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High-resolution path-integral development of financial options

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Author Info

  • Ingber, Lester

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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File URL: http://www.sciencedirect.com/science/article/pii/S0378437100002296
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Bibliographic Info

Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 283 (2000)
Issue (Month): 3 ()
Pages: 529-558

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Handle: RePEc:eee:phsmap:v:283:y:2000:i:3:p:529-558

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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

Related research

Keywords: Options; Eurodollar; Volatility; Path integral; Optimization; Statistical mechanics;

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References

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  1. L. Ingber, 1995. "Path-integral evolution of multivariate systems with moderate noise," Lester Ingber Papers 95pe, Lester Ingber.
  2. 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.
  3. 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.
  4. L. Ingber & H. Fujio & M.F. Wehner, 1991. "Mathematical comparison of combat computer models to exercise data," Lester Ingber Papers 91mc, Lester Ingber.
  5. L. Ingber, 1993. "Adaptive Simulated Annealing (ASA)," Lester Ingber Software asa, Lester Ingber.
  6. 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.
  7. 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.
  8. L. Ingber, 1996. "Canonical momenta indicators of financial markets and neocortical EEG," Lester Ingber Papers 96cm, Lester Ingber.
  9. 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.
  10. L. Ingber, 1984. "Statistical mechanics of nonlinear nonequilibrium financial markets," Lester Ingber Papers 84nn, Lester Ingber.
  11. L. Ingber & J.K. Wilson, 2000. "Statistical mechanics of financial markets: Exponential modifications to Black-Scholes," Lester Ingber Papers 00fm, Lester Ingber.
  12. 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.
  13. L. Ingber, 1994. "Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory," Lester Ingber Papers 94ni, Lester Ingber.
  14. L. Ingber, 1989. "Very fast simulated re-annealing," Lester Ingber Papers 89vf, Lester Ingber.
  15. L. Ingber, 1998. "Data mining and knowledge discovery via statistical mechanics in nonlinear stochastic systems," Lester Ingber Papers 98dm, Lester Ingber.
  16. L. Ingber, 1993. "Simulated annealing: Practice versus theory," Lester Ingber Papers 93sa, Lester Ingber.
  17. L. Ingber & J.K. Wilson, 1999. "Volatility of volatility of financial markets," Lester Ingber Papers 99vv, Lester Ingber.
  18. 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.
  19. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-51.
  20. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  21. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  22. L. Ingber, 1998. "Some Applications of Statistical Mechanics of Financial Markets," Lester Ingber Papers 98sa, Lester Ingber.
  23. Jensen, Michael C., 1978. "Some anomalous evidence regarding market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 95-101.
  24. L. Ingber, 1996. "Adaptive simulated annealing (ASA): Lessons learned," Lester Ingber Papers 96as, Lester Ingber.
  25. L. Ingber, 1996. "Statistical mechanics of nonlinear nonequilibrium financial markets: Applications to optimized trading," Lester Ingber Papers 96nf, Lester Ingber.
  26. L. Ingber, 1999. "A simple options training model," Lester Ingber Papers 99so, Lester Ingber.
  27. Mandelbrot, Benoit B, 1971. "When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 225-36, August.
  28. 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.
  29. L. Ingber, 1986. "Statistical mechanics of neocortical interactions," Lester Ingber Papers 86ni, Lester Ingber.
  30. L. Ingber, 1990. "Statistical mechanical aids to calculating term structure models," Lester Ingber Papers 90ac, Lester Ingber.
  31. 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.
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Citations

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Cited by:
  1. 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.
  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, 2002. "Statistical mechanics of portfolios of options," Lester Ingber Papers 02po, Lester Ingber.
  4. L. Ingber & R.P. Mondescu, 2001. "Optimization of trading physics models of markets," Lester Ingber Papers 01ot, Lester Ingber.

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