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High-resolution path-integral development of financial options

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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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  • L. Ingber, 2000. "High-resolution path-integral development of financial options," Lester Ingber Papers 00hr, Lester Ingber.
  • Handle: RePEc:lei:ingber:00hr
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    1. L. Ingber, 1985. "Statistical mechanics of neocortical interactions: Stability and duration of the 7+-2 rule of short-term-memory capacity," Lester Ingber Papers 85st, Lester Ingber.
    2. L. Ingber, 1984. "Statistical mechanics of nonlinear nonequilibrium financial markets," Lester Ingber Papers 84nn, Lester Ingber.
    3. L. Ingber, 1996. "Canonical momenta indicators of financial markets and neocortical EEG," Lester Ingber Papers 96cm, Lester Ingber.
    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, 1998. "Some Applications of Statistical Mechanics of Financial Markets," Lester Ingber Papers 98sa, Lester Ingber.
    6. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
    7. L. Ingber & J.K. Wilson, 2000. "Statistical mechanics of financial markets: Exponential modifications to Black-Scholes," Lester Ingber Papers 00fm, Lester Ingber.
    8. 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.
    9. L. Ingber, 1994. "Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory," Lester Ingber Papers 94ni, Lester Ingber.
    10. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
    11. L. Ingber, 1996. "Statistical mechanics of nonlinear nonequilibrium financial markets: Applications to optimized trading," Lester Ingber Papers 96nf, Lester Ingber.
    12. 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.
    13. L. Ingber, 1990. "Statistical mechanical aids to calculating term structure models," Lester Ingber Papers 90ac, Lester Ingber.
    14. 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 113-147.
    15. 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.
    16. L. Ingber, 1995. "Path-integral evolution of multivariate systems with moderate noise," Lester Ingber Papers 95pe, Lester Ingber.
    17. 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 225-236, August.
    18. 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 433-451.
    19. L. Ingber, 1998. "Data mining and knowledge discovery via statistical mechanics in nonlinear stochastic systems," Lester Ingber Papers 98dm, Lester Ingber.
    20. L. Ingber & J.K. Wilson, 1999. "Volatility of volatility of financial markets," Lester Ingber Papers 99vv, Lester Ingber.
    21. 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.
    22. L. Ingber, 1993. "Simulated annealing: Practice versus theory," Lester Ingber Papers 93sa, 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, 1989. "Very fast simulated re-annealing," Lester Ingber Papers 89vf, Lester Ingber.
    25. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    26. 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.
    27. 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.
    28. L. Ingber, 1993. "Adaptive Simulated Annealing (ASA)," Lester Ingber Software asa, Lester Ingber.
    29. L. Ingber, 1986. "Statistical mechanics of neocortical interactions," Lester Ingber Papers 86ni, Lester Ingber.
    30. L. Ingber, 1999. "A simple options training model," Lester Ingber Papers 99so, Lester Ingber.
    31. L. Ingber, 1996. "Adaptive simulated annealing (ASA): Lessons learned," Lester Ingber Papers 96as, Lester Ingber.
    32. L. Ingber, 1991. "Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography," Lester Ingber Papers 91ni, Lester Ingber.
    33. 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.
    34. 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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    Cited by:

    1. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    2. Victor Lebreton, 2007. "Le trading algorithmique," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00332823, HAL.
    3. L. Ingber, 2017. "Quantum Path-Integral qPATHINT Algorithm," Lester Ingber Papers 17qa, Lester Ingber.
    4. repec:eee:dyncon:v:78:y:2017:i:c:p:149-163 is not listed on IDEAS
    5. Lester Ingber & Radu Paul Mondescu, 2000. "Optimization of Trading Physics Models of Markets," Papers physics/0007075, arXiv.org.
    6. 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.
    7. L. Ingber & R.P. Mondescu, 2003. "Automated internet trading based on optimized physics models of markets," Lester Ingber Papers 03ai, Lester Ingber.
    8. L. Ingber, 2002. "Statistical mechanics of portfolios of options," Lester Ingber Papers 02po, Lester Ingber.

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