and arbitrage. The market-maker lives on bid-ask spread and do not care about inefficiencies, he considers market is right (prices are fair) and just turn around market prices. He uses IV and don't even have to know anything about HV or models. The arbitrageur point of view is dramatically different. He sees 30% IV on stg and says "I think (anticipate) that realised vol WILL be 40% for the next 3 monthes. So I buy the option." He has to put a 40% vol in the model to manage the position. Obviously, his delta differs from market-delta, and this is going to generate marked-to-market P or L. But putting a vol different from the value he thinks vol WILL have, would simply be a non-consistent attitude (if he uses IV to manage, then implicitly he thinks market is right, so he must not take any position, and put the money on a risk-free acount).The problem is that a trader is always between these 2 extremes...

QuoteSo, do we have a wannabe rogue trader in the making here or what? No, FDAXHunter. You have an exotic product and have no idea of certain parameter. No idea of its historical value, no idea about its market implied value. Then you try to be very conservative. The problem is that you may lose money being conservative while hedging.