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High-resolution path-integral development of financial options

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  • 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
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    as
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    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. Roger Knecktys & Henrik Bette & Rudiger Kiesel & Thomas Guhr, 2022. "Risk Theory and Pricing of "Pay-for-Performance" Business Models," Papers 2212.09585, arXiv.org.
    7. L. Ingber, 2015. "Synergy among multiple scales of neocortical interactions," Lester Ingber Papers 15sc, Lester Ingber.
    8. L. Ingber, 2016. "Path-integral quantum PATHTREE and PATHINT algorithms," Lester Ingber Papers 16pi, Lester Ingber.
    9. L. Ingber, 2017. "Options on quantum money: Quantum path-integral with serial shocks," Lester Ingber Papers 17oq, Lester Ingber.
    10. L. Ingber, 2018. "Quantum calcium-ion interactions with EEG," Lester Ingber Papers 18qc, Lester Ingber.
    11. 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.
    12. L. Ingber, 2019. "Quantum-Classical interactions: calcium ions and synchronous neural firings," Lester Ingber Papers 19qc, Lester Ingber.
    13. 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.
    14. L. Ingber, 2020. "Forecasting with importance-sampling and path-integrals: Applications to COVID-19," Lester Ingber Papers 20fi, Lester Ingber.
    15. Victor Lebreton, 2007. "Le trading algorithmique," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00332823, HAL.
    16. L. Ingber, 2002. "Statistical mechanics of portfolios of options," Lester Ingber Papers 02po, Lester Ingber.
    17. 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.
    18. L. Ingber, 2020. "Revisiting Our Quantum World," Lester Ingber Papers 20rq, Lester Ingber.
    19. Zura Kakushadze, 2015. "Path integral and asset pricing," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1759-1771, November.
    20. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    21. L. Ingber & R.P. Mondescu, 2003. "Automated internet trading based on optimized physics models of markets," Lester Ingber Papers 03ai, Lester Ingber.
    22. repec:lei:ingber:14cm is not listed on IDEAS
    23. 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.
    24. L. Ingber, 2021. "Hybrid classical-quantum computing: Applications to statistical mechanics of financial markets," Lester Ingber Papers 21cq, Lester Ingber.
    25. L. Ingber, 2021. "Hybrid classical-quantum computing: Applications to statistical mechanics of neocortical interactions," Lester Ingber Papers 21hc, Lester Ingber.

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    2. Lester Ingber & Radu Paul Mondescu, 2000. "Optimization of Trading Physics Models of Markets," Papers physics/0007075, arXiv.org.
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    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.

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