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Exercise Boundary of the American Put Near Maturity in an Exponential L\'evy Model

Author

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  • Damien Lamberton
  • Mohammed Mikou

Abstract

We study the behavior of the critical price of an American put option near maturity in the exponential L\'evy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit of the critical price is equal to the stock price, the rate of convergence to the limit is linear if and only if the underlying L\'evy process has finite variation. In the case of infinite variation, a variety of rates of convergence can be observed: we prove that, when the negative part of the L\'evy measure exhibits an $\alpha$-stable density near the origin, with $1

Suggested Citation

  • Damien Lamberton & Mohammed Mikou, 2011. "Exercise Boundary of the American Put Near Maturity in an Exponential L\'evy Model," Papers 1105.0284, arXiv.org.
    • Handle: RePEc:arx:papers:1105.0284
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    2. Baurdoux, Erik J. & Pedraza, José M., 2023. "Predicting the last zero before an exponential time of a spectrally negative Lévy process," LSE Research Online Documents on Economics 119290, London School of Economics and Political Science, LSE Library.
    3. Florian Kleinert & Kees van Schaik, 2013. "A variation of the Canadisation algorithm for the pricing of American options driven by L\'evy processes," Papers 1304.4534, arXiv.org.
    4. Baurdoux, Erik J. & Pedraza, José M., 2024. "Lp optimal prediction of the last zero of a spectrally negative Lévy process," LSE Research Online Documents on Economics 119468, London School of Economics and Political Science, LSE Library.
    5. Kleinert, Florian & van Schaik, Kees, 2015. "A variation of the Canadisation algorithm for the pricing of American options driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3234-3254.

    More about this item

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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