{"created":"2021-03-01T07:02:45.856725+00:00","id":42824,"links":{},"metadata":{"_buckets":{"deposit":"6a361ae8-6450-494f-9960-102068d5fa2a"},"_deposit":{"id":"42824","owners":[],"pid":{"revision_id":0,"type":"depid","value":"42824"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00042824","sets":["62:7433:7434","9:7435:7436"]},"item_8_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2012-02","bibliographicIssueDateType":"Issued"},"bibliographicVolumeNumber":"CIRJE-F-842","bibliographic_titles":[{"bibliographic_title":"Discussion paper series. CIRJE-F"}]}]},"item_8_description_13":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_8_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"This paper proposes a general approximation method for the solution to a second-order parabolic partial differential equation(PDE) widely used in finance through an extension of Léandre's approach(Léandre (2006,2008)) and the Bismut identiy(e.g. chapter IX-7 of Malliavin (1997)) in Malliavin calculus. We present two types of its applications, approximations of derivatives prices and short-time asymptotic expansions of the heat kernel. In particular, we provide approximate formulas for option prices under local and stochastic volatility models. We also derive short-time asymptotic expansions of the heat kernel under general time-homogenous local volatility and local-stochastic volatility models in finance, which include Heston (Heston (1993)) and (λ-)SABR models (Hagan et.al. (2002), Labordere (2008)) as special cases. Some numerical examples are shown.","subitem_description_type":"Abstract"}]},"item_8_description_6":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"Revised in March 2012; forthcoming in Recent Advances in Financial Engineering 2011.","subitem_description_type":"Other"},{"subitem_description":"本文フィルはリンク先を参照のこと","subitem_description_type":"Other"}]},"item_8_publisher_20":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"日本経済国際共同センター"}]},"item_8_relation_25":{"attribute_name":"関係URI","attribute_value_mlt":[{"subitem_relation_type_id":{"subitem_relation_type_id_text":"http://www.cirje.e.u-tokyo.ac.jp/research/dp/2012/2012cf842ab.html","subitem_relation_type_select":"URI"}}]},"item_8_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11450569","subitem_source_identifier_type":"NCID"}]},"item_8_subject_15":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"335","subitem_subject_scheme":"NDC"}]},"item_8_text_21":{"attribute_name":"出版者別名","attribute_value_mlt":[{"subitem_text_value":"Center for International Research on the Japanese Economy"}]},"item_8_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Graduate School of Economics, the University of Tokyo"},{"subitem_text_value":"Mitsubishi UFJ Trust Investment Technology Institute Co.,Ltd. (MTEC)"}]},"item_access_right":{"attribute_name":"アクセス権","attribute_value_mlt":[{"subitem_access_right":"metadata only access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_14cb"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Takahashi, Akihiko"}],"nameIdentifiers":[{"nameIdentifier":"98458","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Yamada, Toshihiro"}],"nameIdentifiers":[{"nameIdentifier":"98459","nameIdentifierScheme":"WEKO"}]}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Malliavin calculus","subitem_subject_scheme":"Other"},{"subitem_subject":"Bismut indentity","subitem_subject_scheme":"Other"},{"subitem_subject":"Integration-by-parts","subitem_subject_scheme":"Other"},{"subitem_subject":"Semigroup","subitem_subject_scheme":"Other"},{"subitem_subject":"Asymptotic expansion","subitem_subject_scheme":"Other"},{"subitem_subject":"Short time asymptotics","subitem_subject_scheme":"Other"},{"subitem_subject":"Heat kernel expansions","subitem_subject_scheme":"Other"},{"subitem_subject":"Derivatives pricing","subitem_subject_scheme":"Other"},{"subitem_subject":"Stochastic volatility","subitem_subject_scheme":"Other"},{"subitem_subject":"Local volatility","subitem_subject_scheme":"Other"},{"subitem_subject":"SABR model","subitem_subject_scheme":"Other"},{"subitem_subject":"λ-SABR models","subitem_subject_scheme":"Other"},{"subitem_subject":"Heston model","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"technical report","resourceuri":"http://purl.org/coar/resource_type/c_18gh"}]},"item_title":"A Remark on Approximation of the Solutions to Partial Differential Equations in Finance","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"A Remark on Approximation of the Solutions to Partial Differential Equations in Finance"}]},"item_type_id":"8","owner":"1","path":["7436","7434"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-01-17"},"publish_date":"2017-01-17","publish_status":"0","recid":"42824","relation_version_is_last":true,"title":["A Remark on Approximation of the Solutions to Partial Differential Equations in Finance"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:16:50.802074+00:00"}