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Option pricing with Weyl-Titchmarsh theory

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  • Yishen Li
  • Jin Zhang

Abstract

In the Black-Merton-Scholes framework, the price of an underlying asset is assumed to follow a pure diffusion process. No-arbitrage theory shows that the price of an option contract written on the asset can be determined by solving a linear diffusion equation with variable coefficients. Applying the separating variable method, the problem of option pricing under state-dependent deterministic volatility can be transformed into a Schrodinger spectral problem, which has been well studied in quantum mechanics. With Weyl-Titchmarsh theory, we are able to determine the boundary condition and the nature of the eigenvalues and eigenfunctions. The solution can be written analytically in a Stieltjes integral. A few case studies demonstrate that a new analytical option pricing formula can be produced with our method.

Suggested Citation

  • Yishen Li & Jin Zhang, 2004. "Option pricing with Weyl-Titchmarsh theory," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 457-464.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:4:p:457-464
    DOI: 10.1080/14697680400008643
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    References listed on IDEAS

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    3. Rhys Andrews & Malcolm J. Beynon & Elif Genc, 2017. "Strategy Implementation Style and Public Service Effectiveness, Efficiency, and Equity," Administrative Sciences, MDPI, vol. 7(1), pages 1-19, February.

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