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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. 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).
    2. 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.
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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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