Hi, gurus:I want to know which exactly models are being used in big banks in America? My focus is on the practice and implementation, not on the acadamic side.Such as BS, B-Tree, implied tree for options on stock. which models being used for options on interest rates, bonds, on exotic options, term structure and so on. Could anyone shed some lights on me? or where can I get such info? Thanks a lot! James

- doublebarrier2000
**Posts:**237**Joined:**

Hi. Your question could take a few pages to explain properly.fROM MY EXPERIENCE WORKING IN A FEW INVESTMENT BANKS IN LONDON there is no exact rule to modelling.Lets look at equity exotics for example. As you'd expect, there is a trade off between model accuracy and implementation. Yeah its cool to have a fancy GARCH model for exotics but, in practice, the calibration of such models is difficult and time consuming. In general, if there's a good closed form model that works, daily P&L and Risk figures are used from it. For pricing, however, traders may take more time and look at more complex models -- according to how complex the structure is they're trying to price.For month-end reporting, it is common that the middle office will use very accurate models as these are the figures that are shown in the balance sheet.Quickly looking at your other points, 1)Quaisi Monte-Carlo is used a lot for path dependent trades (especially in equities)2) FX option markets are pretty mature and all models are vanilla in most cases3)Fixed income uses term structure models of the yield curve. When I first worked in this area they used Hull/White mean reverting model, but, from what I've read, fancier models (eg. forward LIBOR correlation models --see Wilmott magazine) and others are used for FI exotics. Again they need to be calibrated.hope that helps

Thank you so much!I am studying John Hull's book (almost finished) and quite a few papers for theoretical analysis.But I am more interested in what those Quantitative Analysts or Financial Engineers are doing in banks, which models the banks are using currently. Besides those models you introduced, banks also use some models such as simple CRR ,BS, DK Tree, for vallina options, and they must calibrate the models everyday. which is the most important task for them.one way to do that for calibration, they use market price to get an implied vol surface with interpolation,then select one vol from the surface that matches the strike price and maturity of the option they will price. use that vol for CRR Tree, then get the option price. Due to stocks change everyday, they have to do that whole procedure again everyday. Is that right?Or is there any other better way to do the job? All models need calibrating everyday?Your help will be greatly appreciated.James

Last edited by jameshu on September 6th, 2003, 10:00 pm, edited 1 time in total.

Most banks now use some sort of autocalibration for the exotics ... for each deal, the model is calibrated to the deal-appropriate vanilla instruments, and then the newly calibrated model is used to price the exotic. Worse, for each "bump" the same procedure is followed ... one may have 30 or so distinct bumps to generate the bucket delta risks, and another 100 or so to generate the bucket vega risks ... and then one may shift the whole yield curve uniformly by 10bps and repeat the whole process. It gets compute intensive unless you are real careful with the coding.

For exotics, the main points in a "perfect" yield curve model are:1. Multi-factor dynamics2. Volatility smile modeliing for vanillas3. Correct autocorrelation structure4. Arbitrage-free dynamics5. Consistency with models for vanillasThis must be balanced againsta. Quick and accurate calibrationb. Fast valuation of exoticsc. Fast greeksThe main problem is to combine 1.-5. with c. For his reason it might be preferrable to combine a model that accomplishes 1-5 and a.-b. with a model accomplishing 2.-5. and a.-c. Typically, the latter requires instrument-dependent calibration (i.e. dependent on the instrument you wish to price) and some restrictions as to the instruments that can be priced correctly, whereas the former can be done with models that are large enough to accomodate more general calibration procedures (e.g. Libor market models)

There are better ways than the bumping method of Greek computation.Check out the paper "Hedging with Monte Carlo" by Cvitanic et al.:http://math.usc.edu/~cvitanic/papers.htmland also my book at http://martingale.berlios.de (equations 5.13, p129 and 5.40, p150).Following this approach at least all Deltas can be computed from a single path computation which should drastically lower the computational effort. Moreover in general the method of computing "Deltas" by "bumping" is incorrect:.it is correct only if an option has a price process c_t of the formc_t=C(t,S(t)) (*)which is a deterministic function of some underlying asset price S(t).In this case we have a rigorous definition of such deltasD(t)=dC(t,s)/ds evaluated at s=S(t) (**)and perfect replication using these deltas in continuous trading under suitable additional assumptions.Now typically for exotic options the price c_t has no representation (*) for any vector of traded assets S.In consequence definition (**) of "Deltas" as sensitivities is unavailable and bumping S computes the difference quotientof a nonexisting function C. Consider the following example.We have a market with one single asset S(t) following the dynamicsdS(t)=S(t)dW(t), S(0)=1where W(t) is as usual a standard Brownian motion. Interest rates are assumed to be zero.In addition we have a second process X(t) satisfying X(0)=1 anddX(t)=u(t)X(t)dW(t)=a(t)dS(t) with a(t)=u(t)X(t)S(t)^{-1}.Finally we have a derivative H=X(T) expiring at time T. ThenH=X(0)+integral_0^T dX(t)=X(0)+integral_0^Ta(t)dS(t).Thus H can be replicated by trading in S.Now let's see what the method of computing "Deltas" by "bumping" S, recomputing the model price of H and forming adifference quotient produces:at time t=0 we perturb S=S(0) and recompute the value of H,the process X does not care about S and nothing happens.We have Delta(0)=0.It's the same at any other time. We have zero deltas at all times according to the perturbation method.But we cannot hedge H=X(T) with zero hedge weights in S.Here is a more natural example: consider a market with zero interest rates and one single asset S(t) satisfyingdS(t)=v(t)S(t)dW(t).The option payoff at time T is the quadratic variation of the logarithm log(S) on [0,T]:H=integral_0^Tv^2(s)ds.This is totally insensitive to the price level: deltas computed by perturbation of S will be zero.However if the volatility v(t) satisfies0<e<|v(t)|<=Kthe market is complete and so H can be replicated by trading in S.Consequently the perturbation method is incorrect for general exotic options.

Last edited by trc on September 27th, 2003, 10:00 pm, edited 1 time in total.

GZIP: On