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The Peculiar Logic of the Black-Scholes FormulaI will discuss the interplay between assumptions and applications in the context of the Black-Scholes option model. In standard treatments, the Black-Scholes formula is derived from certain assumptions concerning the statistical properties of returns. These assumptions are known to be false for realistic assets. But the striking fact is that, by working backwards from market data using the Black-Scholes formula, one can get a precise measure of the particular ways in which the market believes the assumptions to be unrealistic at any given moment – and thus to extract an unexpected kind of information about market expectations.
Logic and Philosophy of Science
University of California, Irvine