{"id":80,"date":"2016-04-20T17:34:20","date_gmt":"2016-04-20T15:34:20","guid":{"rendered":"http:\/\/eudaimonia-production.com\/?page_id=80"},"modified":"2019-01-14T04:49:21","modified_gmt":"2019-01-14T02:49:21","slug":"quantitative-methods-for-pricing-options-with-exotic-characteristics-and-under-non-standard-hypotheses","status":"publish","type":"post","link":"https:\/\/eudaimonia-production.com\/?p=80","title":{"rendered":"Quantitative Methods for Pricing Options with Exotic Characteristics and under Non-standard Hypotheses"},"content":{"rendered":"<p><strong><a href=\"http:\/\/eudaimonia-production.com\/wp-content\/uploads\/2016\/04\/OblojkaQuantativeMethods.bmp\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-81\" src=\"http:\/\/eudaimonia-production.com\/wp-content\/uploads\/2016\/04\/OblojkaQuantativeMethods.bmp\" alt=\"OblojkaQuantativeMethods\" width=\"208\" height=\"292\" \/><\/a><a href=\"#metadata\">\u0418\u0437\u0434\u0430\u0442\u0435\u043b\u0441\u043a\u0438 \u0434\u0430\u043d\u043d\u0438&#8230;<\/a><\/strong><\/p>\n<p><strong><a href=\"#author\">\u0417\u0430 \u0430\u0432\u0442\u043e\u0440\u0430&#8230;<\/a><\/strong><\/p>\n<p><strong><a href=\"#description\">\u041e\u043f\u0438\u0441\u0430\u043d\u0438\u0435&#8230;<\/a><\/strong><\/p>\n<p><strong><a href=\"#content\">\u0421\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435&#8230;<\/a><\/strong><\/p>\n<p><strong><a href=\"http:\/\/eudaimonia-production.com\/wp-content\/uploads\/2016\/04\/Milev_Tagliani_Quantitative_Methods_for_Pricing_Options_with_Exotic_Characteristics_and_under_Non-standard_Hypotheses.pdf\" target=\"_blank\" rel=\"noopener\">\u0421\u0432\u0430\u043b\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 \u043d\u0430 \u043a\u043d\u0438\u0433\u0430\u0442\u0430 \u0442\u0443\u043a&#8230;<\/a><\/strong><\/p>\n<p><strong><a href=\"http:\/\/booksinprint.bg\/Publication\/Details\/15455f34-8de6-452f-afb4-1eac5cf243d1\" target=\"_blank\" rel=\"noopener\">\u041a\u043d\u0438\u0433\u0430\u0442\u0430 \u0432 \u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u0438\u044f \u0440\u0435\u0433\u0438\u0441\u0442\u044a\u0440 \u043d\u0430 \u0438\u0437\u0434\u0430\u0434\u0435\u043d\u0438\u0442\u0435 \u043a\u043d\u0438\u0433\u0438&#8230;<\/a><\/strong><\/p>\n<hr \/>\n<p><a name=\"metadata\"><\/a><strong>\u0418\u0437\u0434\u0430\u0442\u0435\u043b\u0441\u043a\u0438 \u0434\u0430\u043d\u043d\u0438:<\/strong><\/p>\n<p>&#8220;<span class=\"title\">Quantitative Methods for Pricing Options with Exotic Characteristics and under Non-standard Hypotheses<\/span>&#8221;<\/p>\n<p>\u043a\u043d\u0438\u0433\u0430<\/p>\n<p>\u041f\u044a\u0440\u0432\u043e \u0438\u0437\u0434\u0430\u043d\u0438\u0435<\/p>\n<p>\u0421\u043e\u0444\u0438\u044f, 2012<\/p>\n<p>\u0410\u0432\u0442\u043e\u0440\u0438: Mariyan Milev, Aldo Tagliani<\/p>\n<p>\u041f\u0435\u0447\u0430\u0442\u043d\u043e \u0438\u0437\u0434\u0430\u043d\u0438\u0435:<\/p>\n<p>\u0415\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e \u0438\u0437\u0434\u0430\u043d\u0438\u0435: ISBN 978-954-92924-1-1<\/p>\n<hr \/>\n<p><a name=\"author\"><\/a><strong>\u0417\u0430 \u0430\u0432\u0442\u043e\u0440\u0430:<\/strong><\/p>\n<p>\u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u043f\u043e \u0425\u0440\u0430\u043d\u0438\u0442\u0435\u043b\u043d\u0438 \u0422\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u2013 \u041f\u043b\u043e\u0432\u0434\u0438\u0432\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong><a href=\"http:\/\/eudaimonia-production.com\/wp-content\/uploads\/2016\/04\/OblojkaQuantativeMethods.bmp\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-127\" src=\"http:\/\/eudaimonia-production.com\/wp-content\/uploads\/2016\/04\/Milev.jpg\" alt=\"Milev\" width=\"108\" height=\"172\" \/><\/a><\/strong><br \/>\n\u0421\u0442\u043e\u043f\u0430\u043d\u0441\u043a\u0438 \u0424\u0430\u043a\u0443\u043b\u0442\u0435\u0442, \u043a\u0430\u0442\u0435\u0434\u0440\u0430 \u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0421\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0430<br \/>\n\u0434-\u0440 \u043f\u043e \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0422\u0440\u0435\u043d\u0442\u043e, \u0418\u0442\u0430\u043b\u0438\u044f<br \/>\n\u0414\u0438\u0441\u0435\u0440\u0442\u0430\u0446\u0438\u044f \u043d\u0430 \u0442\u0435\u043c\u0430:<br \/>\n\u041e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u043f\u0446\u0438\u0438 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0437\u0438\u0440\u0430\u0449\u0438 \u0441\u0435 \u0441 \u043f\u0440\u0435\u043a\u044a\u0441\u0432\u0430\u043d\u0438\u044f, \u0441\u0445\u0435\u043c\u0438 \u043d\u0430<br \/>\n\u043a\u0440\u0430\u0439\u043d\u0438 \u0440\u0430\u0437\u043b\u0438\u043a\u0438: \u041c\u043e\u0434\u0435\u043b\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0444\u0438\u043d\u0430\u043d\u0441\u043e\u0432\u0438 \u0434\u0435\u0440\u0438\u0432\u0430\u0442\u0438<br \/>\n\u0443\u0435\u0431\u0441\u0430\u0439\u0442: mariyanmilev.info email: lutermar@mail.bg<br \/>\n\u0410\u0432\u0442\u043e\u0440\u044a\u0442 \u041c\u0430\u0440\u0438\u044f\u043d \u041c\u0438\u043b\u0435\u0432 \u043d\u0430 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u043e\u0442\u043e \u0440\u044a\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u201e\u041f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 MATLAB \u0432<br \/>\n\u0418\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0430\u0442\u0430\u201d \u0438 \u043f\u0440\u043e\u0444. \u0410\u043b\u0434\u043e \u0422\u0430\u043b\u0438\u0430\u043d\u0438 \u0441\u0430 \u0430\u0432\u0442\u043e\u0440\u0438 \u0438 \u043d\u0430 \u043a\u043d\u0438\u0433\u0430\u0442\u0430 \u2018Quantitative Methods for<br \/>\nPricing Options with Exotic Characteristics and under Non-standard Hypotheses\u2019, 2012.<br \/>\n(\u041a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u0438 \u043c\u0435\u0442\u043e\u0434\u0438 \u0437\u0430 \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u043f\u0446\u0438\u0438 \u0441 \u0435\u043a\u0437\u043e\u0442\u0438\u0447\u043d\u0438 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u043f\u0440\u0438<br \/>\n\u043d\u0435\u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u0438 \u0445\u0438\u043f\u043e\u0442\u0435\u0437\u0438), Eudaimonia Production Ltd., Sofia, ISBN: 978-954-92924-1-1.<br \/>\n\u00b7 \u041f\u0440\u0435\u0437 \u041d\u043e\u0435\u043c\u0432\u0440\u0438 2004 \u0430\u0432\u0442\u043e\u0440\u044a\u0442 \u041c\u0430\u0440\u0438\u044f\u043d \u041c\u0438\u043b\u0435\u0432 \u0435 \u043f\u0440\u0438\u0435\u0442 \u0432 \u201e\u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u043e\u0442\u043e \u0434\u043e\u043a\u0442\u043e\u0440\u0441\u043a\u043e<br \/>\n\u0443\u0447\u0438\u043b\u0438\u0449\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u201d \u0432 \u201e\u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0422\u0440\u0435\u043d\u0442\u043e\u201d, \u0433\u0440. \u0422\u0440\u0435\u043d\u0442\u043e, \u0418\u0442\u0430\u043b\u0438\u044f \u0441\u043b\u0435\u0434 \u043a\u043e\u043d\u043a\u0443\u0440\u0441 \u043d\u0430<br \/>\n\u201e\u041c\u0438\u043d\u0438\u0441\u0442\u0435\u0440\u0441\u0442\u0432\u043e \u043d\u0430 \u041e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e\u201d \u043d\u0430 \u0418\u0442\u0430\u043b\u0438\u044f \u0438 \u043f\u0440\u0435\u0437 \u041c\u0430\u0439 2009 \u0443\u0441\u043f\u0435\u0448\u043d\u043e \u0437\u0430\u0432\u044a\u0440\u0448\u0432\u0430<br \/>\n\u0447\u0435\u0442\u0438\u0440\u0438\u0433\u043e\u0434\u0438\u0448\u043d\u0430 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u0434\u043e\u043a\u0442\u043e\u0440\u0430\u043d\u0442\u0441\u043a\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0441 \u043d\u0430\u0443\u0447\u043d\u0438<br \/>\n\u0440\u044a\u043a\u043e\u0432\u043e\u0434\u0438\u0442\u0435\u043b\u0438 \u043f\u0440\u043e\u0444. \u0410\u043b\u0434\u043e \u0422\u0430\u043b\u0438\u0430\u043d\u0438 \u043e\u0442 \u043a\u0430\u0442\u0435\u0434\u0440\u0430 \u201e\u041a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438 \u0421\u0438\u0441\u0442\u0435\u043c\u0438 \u0438 \u0418\u043a\u043e\u043d\u043e\u043c\u0438\u0447\u0435\u0441\u043a\u0438<br \/>\n\u041d\u0430\u0443\u043a\u0438\u201d, \u201e\u0424\u0430\u043a\u0443\u043b\u0442\u0435\u0442 \u043f\u043e \u0418\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0430\u201d \u0438 \u043f\u0440\u043e\u0444. \u0434.\u043c.\u043d. \u041b\u0443\u0447\u0438\u0430\u043d\u043e \u0422\u0443\u0431\u0430\u0440\u043e \u043e\u0442 \u201e\u0424\u0430\u043a\u0443\u043b\u0442\u0435\u0442 \u043f\u043e<br \/>\n\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u0424\u0438\u0437\u0438\u043a\u0430 \u0438 \u041f\u0440\u0438\u0440\u043e\u0434\u043d\u0438 \u043d\u0430\u0443\u043a\u0438\u201d \u0432 \u201e\u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0422\u0440\u0435\u043d\u0442\u043e\u201d, \u0418\u0442\u0430\u043b\u0438\u044f.<br \/>\n\u00b7 \u041e\u0442 2010 \u0433. \u0434-\u0440 \u041c\u0430\u0440\u0438\u044f\u043d \u041c\u0438\u043b\u0435\u0432 \u0435 \u0433\u043b\u0430\u0432\u0435\u043d \u0430\u0441\u0438\u0441\u0442\u0435\u043d\u0442 \u0432 \u043a\u0430\u0442\u0435\u0434\u0440\u0430 \u201e\u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0421\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0430\u201d,<br \/>\n\u201e\u0421\u0442\u043e\u043f\u0430\u043d\u0441\u043a\u0438 \u0424\u0430\u043a\u0443\u043b\u0442\u0435\u0442\u201d, \u201e\u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u043f\u043e \u0425\u0440\u0430\u043d\u0438\u0442\u0435\u043b\u043d\u0438 \u0422\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u2013 \u041f\u043b\u043e\u0432\u0434\u0438\u0432\u201d.<br \/>\n\u00b7 \u041e\u0441\u043d\u043e\u0432\u043d\u0438\u0442\u0435 \u043d\u0430\u0443\u0447\u043d\u0438 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u0438 \u043d\u0430 \u0430\u0432\u0442\u043e\u0440\u0430 \u0441\u0430 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0442\u0430 \u043d\u0430 \u043f\u0440\u0438\u043b\u043e\u0436\u043d\u0430\u0442\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430,<br \/>\n\u0438\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0430\u0442\u0430 \u0438 \u0444\u0438\u043d\u0430\u043d\u0441\u0438\u0442\u0435, \u0432\u043a\u043b\u044e\u0447\u0432\u0430\u0449\u0438 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u043e\u0434\u0435\u043b\u0430 \u043d\u0430 \u0411\u043b\u0430\u043a-\u0428\u043e\u043b\u0441, \u0447\u0438\u0441\u043b\u0435\u043d\u0438<br \/>\n\u043c\u0435\u0442\u043e\u0434\u0438 \u0437\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u043e \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u0430\u043d\u0435 \u0438 \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0444\u0438\u043d\u0430\u043d\u0441\u043e\u0432\u0438 \u0434\u0435\u0440\u0438\u0432\u0430\u0442\u0438, \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u043d\u0430<br \/>\n\u0415\u0432\u0440\u043e\u043f\u0435\u0439\u0441\u043a\u0438 \u0438 \u0410\u043c\u0435\u0440\u0438\u043a\u0430\u043d\u0441\u043a\u0438 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\/>\n\u00b7 \u041f\u043e\u0432\u0435\u0447\u0435\u0442\u043e \u043d\u0430\u0443\u0447\u043d\u0438 \u043f\u0443\u0431\u043b\u0438\u043a\u0430\u0446\u0438\u0438 \u0441\u0430 \u043d\u0430\u043b\u0438\u0447\u043d\u0438 \u043e\u043d\u043b\u0430\u0439\u043d \u0432 \u0431\u0430\u0437\u0438\u0442\u0435 \u043e\u0442 \u0434\u0430\u043d\u043d\u0438 Science Direct,<br \/>\nZentralblatt, Math, Elsevier, Scirus \u0438 MathSciNet \u043d\u0430 American Mathematical Society.<br \/>\n\u00b7 \u041f\u043e\u0432\u0435\u0447\u0435 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044f \u0437\u0430 \u043d\u0430\u0443\u0447\u043d\u0438\u0442\u0435 \u043f\u0443\u0431\u043b\u0438\u043a\u0430\u0446\u0438\u0438 \u0438 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u0442\u0435\u043b\u0441\u043a\u0430\u0442\u0430 \u0434\u0435\u0439\u043d\u043e\u0441\u0442 \u043d\u0430 \u0430\u0432\u0442\u043e\u0440\u0430 \u0435<br \/>\n\u043d\u0430\u043b\u0438\u0447\u043d\u0430 \u043d\u0430 \u043b\u0438\u0447\u043d\u0430\u0442\u0430 \u043c\u0443 \u0443\u0435\u0431 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430: http:\/\/mariyanmilev.info\/pages\/bg_publications.html<\/p>\n<hr \/>\n<p><a name=\"description\"><\/a><strong>\u041e\u043f\u0438\u0441\u0430\u043d\u0438\u0435:<\/strong><\/p>\n<div class=\"display-field\">\n<div>This book is aimed at a reader who has basic knowledges in disciplines like linear algebra, numerical methods, probability and statistics, but does not know how to use them together to solve problems considered in Quantitative Finance such as the option valuation problem, i.e. to be defined a fair value of the option\u2019s price.<\/div>\n<div>For this aim, in this book we present basic definitions of different types of options as well as numerical methods for their evaluation known also as Quantitative methods for pricing options, hence the title of this book.<\/div>\n<div>This book is organized in nine chapters, including a detailed introduction and a conclusion chapter. There is also a short abstract and three appendices dedicated to an implementation of the presented quantitative methods in Matlab and an external discussion of them as well as some additional topics such as classification of M-matrices.<\/div>\n<div>We do not attempt to describe all kinds of Quantitative methods but instead to examine a few of them in depth with the objectives to illustrate certain ideas for pricing options. The book is appropriate for undergraduate and doctoral students, studying applied mathematics or graduate course in business, economics, and financial engineering.<\/div>\n<div>We strongly recommend the first three chapters to students in the undergraduate course of Economics and Finance or in postgraduate course of Mathematical Finance and Derivative Markets. The book is also useful for practitioners and curious people who want to acquire a working knowledge how financial derivatives can be analyzed.<\/div>\n<\/div>\n<p><!--more--><\/p>\n<hr \/>\n<p><a name=\"content\"><\/a><strong>\u0421\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435:<\/strong><\/p>\n<p>1 Introduction 1<br \/>\n1.1 Discrete Double Barrier Knock-out Option Pricing Problem<br \/>\n&#8211; Black-Scholes Equation and Finite Difference Approach 7<br \/>\n1.2 Discrete Barrier Options: New Semi-analytical Approach 11<br \/>\n2 Financial Derivatives 13<br \/>\n2.1 What Are Options? 14<br \/>\n2.1.1 Basic Types of Options: Call and Put Option 15<br \/>\n2.1.2 Payoff Characterization 18<br \/>\n2.1.3 Path-dependent Options or Exotics 19<br \/>\n2.1.4 Single and Double Barrier Options 19<br \/>\n2.2 Option Valuation Problem 25<br \/>\n2.2.1 A Simple Model for Asset Prices 27<br \/>\n2.2.2 The Black-Scholes-Model 29<br \/>\n3 Quantitative Methods in Finance 33<br \/>\n3.1 Binomial Method 33<br \/>\n3.2 Monte Carlo Simulations 35<br \/>\n3.3 The Black-Scholes Valuation Formula 37<br \/>\n3.4 The Black-Scholes-Merton Equation 40<br \/>\n3.5 The Black-Scholes Equation and Heat Equation 43<br \/>\n3.6 Analytical Formulas for the Value of Some Options 45<br \/>\ni<br \/>\n4 General Finite Difference Schemes and Review of Remedies<br \/>\nfor Convergence 51<br \/>\n4.1 Methods of LinesL0-stable Methods 54<br \/>\n4.2 A Fourth Order L0-stable Option Pricing Method 57<br \/>\n4.3 Exponentially Fitted Difference Schemes 58<br \/>\n4.4 Extrapolation Methods for Improving Accuracy 62<br \/>\n4.5 Smoothing the Initial Conditions 65<br \/>\n4.6 Smoothing with Families of Pad?e Approximants 68<br \/>\n4.7 An Explicit Finite Difference Approach for Barrier Options 74<br \/>\n5 Finite Difference Suggestions 77<br \/>\n5.1 Necessary and Sufficient Conditions for Stability 77<br \/>\n5.2 Sufficient Conditions &#8211; Maximum Principle 78<br \/>\n5.3 Crank-Nicolson Method for Barrier Options 80<br \/>\n5.4 Time-step Condition for Crank-Nicolson Method 86<br \/>\n5.5 Crank-Nicolson Variant Scheme 92<br \/>\n5.6 Variants of Implicit and Semi-implicit Schemes 97<br \/>\n5.7 Combination Schemes for the Case ?2 &lt; r 102<br \/>\n6 Semi-analytical Suggestions 105<br \/>\n6.1 Model for Discrete Double Barrier Options 107<br \/>\n6.2 Algorithm for Numerical Valuation 110<br \/>\n6.3 Put-Call Parity for Double Barrier Options 119<br \/>\n7 Numerical Results 121<br \/>\n7.1 Finite Difference Results 121<br \/>\n7.2 Results by Analytical and Numerical Methods 126<br \/>\n8 Modern Methods in Finance: Radial Basis Functions for<br \/>\nPricing American Put Option under Jump Diffusion 137<br \/>\nii<br \/>\n8.1 Distributions and Leptocurtic Properties 138<br \/>\n8.2 The Modified Black-Scholes Integral Equation 140<br \/>\n8.3 Radial Basis Functions Approach 143<br \/>\n8.3.1 Comparison with the Finite Difference Method 143<br \/>\n8.3.2 Advantages of Radial Basis Functions Approach 145<br \/>\n8.4 Discretization by Radial Basis Functions 149<br \/>\n8.5 Numerical Results 153<br \/>\n8.6 Discussion and Conclusions 159<br \/>\n9 Conclusions 161<br \/>\n9.1 Discrete and Continuous Monitoring: Discussion 165<br \/>\n9.2 Modern Quantitative Methods: Discussion 171<br \/>\nBibliography 173<br \/>\nA M-matrices 187<br \/>\nA.1 Tridiagonal Real MatrixJacobi Matrix 188<br \/>\nA.2 Definition and Structure of M-matrices 192<br \/>\nA.2.1 Nonnegative Matrices 193<br \/>\nA.2.2 Irreducible Matrices 194<br \/>\nA.3 Classification of M-matrices 195<br \/>\nA.4 Jacobi and M-matricesInverse of a M-matrix 197<br \/>\nB Matlab Coding 199<br \/>\nB.1 Matlab Coding 199<br \/>\nC Reviewer\u2019s Comments 225<br \/>\nC.1 Report on the Article: Special Finite Difference Schemes for<br \/>\nOptions with Discontinuous Payoff 225<br \/>\nC.2 Review on the Positivity-preserving Schemes 228<br \/>\nC.3 Some Review Comments on the RBF Method: 229<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This book is aimed at a reader who has basic knowledges in disciplines like linear algebra, numerical methods, probability and statistics, but does not know how to use them together to solve problems considered in Quantitative Finance such as the option valuation problem, i.e. to be defined a fair value of the option\u2019s price.<\/p>\n","protected":false},"author":2,"featured_media":272,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-80","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-book"],"_links":{"self":[{"href":"https:\/\/eudaimonia-production.com\/index.php?rest_route=\/wp\/v2\/posts\/80","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eudaimonia-production.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/eudaimonia-production.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/eudaimonia-production.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/eudaimonia-production.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=80"}],"version-history":[{"count":6,"href":"https:\/\/eudaimonia-production.com\/index.php?rest_route=\/wp\/v2\/posts\/80\/revisions"}],"predecessor-version":[{"id":277,"href":"https:\/\/eudaimonia-production.com\/index.php?rest_route=\/wp\/v2\/posts\/80\/revisions\/277"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/eudaimonia-production.com\/index.php?rest_route=\/wp\/v2\/media\/272"}],"wp:attachment":[{"href":"https:\/\/eudaimonia-production.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=80"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eudaimonia-production.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=80"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eudaimonia-production.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=80"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}