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Path Integral Method for Proportional Step and Proportional Double-Barrier Step Option Pricing

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  • Qi Chen
  • Chao Guo

Abstract

Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional step options, the option price changing process is similar to the one dimensional trapezoid potential barrier scattering problem in quantum mechanics; for double-barrier step options, the option price changing process is analogous to a particle moving in a finite symmetric square potential well. Using path integral method, the analytical expressions of pricing kernel and option price could be derived. Numerical results of option price as a function of underlying price, potential and exercise price are shown, which are consistent with the results given by mathematical method.

Suggested Citation

  • Qi Chen & Chao Guo, 2021. "Path Integral Method for Proportional Step and Proportional Double-Barrier Step Option Pricing," Papers 2112.09534, arXiv.org, revised Jun 2022.
    • Handle: RePEc:arx:papers:2112.09534
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    File URL: http://arxiv.org/pdf/2112.09534
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