Home
http://www.faz.net/-hlc-7ew4c
HERAUSGEGEBEN VON WERNER D'INKA, JÜRGEN KAUBE, BERTHOLD KOHLER, HOLGER STELTZNER

F.A.Z.-Column by Emanuel Derman The Sublime to the Ridiculous

How do you manage to develop new financial models or discover exciting mathematical theories? The surprisingly easy advice: Just be reliable.

© AP Vergrößern

Once, twenty years ago, a colleague and I had what seemed like a good idea for a financial model. We wanted to CAT-scan the DAX options market to see what it thought about the future. I am speaking metaphorically, of course.

When technicians do a real CAT scan of your abdomen, they shoot X-rays from all angles through you and collect the scattered rays. From the way the X-rays scatter off your insides, they can reconstruct the interior of your body. How does that apply to the DAX?

The Value of a DAX option

Many investors and speculators buy options on the DAX, betting that it will rise above some higher level or fall below some lower one. The value of the DAX, the Deutsche Bourse German stock index, fluctuates every day, and the magnitude of those fluctuations is called the DAX’s volatility. Since your chance of winning a bet on the DAX is better if the fluctuations are larger, the value of a DAX option depends on the stock’s imagined future volatility. My colleague and I thought of a method to deduce other people’s idea of future DAX volatility by looking at the prices of all options on the DAX (i.e. shooting X-rays from all angles) and backing out from them what people thought its volatility (its interior) would be.

This is how most financial models work. In physics, models predict the future, moving forward in time.  In finance, models extract the future as imagined by other people from the prices that other people are willing to pay for securities today. Having extracted other people’s imaginings and examined them, then, if you think they are wrong, you can bet against them by buying or selling things that will profit if they do turn out to be wrong.

Riding home on the subway that day twenty years ago with a friend, I briefly told him what we conjectured and how we had proved it. My friend was very smart and quick. After listening to me, he snorted. „That’s impossible,“ he exclaimed.  Then, a minute or so later:  „No, you’re right. It’s obvious. Actually, it’s totally trivial!“

Nothing is Really Obvious

The past obviousness of anything you never knew is a delusion. Many things seem clear only once they have been taught to you, once all the prejudices, confusion and competing theories have been omitted. Every iota of discovery comes at the cost of long immersion, hard labor, and struggle. I learned this most dramatically in physics graduate school many years ago, when Prof.  Friedberg, a slightly spacy and disheveled but very clever man, taught us Einstein’s 1905 theory of  relativity.

Prior to Einstein, there were two sets of laws that governed the universe as seen by an observer on earth: For matter, Newton’s 17th Century laws described the motion of particles. For light, Maxwell’s 19th Century laws described the oscillations of waves.

What Einstein Discovered

Einstein postulated that all laws must be universal. The same laws that work on earth must work everywhere, for everyone; they must look exactly the same, even if the person using them is moving and not stationary on our earth. But Einstein noticed a contradiction in the region where Newton and Maxwell overlapped, when light and matter interacted with each other. If Newton’s laws of matter were universal, then Maxwell’s laws for light could not be. And vice versa.

To make an inaccurate analogy: imagine that women habitually walk fast and men always stroll. When they form a couple and take a walk, one of them has to change. Einstein realized that Newton’s laws had to change in order to keep things universal. The result was that though the laws were universal, space and time became relative.

1 | 2 Nächste Seite   |  Artikel auf einer Seite
 
 ()
   Permalink
 
 
 

Hier können Sie die Rechte an diesem Artikel erwerben

Weitere Empfehlungen
Allgemeine Relativitätstheorie Ein Pulsar taucht ab

Die Krümmung des Raums zeigt bei einem schnell rotierenden Neutronenstern einen seltsamen Effekt. Durch die starke Gravitationskraft wird der Pulsar eine Zeitlang für die Beobachtung unsichtbar. Mehr Von Jan Hattenbach

25.01.2015, 16:07 Uhr | Wissen
CD der Woche: Zoot Woman Eine Band macht ernst

Popmusik als das Versprechen, ein anderer Mensch sein zu können, ohne es werden zu müssen: Zoot Woman sind zurück und haben mit Things Are What They Used To Be ein dunkles, unruhiges, intelligentes Album vorgelegt. Mehr

16.10.2014, 12:05 Uhr | Feuilleton
Heute in der Zeitung Psychosen sind des Teufels

Über schrumpfende Gehirne durch Antipsychotika, Einsteins Wirkung im All, raffinierte Ameisenfänger mit Kannenfallen und Handprothesen mit Fingerspitzengefühl berichten wir diesmal in unserer Beilage Natur und Wissenschaft. Mehr

20.01.2015, 23:28 Uhr | Wissen
Tom Petty Hypnotic Eye

Hörprobe: Shadow People Mehr

13.08.2014, 17:00 Uhr | Feuilleton
Album der Woche Und diese Rotzlöffelinnen nennen es Liebe

So lautstark, wie es sich nach zehn Jahren Abstinenz gehört: Die Pop-Frauen von Sleater-Kinney verbinden auf ihrer neuen Platte No Cities To Love Sozialrealismus mit Majestätskrach. Mehr Von Thorsten Gräbe

19.01.2015, 18:08 Uhr | Feuilleton
   Permalink
 Permalink

Veröffentlicht: 08.08.2013, 12:16 Uhr

Narrenfeigheit

Von Ursula Scheer

Eigentlich spielt Satire im Kölner Karneval eine zentrale Rolle. Eigentlich wollten die Jecken für Charlie Hebdo ein Zeichen setzen. Doch jetzt fährt die Angst mit. Mehr 21 54