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High-resolution path-integral development of financial options

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  • L. Ingber

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Abstract

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. 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.

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Bibliographic Info

Paper provided by Lester Ingber in its series Lester Ingber Papers with number 00hr.

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Date of creation: 2000
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Handle: RePEc:lei:ingber:00hr

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References

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  1. L. Ingber & H. Fujio & M.F. Wehner, 1991. "Mathematical comparison of combat computer models to exercise data," Lester Ingber Papers 91mc, Lester Ingber.
  2. L. Ingber, 1993. "Adaptive Simulated Annealing (ASA)," Lester Ingber Software asa, Lester Ingber.
  3. L. Ingber & J.K. Wilson, 2000. "Statistical mechanics of financial markets: Exponential modifications to Black-Scholes," Lester Ingber Papers 00fm, Lester Ingber.
  4. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
  5. Jens Carsten Jackwerth, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance 9803002, EconWPA.
  6. L. Ingber, 1996. "Statistical mechanics of nonlinear nonequilibrium financial markets: Applications to optimized trading," Lester Ingber Papers 96nf, Lester Ingber.
  7. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-47.
  8. L. Ingber, 1990. "Statistical mechanical aids to calculating term structure models," Lester Ingber Papers 90ac, Lester Ingber.
  9. L. Ingber, 1999. "A simple options training model," Lester Ingber Papers 99so, Lester Ingber.
  10. L. Ingber, 1996. "Canonical momenta indicators of financial markets and neocortical EEG," Lester Ingber Papers 96cm, Lester Ingber.
  11. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  12. L. Ingber, 1994. "Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory," Lester Ingber Papers 94ni, Lester Ingber.
  13. Jensen, Michael C., 1978. "Some anomalous evidence regarding market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 95-101.
  14. L. Ingber & R. Srinivasan & P.L. Nunez, 1996. "Path-integral evolution of chaos embedded in noise: Duffing neocortical analog," Lester Ingber Papers 96pi, Lester Ingber.
  15. L. Ingber & M.F. Wehner & G.M. Jabbour & T.M. Barnhill, 1991. "Application of statistical mechanics methodology to term-structure bond-pricing models," Lester Ingber Papers 91as, Lester Ingber.
  16. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  17. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  18. Taylor, Stephen J., 1982. "Tests of the Random Walk Hypothesis Against a Price-Trend Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(01), pages 37-61, March.
  19. L. Ingber & P.L. Nunez, 1995. "Statistical mechanics of neocortical interactions: High resolution path-integral calculation of short-term memory," Lester Ingber Papers 95ni, Lester Ingber.
  20. L. Ingber, 1986. "Statistical mechanics of neocortical interactions," Lester Ingber Papers 86ni, Lester Ingber.
  21. L. Ingber, 1998. "Some Applications of Statistical Mechanics of Financial Markets," Lester Ingber Papers 98sa, Lester Ingber.
  22. Brown, Philip & Kleidon, Allan W. & Marsh, Terry A., 1983. "New evidence on the nature of size-related anomalies in stock prices," Journal of Financial Economics, Elsevier, vol. 12(1), pages 33-56, June.
  23. L. Ingber, 1989. "Very fast simulated re-annealing," Lester Ingber Papers 89vf, Lester Ingber.
  24. L. Ingber, 1998. "Data mining and knowledge discovery via statistical mechanics in nonlinear stochastic systems," Lester Ingber Papers 98dm, Lester Ingber.
  25. L. Ingber, 1984. "Statistical mechanics of nonlinear nonequilibrium financial markets," Lester Ingber Papers 84nn, Lester Ingber.
  26. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
  27. L. Ingber & J.K. Wilson, 1999. "Volatility of volatility of financial markets," Lester Ingber Papers 99vv, Lester Ingber.
  28. L. Ingber, 1993. "Simulated annealing: Practice versus theory," Lester Ingber Papers 93sa, Lester Ingber.
  29. L. Ingber, 1996. "Adaptive simulated annealing (ASA): Lessons learned," Lester Ingber Papers 96as, Lester Ingber.
  30. L. Ingber, 1995. "Path-integral evolution of multivariate systems with moderate noise," Lester Ingber Papers 95pe, Lester Ingber.
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Citations

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Cited by:
  1. L. Ingber, 2002. "Statistical mechanics of portfolios of options," Lester Ingber Papers 02po, Lester Ingber.
  2. L. Ingber & R.P. Mondescu, 2003. "Automated internet trading based on optimized physics models of markets," Lester Ingber Papers 03ai, Lester Ingber.
  3. L. Ingber & C. Chen & R.P. Mondescu & D. Muzzall & M. Renedo, 2001. "Probability tree algorithm for general diffusion processes," Lester Ingber Papers 01pt, Lester Ingber.
  4. Lester Ingber & Radu Paul Mondescu, 2000. "Optimization of Trading Physics Models of Markets," Papers physics/0007075, arXiv.org.

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