AVERAGE OPTIONS FOR JUMP DIFFUSION MODELS

Hiroshi Kunita () and Takuya Yamada
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Hiroshi Kunita: Department of Mathematical Science, Nanzan University, Japan
Takuya Yamada: Department of Mathematical Science, Nanzan University, Japan

Asia-Pacific Journal of Operational Research (APJOR), 2010, vol. 27, issue 02, 143-166

Abstract: In this paper, we study the problem of pricing average strike options in the case where the price processes are jump diffusion processes. As to the striking value we take the geometric average of the price process. Two cases are studied in details: One is the case where the jumping law of the price process is subject to a Gaussian distribution called Merton model, and the other is the case where the jumping law is subject to a double exponential distribution called Kou model. In both cases the price of the average strike option is represented as a time average of a suitable European put option.

Keywords: Mathematical finance for jump diffusion process; Itô's formula for jumps process; Girsanov's theorem for jumps process; option pricing for jump diffusion (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0217595910002612

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