{"_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"}, "item_8_biblio_info_7": {"attribute_name": "\u66f8\u8a8c\u60c5\u5831", "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": "\u30d5\u30a9\u30fc\u30de\u30c3\u30c8", "attribute_value_mlt": [{"subitem_description": "application/pdf", "subitem_description_type": "Other"}]}, "item_8_description_5": {"attribute_name": "\u6284\u9332", "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 L\u00e9andre\u0027s approach(L\u00e9andre (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 (\u03bb-)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": "\u5185\u5bb9\u8a18\u8ff0", "attribute_value_mlt": [{"subitem_description": "Revised in March 2012; forthcoming in Recent Advances in Financial Engineering 2011.", "subitem_description_type": "Other"}, {"subitem_description": "\u672c\u6587\u30d5\u30a3\u30eb\u306f\u30ea\u30f3\u30af\u5148\u3092\u53c2\u7167\u306e\u3053\u3068", "subitem_description_type": "Other"}]}, "item_8_publisher_20": {"attribute_name": "\u51fa\u7248\u8005", "attribute_value_mlt": [{"subitem_publisher": "\u65e5\u672c\u7d4c\u6e08\u56fd\u969b\u5171\u540c\u30bb\u30f3\u30bf\u30fc"}]}, "item_8_relation_25": {"attribute_name": "\u95a2\u4fc2URI", "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": "\u66f8\u8a8c\u30ec\u30b3\u30fc\u30c9ID", "attribute_value_mlt": [{"subitem_source_identifier": "AA11450569", "subitem_source_identifier_type": "NCID"}]}, "item_8_subject_15": {"attribute_name": "\u65e5\u672c\u5341\u9032\u5206\u985e\u6cd5", "attribute_value_mlt": [{"subitem_subject": "335", "subitem_subject_scheme": "NDC"}]}, "item_8_text_21": {"attribute_name": "\u51fa\u7248\u8005\u5225\u540d", "attribute_value_mlt": [{"subitem_text_value": "Center for International Research on the Japanese Economy"}]}, "item_8_text_34": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"subitem_text_value": "Discussion Paper"}]}, "item_8_text_4": {"attribute_name": "\u8457\u8005\u6240\u5c5e", "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": "\u30a2\u30af\u30bb\u30b9\u6a29", "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": "\u8457\u8005", "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": "\u30ad\u30fc\u30ef\u30fc\u30c9", "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": "\u03bb-SABR models", "subitem_subject_scheme": "Other"}, {"subitem_subject": "Heston model", "subitem_subject_scheme": "Other"}]}, "item_language": {"attribute_name": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "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": "\u30bf\u30a4\u30c8\u30eb", "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": ["9/7435/7436", "62/7433/7434"], "permalink_uri": "http://hdl.handle.net/2261/51286", "pubdate": {"attribute_name": "\u516c\u958b\u65e5", "attribute_value": "2017-01-17"}, "publish_date": "2017-01-17", "publish_status": "0", "recid": "42824", "relation": {}, "relation_version_is_last": true, "title": ["A Remark on Approximation of the Solutions to Partial Differential Equations in Finance"], "weko_shared_id": null}