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Asian Strike Options of American Type and Game Type

In: Stochastic Processes And Applications To Mathematical Finance

Author

Listed:
  • Masaya Ishihara

    (Nanzan University, Seto, 464-0062, Japan)

  • Hiroshi Kunita

    (Nanzan University, Seto, 464-0062, Japan)

Abstract

We study Asian strike put options of Europian, American and game type. After changing the variable, we show that the study of these Asian strike options is reduced to the study of Europian, American and game type options for a one dimensional nonstationary Brownian motion (diffusion process) yt with a suitable pay-off function. We get the exercise region of the holder for the American type option and the exercise regions of the holder and the writer for the game type option. Then we study the early exercise premium for the American type option and the early exercise premium of the holder and the early cancellation fee of the writer for the game type option.For the study of the early cancellation fee of the writer, we need an extension of Itô's formula, which involves the local time of the price process yt. We establish the generalized Itô's formula in Appendix.

Suggested Citation

  • Masaya Ishihara & Hiroshi Kunita, 2007. "Asian Strike Options of American Type and Game Type," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 10, pages 173-191, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812770448_0010
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    Cited by:

    1. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.

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