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Penalty American Options

Author

Listed:
  • ZIWEI KE

    (School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia)

  • JOANNA GOARD

    (School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia)

Abstract

We present a new American-style option whereby on the event of exercise before expiry, the holder pays the writer a fee (which will be referred to as a ‘penalty’). The valuation of the option is not straightforward as it involves determining when it is optimal for the holder to exercise the option, leading to a free boundary problem. As most options in the traded markets have short maturities, accurate and fast valuations of such options are important. We derive analytic approximations for the value of the option with short times to expiry (up to 3 months) and its optimal exercise boundary. Some properties of the option, such as the put–call relationship, are explored as well. Numerical experiments suggest that our solutions both for the optimal exercise boundary and option value provide very accurate results.

Suggested Citation

  • Ziwei Ke & Joanna Goard, 2019. "Penalty American Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-32, March.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:02:n:s0219024919500018
    DOI: 10.1142/S0219024919500018
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    References listed on IDEAS

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