IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v283y2000i3p529-558.html
   My bibliography  Save this article

High-resolution path-integral development of financial options

Author

Listed:
  • 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.

Suggested Citation

  • Ingber, Lester, 2000. "High-resolution path-integral development of financial options," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(3), pages 529-558.
    • Handle: RePEc:eee:phsmap:v:283:y:2000:i:3:p:529-558
    DOI: 10.1016/S0378-4371(00)00229-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437100002296
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(00)00229-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. L. Ingber, 1990. "Statistical mechanical aids to calculating term structure models," Lester Ingber Papers 90ac, Lester Ingber.
    2. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    3. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    4. 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.
    5. L. Ingber, 1995. "Path-integral evolution of multivariate systems with moderate noise," Lester Ingber Papers 95pe, Lester Ingber.
    6. 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.
    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. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
    9. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893, October.
    10. 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.
    11. 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.
    12. 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.
    13. L. Ingber, 1984. "Statistical mechanics of nonlinear nonequilibrium financial markets," Lester Ingber Papers 84nn, Lester Ingber.
    14. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    15. L. Ingber, 1993. "Adaptive Simulated Annealing (ASA)," Lester Ingber Software asa, Lester Ingber.
    16. L. Ingber, 1986. "Statistical mechanics of neocortical interactions," Lester Ingber Papers 86ni, Lester Ingber.
    17. L. Ingber, 1999. "A simple options training model," Lester Ingber Papers 99so, Lester Ingber.
    18. L. Ingber, 1996. "Canonical momenta indicators of financial markets and neocortical EEG," Lester Ingber Papers 96cm, Lester Ingber.
    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. L. Ingber & H. Fujio & M.F. Wehner, 1991. "Mathematical comparison of combat computer models to exercise data," Lester Ingber Papers 91mc, Lester Ingber.
    22. L. Ingber, 1996. "Adaptive simulated annealing (ASA): Lessons learned," Lester Ingber Papers 96as, Lester Ingber.
    23. 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(1), pages 37-61, March.
    24. L. Ingber, 1991. "Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography," Lester Ingber Papers 91ni, Lester Ingber.
    25. Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach to Derivative Security Pricing: I. Formalism and Analytical Results," Papers cond-mat/9901277, arXiv.org.
    26. L. Ingber, 1993. "Simulated annealing: Practice versus theory," Lester Ingber Papers 93sa, Lester Ingber.
    27. L. Ingber, 1994. "Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory," Lester Ingber Papers 94ni, Lester Ingber.
    28. L. Ingber, 1998. "Some Applications of Statistical Mechanics of Financial Markets," Lester Ingber Papers 98sa, Lester Ingber.
    29. Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach to Derivative Security Pricing: II. Numerical Methods," Papers cond-mat/9901279, arXiv.org.
    30. 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.
    31. Jensen, Michael C., 1978. "Some anomalous evidence regarding market efficiency," Journal of Financial Economics, Elsevier, vol. 6(2-3), pages 95-101.
    32. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
    33. L. Ingber & J.K. Wilson, 2000. "Statistical mechanics of financial markets: Exponential modifications to Black-Scholes," Lester Ingber Papers 00fm, Lester Ingber.
    34. L. Ingber, 1989. "Very fast simulated re-annealing," Lester Ingber Papers 89vf, Lester Ingber.
    35. 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.
    36. L. Ingber, 1996. "Statistical mechanics of nonlinear nonequilibrium financial markets: Applications to optimized trading," Lester Ingber Papers 96nf, Lester Ingber.
    37. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. L. Ingber, 2018. "Quantum path integral for financial options," Lester Ingber Papers 18qp, Lester Ingber.
    2. L. Ingber, 2018. "Quantum Variables in Finance and Neuroscience," Lester Ingber Papers 18qv, Lester Ingber.
    3. L. Ingber, 2017. "Quantum Path-Integral qPATHINT Algorithm," Lester Ingber Papers 17qa, Lester Ingber.
    4. He, Xin-Jiang & Zhu, Song-Ping, 2017. "How should a local regime-switching model be calibrated?," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 149-163.
    5. Lester Ingber & Radu Paul Mondescu, 2000. "Optimization of Trading Physics Models of Markets," Papers physics/0007075, arXiv.org.
    6. Lester Ingber, 2020. "Developing Bid-Ask Probabilities for High-Frequency Trading," Virtual Economics, The London Academy of Science and Business, vol. 3(2), pages 7-24, April.
    7. Roger Knecktys & Henrik Bette & Rudiger Kiesel & Thomas Guhr, 2022. "Risk Theory and Pricing of "Pay-for-Performance" Business Models," Papers 2212.09585, arXiv.org.
    8. L. Ingber, 2015. "Synergy among multiple scales of neocortical interactions," Lester Ingber Papers 15sc, Lester Ingber.
    9. L. Ingber, 2016. "Path-integral quantum PATHTREE and PATHINT algorithms," Lester Ingber Papers 16pi, Lester Ingber.
    10. Zura Kakushadze, 2015. "Path integral and asset pricing," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1759-1771, November.
    11. L. Ingber, 2017. "Options on quantum money: Quantum path-integral with serial shocks," Lester Ingber Papers 17oq, Lester Ingber.
    12. L. Ingber, 2018. "Quantum calcium-ion interactions with EEG," Lester Ingber Papers 18qc, Lester Ingber.
    13. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    14. Marco Rosa-Clot & Stefano Taddei, 2002. "A Path Integral Approach To Derivative Security Pricing Ii: Numerical Methods," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 123-146.
    15. L. Ingber, 2019. "Quantum-Classical interactions: calcium ions and synchronous neural firings," Lester Ingber Papers 19qc, Lester Ingber.
    16. Victor Lebreton, 2007. "Le trading algorithmique," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00332823, HAL.
    17. 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.
    18. L. Ingber, 2020. "Forecasting with importance-sampling and path-integrals: Applications to COVID-19," Lester Ingber Papers 20fi, Lester Ingber.
    19. L. Ingber & R.P. Mondescu, 2003. "Automated internet trading based on optimized physics models of markets," Lester Ingber Papers 03ai, Lester Ingber.
    20. repec:lei:ingber:14cm is not listed on IDEAS
    21. L. Ingber, 2002. "Statistical mechanics of portfolios of options," Lester Ingber Papers 02po, Lester Ingber.
    22. L. Ingber, 2017. "Evolution of regenerative Ca-ion wave-packet in neuronal-firing fields: Quantum path-integral with serial shocks," Lester Ingber Papers 17qp, Lester Ingber.
    23. L. Ingber, 2021. "Hybrid classical-quantum computing: Applications to statistical mechanics of financial markets," Lester Ingber Papers 21cq, Lester Ingber.
    24. L. Ingber, 2020. "Revisiting Our Quantum World," Lester Ingber Papers 20rq, Lester Ingber.
    25. L. Ingber, 2021. "Hybrid classical-quantum computing: Applications to statistical mechanics of neocortical interactions," Lester Ingber Papers 21hc, Lester Ingber.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. L. Ingber & J.K. Wilson, 2000. "Statistical mechanics of financial markets: Exponential modifications to Black-Scholes," Lester Ingber Papers 00fm, Lester Ingber.
    2. Lester Ingber & Radu Paul Mondescu, 2000. "Optimization of Trading Physics Models of Markets," Papers physics/0007075, arXiv.org.
    3. L. Ingber & R.P. Mondescu, 2003. "Automated internet trading based on optimized physics models of markets," Lester Ingber Papers 03ai, Lester Ingber.
    4. L. Ingber, 1996. "Canonical momenta indicators of financial markets and neocortical EEG," Lester Ingber Papers 96cm, Lester Ingber.
    5. Lester Ingber, 2020. "Developing Bid-Ask Probabilities for High-Frequency Trading," Virtual Economics, The London Academy of Science and Business, vol. 3(2), pages 7-24, April.
    6. L. Ingber, 2020. "Forecasting with importance-sampling and path-integrals: Applications to COVID-19," Lester Ingber Papers 20fi, Lester Ingber.
    7. L. Ingber & J.K. Wilson, 1999. "Volatility of volatility of financial markets," Lester Ingber Papers 99vv, Lester Ingber.
    8. M. Bowman & L. Ingber, 1997. "Canonical momenta of nonlinear combat," Lester Ingber Papers 97cm, Lester Ingber.
    9. L. Ingber, 2002. "Statistical mechanics of portfolios of options," Lester Ingber Papers 02po, Lester Ingber.
    10. L. Ingber, 1993. "ASA-README included with ASA code," Lester Ingber Papers 93as, Lester Ingber.
    11. L. Ingber, 2018. "Quantum path integral for financial options," Lester Ingber Papers 18qp, Lester Ingber.
    12. L. Ingber, 2018. "Quantum Variables in Finance and Neuroscience," Lester Ingber Papers 18qv, Lester Ingber.
    13. L. Ingber, 2018. "Quantum calcium-ion interactions with EEG," Lester Ingber Papers 18qc, Lester Ingber.
    14. L. Ingber, 1998. "Some Applications of Statistical Mechanics of Financial Markets," Lester Ingber Papers 98sa, Lester Ingber.
    15. L. Ingber, 2021. "Hybrid classical-quantum computing: Applications to statistical mechanics of neocortical interactions," Lester Ingber Papers 21hc, Lester Ingber.
    16. L. Ingber, 2022. "Quantum Variables in Finance," Lester Ingber Papers 22qv, Lester Ingber.
    17. 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.
    18. L. Ingber, 2017. "Quantum Path-Integral qPATHINT Algorithm," Lester Ingber Papers 17qa, Lester Ingber.
    19. 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.
    20. L. Ingber, 2021. "Hybrid classical-quantum computing: Applications to statistical mechanics of financial markets," Lester Ingber Papers 21cq, Lester Ingber.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:283:y:2000:i:3:p:529-558. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.