Risk Management: Foundations for a Changing Financial World

CHAPTER 46

MODELS^at

Emanuel Derman

This article analyzes the methodology of modeling in the physical sciences and in finance. Whereas hobbyists’ models aim for realistic resemblance to the object of the model, physics models aim for accurate divination. Financial models, the article argues, can at best aim to extrapolate or interpolate from the known prices of liquid securities to the unknown values of illiquid ones. Financial models are therefore best regarded as a collection of mathematically consistent, parallel “thought universes,” each of which will always be far too simple to resemble the real financial world, but whose exploration as a whole can nevertheless provide valuable insight.

MODEL AIRPLANES

When I was in grade school, we used to build model airplanes from kits. The frame was made of precut pieces of balsa wood, each having been carefully pinned, according to the plans, along a preprinted arc to obtain the appropriate curvature and then cemented, piece to piece, with airplane glue. The fuselage, made of tissue paper, was glued to the balsa frame, trimmed, dampened with water to shrink it taut, and, finally, when dry, lacquered and painted to make it stiff and realistic. The engine was just a long rubber band that ran the internal length of the fuselage, from propeller block at the nose to the tail, wound up by rotating the propeller many times and then let loose to unwind for a flight of perhaps 10 seconds at best. An especially ambitious model builder would ...