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Path Integral

  • Sun-Chong Wang
Chapter
  • 852 Downloads
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 743)

Abstract

Feynman’s method of path integration offers an alternative to the conventional solutions to the Schrodinger’s equation. Path integrals provide not only a new computational approach to quantum mechanics, but also a different conceptual perspective of view. The advantage of path integral manifests itself particularly when the number of particles (or number of degrees of freedom) of the many-body system increases. Furthermore, the formalism derived for the dynamics of a system can, after slight modification, be applied to calculate interesting quantities of systems in thermodynamic equilibrium.

Keywords

Stock Price Option Price Importance Sampling Strike Price Path Integral Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Feynman’s path integral method was best introduced in the following treatises, R.P. Feynman and A.R. Hibbs, “Quantum Mechanics and Path Integrals”, McGraw-Hill, New York (1965)zbMATHGoogle Scholar
  2. L.S. Schulman, “Techniques and Applications of Path Integration”, John Wiley & Sons, Inc., New York (1981)zbMATHGoogle Scholar
  3. The Black-Scholes equation was presented in, F. Black and M. J. Scholes, “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy, 81 (1973) 637–659CrossRefGoogle Scholar
  4. A more general path-integral formula for options pricing with variable volatility was derived in, B.E. Baaquie, “A Path Integral Approach to Option Pricing with Stochastic Volatility: Some Exact Results”, J. de Phys. I (France), 7 (1997) 1733–1753, available at xxx.lanl.gov/cond-mat/9708178 22 Aug 1997CrossRefGoogle Scholar
  5. A path integral Monte Carlo evaluation of options prices can be found in, M.S. Makivic, “Numerical Pricing of Derivative Claims: Path Integral Monte Carlo Approach”, NPAC Technical Report SCCS 650, Syracuse University, 1994Google Scholar
  6. Metropolis-Hastings algorithm was shown in, W.K. Hastings, “Monte Carlo sampling methods using Markov chains and their applications”, Biometrika, 57 (1970) 97–109zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Sun-Chong Wang
    • 1
  1. 1.TRIUMFCanada

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