{"id":7147,"date":"2021-06-10T16:00:51","date_gmt":"2021-06-10T13:00:51","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=7147"},"modified":"2021-08-28T23:08:52","modified_gmt":"2021-08-28T20:08:52","slug":"modeling-relation-between-atm-local-and-implied-volatility-for-microsoft-stocks","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=7147","title":{"rendered":"Modeling relation between atm local and implied volatility for microsoft stocks"},"content":{"rendered":"

<\/p>\n

MODELING RELATION BETWEEN ATM LOCAL AND IMPLIED VOLATILITY FOR MICROSOFT STOCKS<\/p>\n

\u041c\u041e\u0414\u0415\u041b\u042e\u0412\u0410\u041d\u041d\u042f \u0421\u041f\u0406\u0412\u0412\u0406\u0414\u041d\u041e\u0428\u0415\u041d\u041d\u042f \u041c\u0406\u0416 \u041b\u041e\u041a\u0410\u041b\u042c\u041d\u041e\u042e \u0422\u0410 \u041d\u0415\u042f\u0412\u041d\u041e\u042e \u0412\u041e\u041b\u0410\u0422\u0418\u041b\u042c\u041d\u0406\u0421\u0422\u042e \u00ab\u0423 \u0413\u0420\u041e\u0428\u0410\u0425\u00bb \u0414\u041b\u042f \u0410\u041a\u0426\u0406\u0419 MICROSOFT<\/p>\n

\"\"<\/a> \u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 21-29. \u041d\u043e\u043c\u0435\u0440: \u21162, 202<\/strong>1 (2<\/strong>92)<\/strong><\/p>\n

\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\nMaksym BONDARENKO
\nORCID ID: 0000-0002-4792-6420<\/a>
\ne-mail: maksym_bondarenko@outlook.com<\/a>
\nVICTOR BONDARENKO
\nORCID ID: 0000-0003-1663-4799
\ne-mail: vicnbondarenko@gmail.com
\nNational Technical University of Ukraine \u00abIgor Sikorsky Kyiv Polytechnic Institute\u00bb<\/p>\n

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\n\u00ab\u041a\u0438\u0457\u0432\u0441\u044c\u043a\u0438\u0439 \u041f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0406\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406\u0433\u043e\u0440\u044f \u0421\u0456\u043a\u043e\u0440\u0441\u044c\u043a\u043e\u0433\u043e\u00bb<\/p>\n

DOI<\/strong>:<\/strong>\u00a0https:\/\/www.doi.org\/10.31891\/2307-5740-2021-292-2-4<\/a>
\n\u00a0<\/strong>\u041d\u0430\u0434\u0456\u0439\u0448\u043b\u0430 \/ Paper received :<\/strong> 09.03.2021
\n\u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430 \/ Paper Printed :<\/strong> 01.06.2021<\/p>\n

\u00a0<\/strong>\u0410\u043d\u043e\u0442\u0430\u0446\u0456\u044f<\/strong> \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0In this work simple linear and polynomial regression to model the relation between at-the-money (ATM) implied and at-the-money local volatility of Microsoft stocks has been applied.
\nLocal volatility is extracted from the set of Vanilla option prices on Microsoft stocks by assuming that Microsoft stock price follows Dupire local volatility process. ATM Local volatility is then used in linear regression predictor while implied volatility is a resulting variable.
\nThe model is validated by predicting out-of-sample implied volatility with local volatility. The statistical significance and predictive ability of such model have been measured and autocorrelation tendencies have been studied.<\/p>\n

The conclusion that assumptions to use linear regression are held has been made. No autocorrelation tendencies were discovered in the time series.
\nFinally, the conclusion that both the 1st and the 3rd order linear regression models demonstrate good predictive ability of local volatility over out-of-sample implied volatility has been made. None of the models proves statistical significance of local volatility as a predictor of the implied volatility but both can be actually used for practical purpose as they predict well out-of-the-sample implied volatilities.\u00a0 This is an important practical result as it means that complex non-linear relationship between implied and local volatilities formalized by Dupire can actually be reduced to simplier linear relationship that demonstrates reasonable discrepancies.
\nDespite the 3rd order model fits the data better, but for the reasons of overfitting in general it\u2019s safer to apply the 1st order model as it demonstrates more stable predictions over datasets with jumps.
\n\u00a0 \u00a0 \u00a0Keywords:<\/strong> regression; implied volatility; calibration; Microsoft stocks; Dupire model; statistical significance; predictive ability.<\/p>\n

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\u0437\u0432\u2019\u044f\u0437\u043a\u0443, \u044f\u043a\u0438\u0439 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0443\u0454 \u0440\u043e\u0437\u0443\u043c\u043d\u0456 \u0440\u043e\u0437\u0431\u0456\u0436\u043d\u043e\u0441\u0442\u0456. \u041d\u0435\u0437\u0432\u0430\u0436\u0430\u044e\u0447\u0438 \u043d\u0430 \u0442\u0435, \u0449\u043e \u043c\u043e\u0434\u0435\u043b\u044c \u0442\u0440\u0435\u0442\u044c\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0443 \u043a\u0440\u0430\u0449\u0435 \u043f\u0456\u0434\u0445\u043e\u0434\u0438\u0442\u044c \u0434\u043b\u044f \u0434\u0430\u043d\u0438\u0445, \u0437 \u043f\u0440\u0438\u0447\u0438\u043d \u043f\u0435\u0440\u0435\u0432\u0438\u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f, \u0437\u0430\u0433\u0430\u043b\u043e\u043c \u0431\u0435\u0437\u043f\u0435\u0447\u043d\u0456\u0448\u0435 \u0437\u0430\u0441\u0442\u043e\u0441\u043e\u0432\u0443\u0432\u0430\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u044c 1-\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0443, \u043e\u0441\u043a\u0456\u043b\u044c\u043a\u0438 \u0432\u043e\u043d\u0430 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0443\u0454 \u0431\u0456\u043b\u044c\u0448 \u0441\u0442\u0430\u0431\u0456\u043b\u044c\u043d\u0456 \u043f\u0440\u043e\u0433\u043d\u043e\u0437\u0438 \u0449\u043e\u0434\u043e \u043d\u0430\u0431\u043e\u0440\u0456\u0432 \u0434\u0430\u043d\u0438\u0445 \u0437\u0456 \u0441\u0442\u0440\u0438\u0431\u043a\u0430\u043c\u0438.
\n\u00a0 \u00a0 \u00a0\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u0440\u0435\u0433\u0440\u0435\u0441\u0456\u044f, \u043d\u0435\u044f\u0432\u043d\u0430 \u0432\u043e\u043b\u0430\u0442\u0438\u043b\u044c\u043d\u0456\u0441\u0442\u044c, \u043a\u0430\u043b\u0456\u0431\u0440\u043e\u0432\u043a\u0430, \u0430\u043a\u0446\u0456\u0457 Microsoft, \u043c\u043e\u0434\u0435\u043b\u044c \u0414\u044e\u043f\u0456\u0440\u0430, \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0447\u043d\u0430 \u0437\u043d\u0430\u0447\u0438\u043c\u0456\u0441\u0442\u044c, \u043f\u0440\u0435\u0434\u0438\u043a\u0430\u0442\u0438\u0432\u043d\u0430 \u0437\u0434\u0430\u0442\u043d\u0456\u0441\u0442\u044c.<\/p>\n

References<\/strong><\/p>\n

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