Asian Strike Options of American Type and Game Type

Masaya Ishihara and Hiroshi Kunita
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Masaya Ishihara: Nanzan University, Seto, 464-0062, Japan
Hiroshi Kunita: Nanzan University, Seto, 464-0062, Japan

Chapter 10 in Stochastic Processes and Applications to Mathematical Finance, 2007, pp 173-191 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe 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.

Keywords: Stochastic Calculus; Mathematical Finance; Insider Trading; Stochastic Control; Real Options; Filtering Model of Credit Risks; Stochastic Growth Models (search for similar items in EconPapers)
Date: 2007
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