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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">finance</journal-id><journal-title-group><journal-title xml:lang="ru">Финансы: теория и практика/Finance: Theory and Practice</journal-title><trans-title-group xml:lang="en"><trans-title>Finance: Theory and Practice</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2587-5671</issn><issn pub-type="epub">2587-7089</issn><publisher><publisher-name>Financial University under The Government of Russian Federation</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26794/2587-5671-2023-27-6-44-53</article-id><article-id custom-type="elpub" pub-id-type="custom">finance-2510</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИНАНСОВЫЕ РЫНКИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>FINANCIAL MARKETS</subject></subj-group></article-categories><title-group><article-title>Обработка пропусков в рыночных данных на примере задачи оценки кривой доходностей облигаций</article-title><trans-title-group xml:lang="en"><trans-title>Treatment of Missing Market Data: Case of bond Yield Curve Estimation</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3491-1561</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Макушкин</surname><given-names>М. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Makushkin</surname><given-names>M. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Михаил Сергеевич Макушкин — аспирант, Базовая кафедра инфраструктуры финансовых рынков</p><p>Москва</p></bio><bio xml:lang="en"><p>Mikhail S. Makushkin — postgraduate student, Department of Financial Market Infrastructure</p><p>Moscow</p></bio><email xlink:type="simple">mikhailmakushkin@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9396-4161</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Лапшин</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Lapshin</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Виктор Александрович Лапшин — кандидат физико-математических наук, доцент, Лаборатория по финансовой инженерии и риск-менеджменту, Школа финансов</p><p>Москва</p></bio><bio xml:lang="en"><p>Victor A. Lapshin — Cand. Sci. (Phys.-Math.), Assoc. Prof., Financial Engineering and Risk Management Laboratory, School of Finance</p><p>Moscow</p></bio><email xlink:type="simple">vlapshin@hse.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>НИУ ВШЭ</institution><country>Россия</country></aff><aff xml:lang="en"><institution>National Research University Higher School of Economics</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2023</year></pub-date><pub-date pub-type="epub"><day>27</day><month>12</month><year>2023</year></pub-date><volume>27</volume><issue>6</issue><fpage>44</fpage><lpage>53</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Макушкин М.С., Лапшин В.А., 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Макушкин М.С., Лапшин В.А.</copyright-holder><copyright-holder xml:lang="en">Makushkin M.S., Lapshin V.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://financetp.fa.ru/jour/article/view/2510">https://financetp.fa.ru/jour/article/view/2510</self-uri><abstract><p>Пропуски в рыночных данных — частая проблема в финансовых исследованиях, которой уделяется относительно мало внимания на практике. Обработка пропусков, как правило, выполняется эвристически и является лишь вспомогательным шагом исследований. Целью нашей работы является разработка практических рекомендаций по работе с пропусками в рыночных данных. Проблема иллюстрируется на примере задачи оценки временной структуры процентных ставок на российском рынке государственных облигаций. Мы сравниваем три различных метода заполнения пропусков в данных — заполнение последним значением, фильтр Калмана и EM-алгоритм — с простой стратегией удаления пропусков. Мы приходим к выводу, что эффект от заполнения пропусков на качество оценки кривой зависит от чувствительности модели кривой доходностей к рыночным данным. Для слабо чувствительных к данным моделей, например для модели кривой доходностей Нельсона-Зигеля, эффект от заполнения пропусков минимален. Для более чувствительных моделей кривой, таких как бутстрэп, за счет заполнения пропусков удается достичь статистически значимого улучшения качества оценки срочной структуры процентных ставок. При этом данный результат не зависит от способа заполнения пропусков. И простой метод заполнения последним значением, и более сложный EM-алгоритм дают схожие результаты. Рекомендация исследования состоит том, что на практике при оценке кривой доходностей в условиях неполных данных необходимо либо использовать слабо чувствительные к данным параметрические модели кривой доходностей, либо заполнять пропуски в данных перед использованием чувствительных моделей.</p></abstract><trans-abstract xml:lang="en"><p>Missing observations in market data is a frequent problem in financial studies. The problem of missing data is often overlooked in practice. Missing data is mostly treated using ad hoc methods or just ignored. Our goal is to develop practical recommendations for treatment of missing observations in financial data. We illustrate the issue with an example of yield curve estimation on Russian bond market. We compare three methods of missing data imputation — last observation carried forward, Kalman filtering and EM–algorithm — with a simple strategy of ignoring missing observations. We conclude that the impact of data imputation on the quality of yield curve estimation depends on model sensitivity to the market data. For non-sensitive models, such as Nelson-Siegel yield curve model, final effect is insignificant. For more sensitive models, such as bootstrapping, missing data imputation allows to increase the quality of yield curve estimation. However, the result does not depend on the chosen data imputation method. Both simple last observation carried forward method and more advanced EM–algorithm lead to similar final results. Therefore, when estimating yield curves on the illiquid markets with missing market data, we recommend to use either simple non-sensitive to the data parametric models of yield curve or to impute missing data before using more advanced and sensitive yield curve models.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>кривая бескупонной доходности</kwd><kwd>срочная структура процентных ставок</kwd><kwd>рынок облигаций</kwd><kwd>метод Нельсона-Зигеля</kwd><kwd>ликвидность рынка</kwd><kwd>пропуски в данных</kwd><kwd>развивающиеся рынки</kwd></kwd-group><kwd-group xml:lang="en"><kwd>yield curve</kwd><kwd>term structure of interest rates</kwd><kwd>bond market</kwd><kwd>Nelson-Siegel method</kwd><kwd>liquidity level</kwd><kwd>missing data</kwd><kwd>emerging markets</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Макушкин М. С., Лапшин В. А. 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