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What are the typical assumptions for quant models for each asset class and what distortions do they produce?

October 29th, 2020, 7:15 pm

We all know that there are simplifying assumptions made for many (most?) quant models from Black Scholes onwards.

But naturally these assumptions tend to create abstract worlds and many adjustments are needed to bring the models closer to reality.

It would be useful to have an orderly table of such assumptions and a corresponding list of "fixes", with critiques of various approaches.
 
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Alan
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Re: What are the typical assumptions for quant models for each asset class and what distortions do they produce?

October 31st, 2020, 4:29 pm

A good idea for this FAQ, but would be a textbook, and I doubt you'll get a taker at this point in time. To narrow the scope, if there's a troublesome assumption you can't find relaxed/fixed by diligent googling, post a question and maybe somebody will have an answer.

To kick things off, I'd say the most troublesome assumption in quant finance is:
"Security prices are determined by stochastic processes", like casino games.  If someone knows a "fix" for that one that doesn't throw out the baby with the bathwater, or says the whole field should just commit seppuku, etc -- I'd like to hear it.

Resolve that one, and maybe the rest is a cakewalk.  :D
 
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Re: What are the typical assumptions for quant models for each asset class and what distortions do they produce?

October 31st, 2020, 5:48 pm

A good idea for this FAQ, but would be a textbook, and I doubt you'll get a taker at this point in time. To narrow the scope, if there's a troublesome assumption you can't find relaxed/fixed by diligent googling, post a question and maybe somebody will have an answer.

To kick things off, I'd say the most troublesome assumption in quant finance is:
"Security prices are determined by stochastic processes", like casino games.  If someone knows a "fix" for that one that doesn't throw out the baby with the bathwater, or says the whole field should just commit seppuku, etc -- I'd like to hear it.

Resolve that one, and maybe the rest is a cakewalk.  :D
Thanks, Alan, and indeed, it's a great winter research question and maybe the basis for a book.  Would also be nice as a community resource.

Just to be clear, I am not asking the question for lack of my own aptitude with Google; it was more to revive the FAQ type of thread and see what else might happen.
 
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Alan
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Re: What are the typical assumptions for quant models for each asset class and what distortions do they produce?

October 31st, 2020, 7:43 pm

Fair enough. Here's a mini list of sequential issues and fixes for GARCH-type processes, which I'm currently involved with --  and so have on my mind:

Problem: time-varying heteroskedasticity an issue in many financial regressions:
Solution: ARCH(q) regression models (Engle, 1982)

Problem: too many lags, q, in ARCH(q) models make them very unwieldy.
Solution: infinite recursive ARCH lags via GARCH(1,1) (Bollerslev, 1986)

Problem: GARCH(1,1) says market drops and rallies will impact volatility equally.
Solution: GJR-GARCH(1,1) (Glosten, Jagannathan and Runkle, 1993)

Problem: GJR-GARCH(1,1) fits still have too little skewness and kurtosis.
Solution: my fav, among others, GM(K)-GJR-GARCH (GM(K)=Gaussian mixture with K components; Alexander and Lazar, 2006, among others).

Problem: Garch-in-mean effects are ambiguous for all existent GARCH-type models.
Solution: Lewis (forthcoming, 2021), extending GM(K)-GJR-GARCH.  :D  

Forthcoming refers to a chapter from my Equity Risk Premium (ERP) book, a current project. My interest is that the 'Garch-in-mean' term is essentially an ERP estimate.
 
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Re: What are the typical assumptions for quant models for each asset class and what distortions do they produce?

October 31st, 2020, 9:33 pm

Great - that is a very nice exposition.

For the beginners/younger students, I will just lay out the key assumptions/issues with Black Scholes. Noted the thread where some you were going deeper into the terminology and the math, which is also a good exercise, but really it's the breaks on assumptions that might be the Achille's Heel of BSM.

1) constant risk-free rate
2) constant volatility
3) frictionless trading (no transaction costs)
4) unlimited supply of assets; no short selling restrictions
5) no dividends
6) lognormal random walk 
7) European options only (e.g., no early exercise)
8) no arbitrage
9) no taxes

Naturally these are very well-known to the more experienced people here, but it is an astonishing array of caveats for those new to finance.

Personally, I'd be happy to envision a world without taxes, but a no-arb world doesn't seem like too much fun!
 
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Re: What are the typical assumptions for quant models for each asset class and what distortions do they produce?

November 1st, 2020, 4:21 pm

Why not make an online course for this, Alan?
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
 
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Alan
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Re: What are the typical assumptions for quant models for each asset class and what distortions do they produce?

November 3rd, 2020, 4:14 pm

Something to think about. But first have to finish my ERP book!
 
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Cuchulainn
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Re: What are the typical assumptions for quant models for each asset class and what distortions do they produce?

November 4th, 2020, 7:46 pm

Something to think about. But first have to finish my ERP book!
You could give the book free with the course! 
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
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