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Analytical pricing of American options

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Abstract

By using the homotopy analysis method, we derive a new explicit approximate formula for the optimal exercise boundary of American options on an underlying asset with dividend yields. Compared with highly accurate numerical values, the new formula is shown to be valid for up to 2 years of time to maturity, which is ten times longer than existing explicit approximate formulas. The option price errors computed with our formula are within a few cents for American options that have moneyness (the ratio between stock and strike prices) from 0.8 to 1.2, strike prices of 100 dollars and 2 years to maturity.

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Authors and Affiliations

  1. Postdoctoral Research Station, Research Center, Shanghai Stock Exchange, Shanghai, 200120, China

    Jun Cheng

  2. School of Management and Engineering, Nanjing University, Nanjing, 210093, China

    Jun Cheng

  3. School of Economics and Finance, The University of Hong Kong, Pokfulam Road, Hong Kong, China

    Jin E. Zhang

  4. Department of Accountancy and Finance, School of Business, University of Otago, Dunedin, 9054, New Zealand

    Jin E. Zhang

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  1. Jun Cheng
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  2. Jin E. Zhang
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Correspondence to Jin E. Zhang.

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Cheng, J., Zhang, J.E. Analytical pricing of American options. Rev Deriv Res 15, 157–192 (2012). https://doi.org/10.1007/s11147-011-9073-6

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  • DOI: https://doi.org/10.1007/s11147-011-9073-6

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