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Black–Scholes like closed form formulas and numerical solutions for American style options

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  • Michael, Fredrick

Abstract

In this letter we show how a variation approach to a portfolio containing a European style option instrument when transformed to an American style instrument can lead to a Black–Scholes style PDE, a backwards partial differential equation, and a Black–Scholes like equality portfolio closed form solution for said American style derivative.

Suggested Citation

  • Michael, Fredrick, 2020. "Black–Scholes like closed form formulas and numerical solutions for American style options," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    • Handle: RePEc:eee:phsmap:v:550:y:2020:i:c:s0378437120301424
    DOI: 10.1016/j.physa.2020.124379
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    References listed on IDEAS

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    1. Zhongkai Liu & Tao Pang, 2016. "An efficient grid lattice algorithm for pricing American-style options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 36-55.
    2. Wallner, Christian & Wystup, Uwe, 2004. "Efficient computation of option price sensitivities for options of American style," CPQF Working Paper Series 1, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
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    Cited by:

    1. Zaevski, Tsvetelin S., 2022. "Pricing discounted American capped options," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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