Paper: ... Exponential Modifications to Black-Scholes

[Lester Ingber]

The PostScript paper http://www.ingber.com/markets99_exp.ps.Z also can
be retrieved uncompressed for awhile as
http://www.alumni.caltech.edu/~ingber/markets99_exp.ps

          %A L. Ingber
          %A J.K. Wilson
          %R Statistical Mechanics of Financial Markets:
             Exponential Modifications to Black-Scholes
          %I DRW Investments LLC
          %C Chicago, IL
          %D 1999
          %O URL http://www.ingber.com/markets99_exp.ps.Z
                 http://www.alumni.caltech.edu/~ingber/markets99_exp.ps

	The Black-Scholes theory of option pricing has been considered
	for many years as an important but very approximate
	zeroth-order description of actual market behavior.  We
	generalize the functional form of the diffusion of these
	systems and also consider multi-factor models including
	stochastic volatility.  We use a previous development of a
	statistical mechanics of financial markets to model these
	issues.  Daily Eurodollar futures prices and implied
	volatilities are fit to determine exponents of functional
	behavior of diffusions using methods of  global optimization,
	Adaptive Simulated Annealing (ASA), to generate tight fits
	across moving time windows of Eurodollar contracts.  These
	short-time fitted distributions are then developed into
	long-time distributions using a robust non-Monte Carlo
	path-integral algorithm, PATHINT, to generate prices and
	derivatives commonly used by option traders.  The results of
	our study show that there is only a very small change in at-the
	money option prices for different probability distributions,
	both for the one-factor and two-factor models.  There still are
	significant differences in risk parameters, partial
	derivatives, using more sophisticated models, especially for
	out-of-the-money options.

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