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However, this approach cannot be applied to exotic derivatives (such as barrier options) directly, although a large volume of exotic derivatives are actively traded in the current options market. An alternative approach is to solve the corresponding partial integro-differential equation (PIDE) numerically, which is, in fact, time-consuming and is not computationally tractable in general. In this paper, we apply the so-called homotopy analysis method (HAM) to solve the corresponding PIDE in a semi analytic form, being obtained from the following three steps: (1) Apply the Fourier transform to convert the PIDE to an ordinal differential equitation (ODE), and construct a differential system of ODEs. (2) Solve the system of ODEs, where each differential equation is shown to have an analytical solution. (3) Express the option price using the sum of infinite series, where each term may be expressed analytically and derived by applying Steps (1) and (2) recursively. To illustrate our technique more precisely, we take the variance gamma model as an example and provide the semi-analytic form. Numerical examples demonstrate a fast convergence of our proposed method to the prices of European and down-and-out call options with a few number of terms. 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Application of Homotopy Analysis Method to Option Pricing Under Lévy Processes
http://hdl.handle.net/2241/00146100
http://hdl.handle.net/2241/001461009b9770ba-f1b3-475b-bc2e-0e0da32fa74f
名前 / ファイル | ライセンス | アクション |
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APFM_21-1 (176.2 kB)
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Item type | Journal Article(1) | |||||
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公開日 | 2017-05-16 | |||||
タイトル | ||||||
タイトル | Application of Homotopy Analysis Method to Option Pricing Under Lévy Processes | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
著者 |
Sakuma, Takayuki
× Sakuma, Takayuki× Yamada, Yuji |
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著者別名 |
山田, 雄二
× 山田, 雄二 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | Option pricing under the Lévy process has been considered an important research direction in the field of financial engineering, where a closed-form expression for the standard European option is available due to the existence of analytically tractable characteristic function according to the Lévy–Khinchin representation. However, this approach cannot be applied to exotic derivatives (such as barrier options) directly, although a large volume of exotic derivatives are actively traded in the current options market. An alternative approach is to solve the corresponding partial integro-differential equation (PIDE) numerically, which is, in fact, time-consuming and is not computationally tractable in general. In this paper, we apply the so-called homotopy analysis method (HAM) to solve the corresponding PIDE in a semi analytic form, being obtained from the following three steps: (1) Apply the Fourier transform to convert the PIDE to an ordinal differential equitation (ODE), and construct a differential system of ODEs. (2) Solve the system of ODEs, where each differential equation is shown to have an analytical solution. (3) Express the option price using the sum of infinite series, where each term may be expressed analytically and derived by applying Steps (1) and (2) recursively. To illustrate our technique more precisely, we take the variance gamma model as an example and provide the semi-analytic form. Numerical examples demonstrate a fast convergence of our proposed method to the prices of European and down-and-out call options with a few number of terms. Note that this method is easy to implement and can be applied to other types of options under general Lévy processes. | |||||
書誌情報 |
Asia-Pacific financial markets 巻 21, 号 1, p. 1-14, 発行日 2014-03 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 1387-2834 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA11224457 | |||||
DOI | ||||||
識別子タイプ | DOI | |||||
関連識別子 | 10.1007/s10690-013-9175-2 | |||||
権利 | ||||||
権利情報 | © Springer Japan 2013 | |||||
権利 | ||||||
権利情報 | The final publication is available at Springer via http://dx.doi.org/10.1007/s10690-013-9175-2 | |||||
著者版フラグ | ||||||
値 | author | |||||
出版者 | ||||||
出版者 | Springer Japan |