Quant Theory, Better, Stronger and Faster

When people talk about how a new revolution in economics and finance is right around the corner, or already ongoing, I hear more of a wish than a promise. I heard it first when there was that article about how economics needs to ditch math that was beaten up by economists a few months ago, and I heard it in the Eichengreen piece. Finance is already incredibly statistical and empirical; one can’t even begin to approach the literature without a deep understanding of panel data and time series methods.

What I’d argue is that we need newer theory more than newer statistics. I’ll talk about the Efficient Market Hypothesis soon, but for now, how’s that theory looking from the quant side?

When I think of a stock, I think of this workhorse:

What’s a P/E ratio? Save that for the MBAs! There it is, a mean and a normal distributed volatility (the sigma in the second term). Glorious.

True story: Me and Ms. Rortybomb, an ethnomusicologist who, at last note, does not know the difference between a stock and a bond, were at a bookstore. On the math shelf was Applied Stochastic Control of Jump Diffusions. Bernt Øksendal is a superman – his book Stochastic Differential Equations is fantastic, a great high-end intro.

I pointed out to Ms. Rortybomb “this book may change the very idea of how we do quant work.” “Really? That would be great, given the financial crisis and all.” “I know. Check this bad boy out. This equation is how we used to do things [point to equation above]. In the future we may do it like this” and I point to these equations from the book:

“Haha. That’s funny. But seriously, where’s the new deal?”

Me, “why is that funny? That’s going to be intense. I fear the science is too tight for most quants, though those who can pull that off are going to be super-sweet.”

“No, but seriously, I thought everything was going to be different because of the crisis with finance and economics. I mean, isn’t it going to be less crazy math and equations and stuff?”

Me, “What do you mean not different? There are two additional integral signs we are talking about.”

“But isn’t there going to be more looking at the actual stuff and less leverage and betting and computers and stuff? I thought all this math was discredited.”

Me, “Discredited? Oh no, with those two additional integration signs I’m more comfortable taking on more leverage than ever before. Trust me, next time we are going to do it way better with these two additional integral signs.”

Her, getting sad, “Next time? Really? Next time – it’s not going to be any different?”

No. It’ll be the same, with just more math stuffed on top of the old math. Trust me, I’m going to integrate the hell out of your 401(k) with that second equation when I get the chance. If you are uncomfortable with that second equation as my whole approach, you may want to use this crisis as an opportunity to push for better regulation.

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7 Responses to Quant Theory, Better, Stronger and Faster

  1. Marco says:

    At first, thanks for your great blog. Nice to have an inside view into the industry. That I share most of your views just adds to that, of course..
    Well, as far as you’re concerned about the synthesis of theory and maths on an economic level, what does strike me first when I see a stock-price-model using a Lévy-process like that described in your post is: Where has the first fundamental theory of economics gone, “diminishing returns to scale”, usually taught at the very beginning of every economics course? As far as I see it, such models grow with a certain normally distributed rate of return “forever”.
    I’m not that deep into financial engineering nor differential equations, but wouldn’t that be the proper foundation of every model reflecting investment and returns? How come that this widely accepted economic theory doesn’t seem to be incorporated in financial models at all? Or put otherwise: What is the justification for diminishing returns being left aside?
    Not that I’m a skeptic as regards “endless growth”, but in economic growth theory many models deal with how to sustain such a positive rate of return. As to the fact that financial investments basically can only reflect investments into real capital, there should be a theoretical foundation of strictly positive returns in the long-run for stock-pricing-models, too. Is there any?

    Kind regards, Marco

  2. SBMA says:

    Whyyyyy.

    Go figure out how to create aluminum compounds from dirt and sea water instead. Its gonna be a bitch when we run out of aluminum.

  3. Jacob says:

    Haha, this was great. Actually, I’d love to hear your practitioner’s opinion on how you think returns should be modeled. Obviously they aren’t actually Gaussian, but is that a good enough simplifying assumption for pricing purposes? Do you buy the Levy distribution approach? What about Extreme Value Theory? t on 4 df? Cauchy?! Jump models, diffusion models, or both?

    Or are you more of a Nicholas Taleb”F it, I’m buying OTM puts and a shotgun” type?

  4. racerx says:

    ∫1/cabin ∂(cabin) = natural log cabin + c = house doesn’t float so it’s underwater.

  5. Terry Ivanauskas says:

    Following the reader SBMA, I think the world will be a very nice place to live when financial engineering becomes boring and engineers start to use their brains to develop more productive e clean technologies instead of trying to beat the market.

  6. Mike says:

    Macro,

    it’s been a while, but the returns are constant. The mu in the first half of the equation equals the expected return in the real world, the interest-rate in the risk-neutral space. The expected rate of the return is, if memory serves, (mu – dividend stream – sigma^2/2)*t.

    That the long term growth, in a risk-neutral space, should look like the interest rate forever, makes sense (if it was less, it would be bid down, more, up). That the dividend stream leaking out of it reducing the value is what MM/gordon growth model teaches us. In practice, we aren’t looking out at the infinite horizon though – more like 5 years.

    That the expected return on the stock isn’t included in BS (the stock price and the vol is instead) is one of those counter-intuitive concepts that always throws the newbies.

    Speaking of theory elegantly working within models that may not deal with the real world, how well does Returns to Scale actually work in real life? I know there’s a quasi-move to deal with a limit of the size of the market, but in grad school how much do people run with diminishing returns?

    racerx, hahaha.

  7. Andrew says:

    Actually, I’d like to hear more about Ms Rortybomb.

    It’s been nearly forty years since the original Black-Scholes-Merton formulation, so I guess it makes sense that new whizzy ways of describing price evolution of a financial asset come along.

    One of my favorite films is “Rob Roy,” with Liam Neesson, Jessica Lange, Tim Roth and John Hurt. In one scene, the elder villain Montrose (John Hurt) is looking at the other Cunningham (Tim Roth), who has stolen money lent to the hero (Liam Neesson):

    “There’s something here that I do not see. Killearn and you have some hand in matters that is hid from sight. This tells me that you are in cash, yet I know you are without means.”

    Montrose, to use the current idiom, cannot quite connect the dots. So it is sometimes in the futures we model: the elements are hidden in plain sight, but how they combine (subprime plus securitization plus CDO plus CDS plus bubble) defeats the chain of logic. And I’m not sure that a couple of extra integral signs in the end will help him, or us.

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