QuoteOriginally posted by: FermionQuoteOriginally posted by: FermionWhat does "delta" mean when you have multiple underlyings? A vector of deltas for each underlying? Or a single delta for some sort of "Market" value? Or what?Likewise "implied vol".I tried to follow this thread, but find I cannot without knowing the answers to these questions.Does anyone have any references where these quantities are explicitly defined for an "exotic product on multiunderlyings"?No answers from anyone? Am I being obtuse?here we go. you have a product whose value V is a function of many underlyings V=V(S1,S2,S3,..., volsurface(S1), volsurface(S2),..., params params params, etc etc).the delta is the vector of partial derivatives d V dS(i).In some special cases it makes sense to talk about a single delta, e.g. basket options when V(Sum w(i) S(i)) but it is just a trick for ease of calculation.Implied vols? of course there is a surface per underlying.Your PL for small moves will be the first order expansion of V: PL = SUM dV /d X(i) * dX(i) + dV/dt * dt where X is all your possible variables, so it includes the volsurfaces , the params, good luck.V of course can be more than one position, it can be the whole book...All of the above is, I think, in the main books.As a final comment, day to day PL attribution in an exotic book can be difficult, but it is not too difficult, given enough computational power.PL attribution to single trades is instead much more difficult, because single trades merge into the portfolio, hopefully saving money on the hedging. hopefully.

Money,re: the task your boss has set you. If I understand correctly, they want to understand from the PL whether the correlation paramenter being used is right.As Paul said, there might be many effects of larger order of magnitude that are obfuscating the correlation impact on the PL, one of them being the model itself.Assuming you can work out the delta PL correctly, the vega PL due to the change in volsurface (or maybe you use only one vol number? ), the effect of discrete moves, etc etc,then in theory you could try to deduce something on your correlation. In practice, I believe it would be massively difficult, because numerically the problem is similar to subtracting large numbers, i.e prone to large relative errors. IMHO you should look elsewhere to evaluate your correlation: your method of just looking it up on bloomberg is endearingly naive. I beg you to at least compute the timeseries of the rolling correlation. And go back a few years for god's sakeyou will see what a shitty number correlation is (I am sure you are aware of this). if you are lucky, it will be range bound in a smallish interval, say 10points. then what number you use in that interval does not matter much from a hedging point of view, though of course it will probably make a difference between showing a loss or a profit on our initial trade (if so, well one shuld have thought about it earlier...)if you are unlucky, it will widely dispersed, say over 50 points. not uncommon. finally: there are IDB markets in correlation. if your correlation exposure is covered by the market, then you should try to mark your book to market value or some approximation of it. Whether you should hedge with parameters implied from the market is a vexing academic question: the answer is an obvious yes for any trader that has to mark to market, of course, because that covers against the short term, small moves. And in the long term we're all dead, especially if there are big moves.PS no offence, but I would still love to know where you work

1) What does abbrevation, such as, IMHO, IDB .. etc. stand for ?2) In this case, how should I get the correct correlation figure to use (in the latter case of +50 points dispersion). I think, under such scenario, using expontial weighted moving average of historical correlation will not help at all. Also, using these kind of methodolgies (e.g. bootstrapping corrleation, Exp. Moving Average), how can I ensure the computed correlation will still be POSITIVE-DEFINITE ???3) ANy reference, material...are u working in a major houses as an exotic trader/quant ???

OK, is it true that:E[P&L | St] = 1/2 * Gamma1 * S1^2 [ (Sigma1_Project) ^ 2 - (Sigma1_True) ^ 2] + ... 1/2 * Gamman * Sn^2 [ (Sigman_Project) ^ 2 - (Sigman_True) ^ 2] + ... Cross_Gamma12 * S1 * S2 * (Sigma1_Project * Sigma2_Project * Correlation_Project - Sigma1_True * Sigma2_True * Correlation_True) + ... Cross_Gamma (n) (n-1) * Sn * S(n-1) * (Sigma(n)_Project * Sigma(n-1)_Project * Correlation_Project - Sigma(n)_True * Sigma(n)_True * Correlation_True) + ...where Sigma(n)_Project = the vol. input by the trader to the model Sigma(n)_true = the REALIZED vol. (not known at foresight) Correlation(n) (n-1)_Project = corr. matrix inputted by trader Corrleation(n) (n-1)_True = Realized CorrelationWell, since I keep track of the result everday ? HOw should I compute the REALIZED VOLATILITY AND CORRELATION ???WHat rolling window should I use ???Any thoughts ?Mr. MOney

QuoteOriginally posted by: Money1) What does abbrevation, such as, IMHO, IDB .. etc. stand for ?IDB: inter dealer broker. it is the OTC market between professionalsIMHO: in my humble opinionQuote2) In this case, how should I get the correct correlation figure to use (in the latter case of +50 points dispersion). I think, under such scenario, using expontial weighted moving average of historical correlation will not help at all. Also, using these kind of methodolgies (e.g. bootstrapping corrleation, Exp. Moving Average), how can I ensure the computed correlation will still be POSITIVE-DEFINITE ???different houses do it in different ways, and do not like to talk about it too much. sorry...are you alone there? that is a problem. normally a house builds its expertise ad hence its methodologies over years, via discussions of a core group of traders and quants.Quoteare u working in a major houses as an exotic trader/quant ???yesmoney, i told you long time ago, when you were asking about how to price a complex exotic, that the best way would have been to buy it from a major house, package it and thensell it to your customer. I was not joking.it sounds to me like your place went ahead and traded it, and it sounds like you are beginning to run into problems, and it is likely that it will get worse.a piece of friendly advice: get out of there as soon as you can, and try to get hired by a big house, and get trained there

QuoteOriginally posted by: granchiohere we go. you have a product whose value V is a function of many underlyings V=V(S1,S2,S3,..., volsurface(S1), volsurface(S2),..., params params params, etc etc).the delta is the vector of partial derivatives d V dS(i).In some special cases it makes sense to talk about a single delta, e.g. basket options when V(Sum w(i) S(i)) but it is just a trick for ease of calculation.Well, I understood those possibilities. Unfortunately the term "exotic product of multiunderlyings" doesn't state that it is a basket. It wasn't clear to me that the term delta didn't refer to sensitivity to some other "price" implied by the definition of the exotic. Even though Paul referred to "deltas" (plural) it wasn't clear to me that he didn't intend repeated hedging to a single delta rather than separately hedging each underlying. Even a simple vector doesn't take account of correlations between underlyings. Perhaps I have too much imagination.....QuoteImplied vols? of course there is a surface per underlying.Again, this wasn't clear. Even if it is a basket, then the value of the basket has a volatility and an implied volatility too. I guess you are telling me that the normal assumption for delta and implied vol of an exotic product of multiple underlyings, if it is not made explicit otherwise, is a vector of deltas and implied vol surfaces for each underlying. This certainly makes sense to me and was my natural inclination but I hesitated to assume that each underlying was being seperately hedged, because even trying to hedge a single underlying w.r.t ivs rather than the current volatility doesn't tell you how to hedge your overall position with respect to current volatility. Is it normal to hedge multiple underlyings at this level? Do others agree that this is normal useage for delta and implied vol? I'll try to re-read the thread assuming this and see if I can fathom it out.As you can see, I have no experience of how traders normally operate with multiple underlyings, but I am full of questions.... Thanks.

Hi WIlmott,1) I now do the most simple case:OK, for a plain-vanilla call, I should have this formula:E[P&L | St] = 1/2 * Gamma1 * S1^2 [ (Sigma1_Project) ^ 2 - (Sigma1_True) ^ 2] (same formula nomatter in wilmott book, other papers, DB book)Let's say it is a 3 MONTH CALL,how should I get the REALIZED VOLATILITY ?Does it MEAN ON EVERY NEW VALUATION DATE, I should use the new date and take out from the rolling-window the most obsoletedate before computing the VARIANCE and STANDARD DEVIATION.This is almost done except to get the REALIZED VOLATILITY2) NOw, I am trying to see if I can use the same formula (i.e.E[P&L | St] = 1/2 * Gamma1 * S1^2 [ (Sigma1_Project) ^ 2 - (Sigma1_True) ^ 2] )in other SINGLE-UNDERLING EQUITY DERIVATIVE PRODUCTS(e.g. sum of strip of barrier options = a package)Can I do that ??3) Did the formula I posted before on multi-underings is CORRECT OR NOT ?E[P&L | St] = 1/2 * Gamma1 * S1^2 [ (Sigma1_Project) ^ 2 - (Sigma1_True) ^ 2] + ...1/2 * Gamman * Sn^2 [ (Sigman_Project) ^ 2 - (Sigman_True) ^ 2] + ...Cross_Gamma12 * S1 * S2 * (Sigma1_Project * Sigma2_Project * Correlation_Project -Sigma1_True * Sigma2_True * Correlation_True) + ...Cross_Gamma (n) (n-1) * Sn * S(n-1) * (Sigma(n)_Project * Sigma(n-1)_Project * Correlation_Project -Sigma(n)_True * Sigma(n)_True * Correlation_True) + ...Any thoughts on this subject ???I implemented teh spreadhsheet using this formula. However, cannot reconcile the P&L...

any thoughts ???

Big Problem:Finally, with painfully trial & error, I found out that the HE formula (for one underlying):E[P&L | St] = 1/2 * Gamma * S^2 [ (Sigma_Projected) ^ 2 - (Sigma_Realized) ^ 2] can only be APPLIED TO SIMPLE CALL OPTION.I read through the derivation VERY CAREFULLY... There are a lot of assumptionse.g. plug in BS formula, theta closed-form formulabefore he gets the final formula...That's why I am now using this formula for a single underlying structured product. I cannot reconcile the P&L due to vol. mismatch.What can be done in this case ????Or perhaps I am wrong ???ANy comment ???If that is the case, then the formula:E[P&L | St] = 1/2 * Gamma1 * S1^2 [ (Sigma1_Project) ^ 2 - (Sigma1_True) ^ 2] + ...1/2 * Gamman * Sn^2 [ (Sigman_Project) ^ 2 - (Sigman_True) ^ 2] + ...Cross_Gamma12 * S1 * S2 * (Sigma1_Project * Sigma2_Project * Correlation_Project -Sigma1_True * Sigma2_True * Correlation_True) + ...Cross_Gamma (n) (n-1) * Sn * S(n-1) * (Sigma(n)_Project * Sigma(n-1)_Project * Correlation_Project -Sigma(n)_True * Sigma(n)_True * Correlation_True) + ...for mulit-underlyings cannot be used as well.(since my products is a worst-of-basket plus some digital payouts on some observation dates which canlead to early redemption of the product)As said, what can be done in this case ???ANybody help out ?? I need to show sth. to my boss....Help !!!!

To be specific:take a look (See ch2, pg 8-9) of this paper:www.cam.wits.ac.za/mfinance/projects/TomMcWalter.pdf You can see that the author plugged in BS + theta closed-form formula to derive the HE formula.OK, now take a look on Wimott's book: (Paul wilmott on Quantitatative Finance)In CH23 (Discrete Hedging), on page 321, he argued that the leading order random term in hedged porfoilio is:1/2 * sig ^ 2 * elison ^ 2 * S^2 * GammaThis formula is NOT BASED ON ANY ASSUMPTION (i.e. NO BS formula, NO Assumption of instrument being a simple call/put... etc.)Actually, I can get this same formula even using those equations in the FIRST PAPER I MENTIONED (i.e. www.cam.wits.ac.za/mfinance/projects/TomMcWalter.pdf )OK, in equation (2.5), let's assume that r = 0 and delta t is very small (say one day)Then HE ~ delta PI = (Theta) dt + 1/2 * sig ^ 2 * elison ^ 2 * S^2 * Gamma (Using equation (2.3) and (2.4))First-term is NON-STOCHASTIC,thus the same conclusion ....SO my question once again:Can I use this formula HE = 1/2 * sig ^ 2 * elison ^ 2 * S^2 * Gammato other NON-VANILLA STRUCTURED PRODUCTS ???Thanks

It is me again.Finally I start to understand more about the DIFFERENT COMPONENTS (AS DR. WILMOTT said)(1) In this paper (www.cam.wits.ac.za/mfinance/projects/TomMcWalter.pdf) and Paul Wilmott's Quantitatative Finance,the listed P&L FORMULA IS CATERING the RANDOM P&L element.Nomatter which method used, the RANDOM P&L FORMULA IS THE SAME (actually the way how P.W. presents look more general).i.e. RANDOM P&L EFFECT = 1/2 * S^2 * sig ^ 2 * [ (elison ^ 2) - 1] * GammaThis formula SHOULD BE INDEPENDENT ON ANY STRUCTURE. Am I right ?But my questiion: how do I know the elison ??? What I only know is elison ~ N(0, 1)And what I get everyday is the REALIZED STOCK PRICE... I am NOT SIMULATING THE STOCK PROCESS.My task is to break down the realized P&L into different components to present to my boss.There is no way to know elison realized ???(2)NOw, I get it crystal clear. The formula I saw at the book published by Deutsche Bank is ON THE DETERMINSTIC ONE:i.e. DETERMINSTIC P&L EFFECT = 1/2 * S^2 * Gamma * [ (Vol_actual ^ 2) - (Vol_Implied ^ 2) ] (vol_implied means the one guessed by Trader using implied vol. of other similar tenure options)Well, again, is this DETERMINSTIC P&L FORMULA applicable to any derivatives universally ???I don't follow the proof quite closely.(3)So Daily P&L = RANDOM P&L EFFECT + DETERMINSTIC P&L EFFECT = (1/2 * S^2 * Vol_Implied ^ 2 * [ (elison ^ 2) - 1] * Gamma ) + (1/2 * S^2 * Gamma * [ (Vol_actual ^ 2) - (Vol_Implied ^ 2) ] )Is my formula now OK for a SINGLE UNDERLYING STRUCTURE ????MY question: In reality, only the 2nd term DOMINATES IN THE P&L CALCULATION. Can I discard the 1st term effect since I have no way to tell what's the elison from daily closing stock price .... (as mentioned in (1) above)AM I right ??? ===========================================================================================Next phase,What is the formula for RANDOM P&L Effect due to CORRELATION ????For the determinstic part, I think the formula I posted many times before here, should be right..E[P&L | St] = 1/2 * Gamma1 * S1^2 [ (Sigma1_Project) ^ 2 - (Sigma1_True) ^ 2] + ... 1/2 * Gamman * Sn^2 [ (Sigman_Project) ^ 2 - (Sigman_True) ^ 2] + ... Cross_Gamma12 * S1 * S2 * (Sigma1_Project * Sigma2_Project * Correlation_Project - Sigma1_True * Sigma2_True * Correlation_True) + ... Cross_Gamma (n) (n-1) * Sn * S(n-1) * (Sigma(n)_Project * Sigma(n-1)_Project * Correlation_Project - Sigma(n)_True * Sigma(n)_True * Correlation_True) + ...Sorry for the verbose email. But I do believe somebody here working in major houses must have done that !!!ANy thoughts ???

Any thoughts ? Hello ....

Is anyone willing to take a look at my spreadsheet and show me what's wrong with my computation ....help ...Mr. Money

QuoteOriginally posted by: granchioMoney,re: the task your boss has set you. If I understand correctly, they want to understand from the PL whether the correlation paramenter being used is right.As Paul said, there might be many effects of larger order of magnitude that are obfuscating the correlation impact on the PL, one of them being the model itself.Assuming you can work out the delta PL correctly, the vega PL due to the change in volsurface (or maybe you use only one vol number? ), the effect of discrete moves, etc etc,then in theory you could try to deduce something on your correlation. In practice, I believe it would be massively difficult, because numerically the problem is similar to subtracting large numbers, i.e prone to large relative errors. IMHO you should look elsewhere to evaluate your correlation: your method of just looking it up on bloomberg is endearingly naive. I beg you to at least compute the timeseries of the rolling correlation. And go back a few years for god's sakeyou will see what a shitty number correlation is (I am sure you are aware of this). if you are lucky, it will be range bound in a smallish interval, say 10points. then what number you use in that interval does not matter much from a hedging point of view, though of course it will probably make a difference between showing a loss or a profit on our initial trade (if so, well one shuld have thought about it earlier...)if you are unlucky, it will widely dispersed, say over 50 points. not uncommon. finally: there are IDB markets in correlation. if your correlation exposure is covered by the market, then you should try to mark your book to market value or some approximation of it. Whether you should hedge with parameters implied from the market is a vexing academic question: the answer is an obvious yes for any trader that has to mark to market, of course, because that covers against the short term, small moves. And in the long term we're all dead, especially if there are big moves.1) "then in theory you could try to deduce something on your correlation. In practice, I believe it would be massively difficult, because numerically the problem is similar to subtracting large numbers, i.e prone to large relative errors. "can u explain with an example ? I don't get it...2) "I beg you to at least compute the timeseries of the rolling correlation. And go back a few years for god's sakeyou will see what a shitty number correlation is..."I've implemented the bootstrapping method. Should I expect to get close distribution using this method VS. rolling window methodology ? You know what, I can save a lot of time downloading data + vba codes using bootstrapping.3) Anyway, what's the catch ? the traders here seems to use a conservative correlation no. by bumping it up & down the historical correlation... Then they know what is safe ... Why the quant spend so many hr. building an estimation model on correlation ???Mr. Money

sorry money, too many questions, not enough time.but on 3):of course you do have to do that, only sensible thing to do. I do not know personally any quants that build estimation models for correlation (though certainly there are some). IMHO it would be a huge waste of time.