How to become the master of simulation?

[Dimatrix]

G'day everybody.



I need some advice. So far we've been selling our products showing backtestings and a lot of bla bla. I suggested to additionally use results from simulations with a grid of risk parameters to show the customers, what game they're actually playing with the payoff. Many don't seem to understand, that they're sometimes betting on vol or something else and not the direction of the underlying. So far so good. Now what? I will try to start simple and get into more difficult asset simulations later:


[list]

[*]Start: Simulate stocks

[*]Simulate currencies

[*]Simulate stock baskets

[*]Simulate currency baskets

[*]End: Simulate commodities (not all, oil is enough)

I'm thinking about using lognormal stock prices with a consensus of analyst recommendations for the drift (expected drift) and implied vol. I need models which describe realistic price movements of assets. So I'm not sure if geometrical Brownian motion is the right choice, maybe one needs to take care of fat tails. As you see, I just don't know what to use. I think all this issues are treated in risk management but there are many books out there. We won't need the results of the simulations for a risk book or in accounting, so the models don't need to be too sophisticated. I was thinking about buying Glassermanns Monte Carlo Book for the simulation techniques and maybe some of the riskbooks such as thisfor the simulation of commodities. What I would love to have (and didn't find) is a book with realistic stochastic models for all asset classes.

[*]Does the stuff above make sense to you?

[*]Is there a book which summarizes the most realistic models for the asset classes above?

[*]Any other advice or book recommendations?

Thanks a lot for your help.
[/list]

[jungle]

[i]What I would love to have (and didn't find) is a book with realistic stochastic models for all asset classes.[/i]



Well, yes... Smiley



You could try using a variance gamma process, rather than GBM.

[chiral3]

I have so much to say on this topic but no real motivation this instant.  I have done a considerable amount of work in this area and my philosophy is always evolving. 



At its most basic, though, you need scenario generators across asset classes.  These are the usual EQ and FX models.  Commodities gets a bit more complex (mean reversion with jumps) and IR is the most interesting as you have all the usual short rate models to consider depending on what kind of yield curve dynamics you are trying to reproduce (I am dealing with a HW now that stays inverted if calibrated whilst inverted, etc.).  If you are in one market it is not so interesting, but in multiple you have all those correlations to deal with in your fx and ir processes (even if you aren't risk managing your rho risk, you need the r vector for your other processes and you need to generate term structures anyway).  Term structure of vol is also very important, so you will want SV ideally, also.  Also, I don't know how important these are for backtesting.  I find them important for valuation and for projection/stress testing.  By the latter I mean evolving my position and hedges out in time to see how they perform.



That being said you can either a) buy these from one of the million vendors out there or b) create your own internal libs.  The pros for a) is that it is ready to go and use.  The downside is the black box nature coupled with the inflexibility of most of the products.  The pros of b) are the counter of a's cons coupled with the learning experience.  The cons are the amount of work and time that will be required.  My rule is measure twice and cut once.  Therefore, before you begin, figure out exactly what you want and exactly how you are going to do it (i.e., eq, vol, fx, and ir in C++ utilizing boxmuller for the cholesky with........)



Regarding your concern about leptokurtic returns of risk factors:  this is minor at this point in your development.  There are methods for dealing with this (such as modifying the drift - see Lo I think) and, without everything I just mentioned, rather minor until you address the above.



So far as simulation, I have an excellent cookbook, but I can't put it up publicly here.  Email me if you'd like it.

[quantie]

I'd recommend the book by glasserman there is all that is to it in there. If you want to get realistic dependence you could use copulas but then you'd have to estimate these by fitting them to data and not just throw in a single dependence parameter to make it interesting..

[Dimatrix]

Thanks everyone for the advice.

Chiral3 you mention very important things, especially the scenario generators across asset classes. I planned to follow the rule: Think big, start small. Means, I will keep in mind what the perfect library should do, but start small. To be honest, I can't even start big since I will need to learn some of that stuff. So I might start with a vol class which is used by other classes and will return deterministic vol in the beginning. If my scenarios will work and there is some time and money, I will do the next step and adjust the class so that it will return stochastic vol. The same for interest rates. I might start with deterministic or maybe forward rates and than stochastic. If I get say equities working, I will proceed. Commodities will come at the end, as you say they're more complex. The problem is, that this library will be used by our sales guys, which don't know how to calibrate etc... I can't make it too complex. We're not a bank, our customers are Asset Managers which will hardly know what stochastic vol is, so starting with basic models seems to be a good idea. Anyone else a book recommendation on this topic? I have some money left for books and I would love to buy more good ones, where half of the book is not filled with basics. Thank you

[JumpStart]

In addition to Glassermann's book as mentioned by others I think you should have Cont & Tankov's book on your shelf which is particularly geared for VG and other Levy processes.

[CDS]

having done a bunch of simulations for a comp. finance class this semester, I'd definitely suggest glasserman's book...for stuff like simulating interest rates, variance reduction techniques, american option etc. on the other hand if you want to move to credit i didnt find personally any good book. But if you;re already experienced with other Monte Carlo stuff and you know basic theory (Schonbucher+Duffie) you can get away with it...

[aaron]

I think you may be going down a hard road, that will not lead to your destination.



Realistic marketwide simulation is extraordinarily difficult. A single spot price is easy, but aligning it to produce both realistic dynamics and forward curve evolution is extremely difficult. Then you'll have products affected by volatility surfaces and intermarket spreads.



Commercial products use highly simplified models (like multivariate Normal with block diagonal covariance matrices) that don't come close to being arbitrage-free or giving realistic distributions of anything but large, diversified portfolios.



What's important for your application, as I understand it, is to ensure you have a risk factor that allows your strategy to lose money. Presumably, your strategy was built using some kind of a model, and that model showed it had a great Sharpe ratio. If you simulate using that model, you won't capture the risk.



I don't like using a lot of parameters in these simulations. You have to fit these parameters on either historical or implied data, and there just aren't enough data for more than few to be done accurately. It's much better to have a simple model with good fitting than the perfect model you can't calibrate. The effect of omitted parameters will show up in your fit for the ones you do have.



But the key is to be sure you have captured the most important market variables (so you get good correlations with major asset classes) and at least one parameter that goes directly to the ability of the strategy to produce excess returns.



This means you'll have a different simulation for each strategy, but the damage you do to these simulations in order to link them together offsets any gain from consistency.

[chiral3]

Just to expand on Aaron's comments "Realistic marketwide simulation is extraordinarily difficult" and "Commercial products use highly simplified models ..."  Often commercial products are for economic/reg capital and stress testing.  They also contain only the most simple models because they are easier to market if they are not prone to calibration error.  You don't get nearly the number of paths you need for, say, pricing or projecting a portfolio to test hedges.  The issue is, even if you were doing quarterly for five years, that is twenty points where you have to stop, recalibrate and create the surface, have term structure of rates dynamically drive the equity scenarios, etc., dividend yield curve, etc.  and get an arbitrage free answer.  It gets 1) highly intensive and 2) prone to calibration error, etc.  If you have a large portfolio you can take advantage of the size and employ variance reduction to reduce the number of paths in a pricing situation, but a robust cross process scenario generator is often quite difficult.



I was just having this discussion at my shop yesterday with my US and European colleagues.  We have some internal and external tools in this area catering to a wide array of our needs.  However, as I have alluded to, there are a number of trade-offs.  One idea, that perhaps I am more keen on than my colleagues, was taking advantage of the fact that in a resource intensive environment, there are often other shops/desks within your organization that may have this need.  I saw some benefit from reaching out across the quant desk and seeing who has a need for it and combing resources.  Getting an engine into a version controlled environment where we can all work on pieces.  Easier said than done, but what this accomplishes is 1) it doesn't kill half a quant team by spreading the problem out over a larger team 2) it promotes cross pollination ideas thereby hedging groupthink and idiosyncratic thinking that propagates at the group level, and 3) it solves the increasingly difficult issue of model consistency.  More and more people need to explain to a global head why the European model and the US model are giving very different answers when they both used 1fHW, heston vol, and 2000 paths.



I'll shut up now.............

[Dimatrix]

[i]I'll shut up now.....[/i]



Please don't! Everything you say is helpful. All the comments above seem to point out, that the whole simulation stuff is more an art. So the books out there can probably tell how to simulate in general, but are maybe not applied enough to teach you how people do it in industry. So to the answer to the question:



How to become the master of simulation?



seems to be: Go to a good shop, and learn it there. Anyways, I'm currently reading a lot about Levy-Processes, which really made my world bigger. Cont and Tankov's book is fantastic. I'm just saying it, to point out, that I'm trying to follow the advice given here. Much appreciated.