w4reading_2 - FINANCIAL ANALYSTS JOURNAL G l o ba l Fi n a...

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28 www.cfa pubs .org ©2009 CFA Institute FINANCIAL ANALYSTS JOURNAL Global Financial Crisis Models Emanuel Derman To confuse the model with the world is to embrace a future disaster driven by the belief that humans obey mathematical rules. 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 follow the instructions very carefully—sanding off, for example, any excess glue on the frame so as to leave no imperfections whatsoever. What was “model” about model airplanes? The Zippy model airplane that I remember building was smaller than a real Zippy (I assumed that an actual Zippy airplane existed somewhere in the world of real airplanes). It was lighter than a real airplane and made of different materials. But it did capture two essential features of the putatively real Zippy: appearance and flight. The model looked a lot like an airplane, and it could fly, if only briefly. Nevertheless, the model was not the thing itself. It was a model Zippy. It lacked seats, ailerons, and proper windows and doors, among many other real-life details. Which features are important depends on the model user. In my case, had I been three or four years old, crudely shaped wings, a body, and a throaty airplane engine noise might have satisfied me. When I was about 10 years old, appearance and flight sufficed. When I was a few years older, I would have wanted a combustion engine and radio control. But none of these model Zippys, however complex, would have been the real thing. What constrains the construction of a model Zippy? 1. The user and his or her needs: What aspects of the real airplane and its features is the user most interested in simulating, testing, or playing and tinkering with? An engineer needs a model different from that of a child. 2. Engineering and construction: How does one put together a reliable and effective model, with the key features as accurate as possible? 3. Science: Even though the Wright brothers probably did not know the partial differential equations of fluid flow, heavier-than-air flight was built on the science of mechanics and aerodynamics, Newton’s laws, and the Navier–Stokes equations.
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