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arXiv · 2112.09534

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

Qi Chen·Chao Guo
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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.

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Qi Chen, Chao Guo. 2021-12-16. Path Integral Method for Proportional Step and Proportional Double-Barrier Step Option Pricing. https://arxiv.org/abs/2112.09534

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