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Hokkaido University Preprint Series in Mathematics >
Dynamic models of asset prices with long memory
| Title: | Dynamic models of asset prices with long memory |
| Authors: | Anh, V. Browse this author | | Inoue, A. Browse this author |
| Issue Date: | May-2001 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 526 |
| Start Page: | 1 |
| End Page: | 21 |
| Abstract: | This paper introduces a class of AR( oo )-type models for mean-square continuous processes with stationary increments. The models allow for short- or long-memory dynamics in the processes. Their solutions are shown to have a semimartingale representation. The models are used to describe the dynamics of asset prices, which reduce to the traditional Black-ScholPB model as a special case. It is shown that there exists an equivalent martingale measure under which the behaviour of the discounted price process is equal to that in the Black-Scholes environment. As a result, the European option price is given by the Black-Scholes formula. The variance of the log price ratio is also obtained. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69276 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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