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Calculated Shard: 67 (from laksa078)

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curl -X POST \
  'http://laksa067.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://quantra.quantinsti.com/glossary/Realized-Volatility\')), getAhrefsUnparsedNoserviceFromURL(\'https://quantra.quantinsti.com/glossary/Realized-Volatility\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/quantra.quantinsti.com\/glossary\/Realized-Volatility","crawl_time":1775258072,"first_indexed_time":1532265598,"http_code":200,"src_unparsed":"com,quantinsti!quantra,\/glossary\/Realized-Volatility s443","src_root_hash":"8807174087797005267","history_drop_reason":null,"meta_title":"Realized Volatility","meta_descriptions":["Realized volatility refers to the measure of daily changes in the price of a security over a particular period of time."],"attrs_boilerpipe_text":"Introduction\nRealized volatility refers to the measure of daily changes in the price of a security over a particular period of time. It assumes the daily mean price to be zero in order to provide movement regardless of direction.  It is different from Implied volatility in the sense that realized volatility is the actual change in historical prices, while implied volatility predicts future price volatility. Realized volatility can be calculated by firstly calculating continuously compounded daily returns using the following formula:\nwhere,\nLn = natural logarithm\n \nPt = Underlying Reference Price (“closing price”) at day t\nPt–1 = Underlying Reference Price at day immediately preceding day t\nThen, by plugging the value of Rt in the formula below:\nwhere,\nVol = Realized volatility\n252 = approximate number of trading days in a year\nt = a counter representing each trading day\nn = number of trading days in the specific time frame\nRt = continuously compounded daily returns\n \nAll the concepts covered in this post are taken from the Quantra course on \nOptions Volatility Strategies: Greeks, GARCH & Python Backtesting\n.\nYou can preview the concepts taught in this course by clicking on the free preview button.\nNote: \nThe links in this tutorial will be accessible only after logging\ninto \nquantra.quantinsti.com\n and enrolling for the free preview of the course.\n   \nAdvantages\nThe realized volatility is the measure of the historical performance of an asset which implies that one comes to know if the asset’s price has been fluctuating a lot or not. Hence, the asset’s volatility is predicted by the historical performance.\nThe realized volatility also concentrates on the time period and hence you can analyse a particular time period in this manner.\nFor measuring the implied volatility (future volatility), an analysis of historical performance is always helpful. Hence, realized volatility is the base of implied volatility.\nDisadvantages\nThe only disadvantage of the realized volatility is that it does not take into account the current price and also does not look into the future volatility, unlike implied volatility. Hence, realized volatility is actually directionless and simply chases the upward and downward trends of the historical data.\nLet us find out realized volatility with the help of Python. We begin with extracting the data from yahoo finance. We will take Amazon’s data here.\n \n# For data manipulation\nimport pandas as pd\nimport numpy as np\n# To fetch financial data\nimport yfinance as yf\n# Download the price data of Apple from Jan 2019 to Dec 2019\n# Set the ticker as 'AAPL' and specify the start and end dates\nprice_data_AMZN= yf.download('AMZN', start='2020-11-06', end='2023-1-3', auto_adjust = True)\nprice_data_AMZN\nOutput:\n[*********************100%***********************]  1 of 1 completed\nOutput:\n \nOpen\nHigh\nLow\nClose\nVolume\nDate\n \n \n \n \n \n2020-11-05\n165.998505\n168.339996\n164.444000\n166.100006\n115786000\n2020-11-06\n165.231995\n166.100006\n161.600006\n165.568497\n92946000\n2020-11-09\n161.551498\n164.449997\n155.605499\n157.186996\n143808000\n2020-11-10\n154.751007\n155.699997\n150.973999\n151.751007\n131820000\n2020-11-11\n153.089005\n156.957504\n152.500000\n156.869507\n87338000\n...\n...\n...\n...\n...\n...\n2022-12-23\n83.250000\n85.779999\n82.930000\n85.250000\n57433700\n2022-12-27\n84.970001\n85.349998\n83.000000\n83.040001\n57284000\n2022-12-28\n82.800003\n83.480003\n81.690002\n81.820000\n58228600\n2022-12-29\n82.870003\n84.550003\n82.550003\n84.180000\n54995900\n2022-12-30\n83.120003\n84.050003\n82.470001\n84.000000\n62401200\n542 rows × 5 columns\nNow, let us plot the data.\n \nimport matplotlib.pyplot as plt\n\n%matplotlib inline\n# Compute the logarithmic returns using the Closing price\nprice_data_AMZN['Log_Ret'] = np.log(price_data_AMZN['Close'] \/ price_data_AMZN['Close'].shift(1))\n# Compute Volatility using the pandas rolling standard deviation function\nprice_data_AMZN['Realized Volatility'] = price_data_AMZN['Log_Ret'].rolling(window=252).std() * \nnp.sqrt(252)\n# Plot the AMZN Price series and the Volatility\nprice_data_AMZN[['Close']].plot(subplots=True, color='blue',figsize=(8, 6))\nplt.title('Close price', color='purple', size=15)\n# Setting axes labels for close prices plot\nplt.xlabel('Dates', {'color': 'orange', 'fontsize':15})\n\nplt.ylabel('Prices', {'color': 'orange', 'fontsize':15})\nprice_data_AMZN[['Realized Volatility']].plot(subplots=True, color='blue',figsize=(8, 6))\n\n \nplt.title('Realized Volatility', color='purple', size=15)\n# Setting axes labels for realized volatility plot\nplt.xlabel('Dates', {'color': 'orange', 'fontsize':15})\nplt.ylabel('Realized volatility', {'color': 'orange', 'fontsize':15})\n# Rotating the values along x-axis to 45 degrees\nplt.xticks(rotation=45)\nOutput:\nThe output above shows a steep rise in the realized volatility between November 2021 and January 2023.\nWhat to do next? \nGo to \nthis\n course \nClick on '\nFree Preview\n'\nGo through 10-15% of course content \nDrop us your comments, queries on \ncommunity\n \n \nAbout the Course Author\nIMPORTANT DISCLAIMER: \nThis post is for educational purposes only and is not a solicitation or recommendation to buy or sell any securities. Investing in financial markets involves risks and you should seek the advice of a licensed financial advisor before making any investment decisions. Your investment decisions are solely your responsibility. The information provided is based on publicly available data and our own analysis, and we do not guarantee its accuracy or completeness. By no means is this communication sent as the licensed equity analysts or financial advisors and it should not be construed as professional advice or a recommendation to buy or sell any securities or any other kind of asset.","attrs_markdown":"NEW\n\n\\+\n\n\\-\n\n\\-\n\nBuild Trading Algos, Use AI & Manage Risk \\| Live Virtual Class\n\nJoin Bootcamp\n\nx\n\n[![Quantra](data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)](https:\/\/quantra.quantinsti.com\/)\n\n- ![Search](https:\/\/d37y0qrjxmff6w.cloudfront.net\/production-new\/static\/images\/icons\/search-icon.cb9e1fde700e33c9.webp)![Search](https:\/\/d37y0qrjxmff6w.cloudfront.net\/production-new\/static\/images\/icons\/search-icon-green.41728036e5a6f411.webp)\n  \n  ![Search](data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)![Search](data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)\n  \n  Speak Now\n  \n  ![Mic Blue](data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)\n- [Courses LIVE CLASS![arrow](data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)](https:\/\/quantra.quantinsti.com\/courses?section=courses)\n  ### Premium Courses\n  - 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It assumes the daily mean price to be zero in order to provide movement regardless of direction. It is different from Implied volatility in the sense that realized volatility is the actual change in historical prices, while implied volatility predicts future price volatility. Realized volatility can be calculated by firstly calculating continuously compounded daily returns using the following formula:\n\n![](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/XWeZ5dIY\/rv1.png)\n\nwhere, **Ln = natural logarithm**\n\n**Pt = Underlying Reference Price (“closing price”) at day t**\n\n**Pt–1 = Underlying Reference Price at day immediately preceding day t**\n\nThen, by plugging the value of Rt in the formula below:\n\n![](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/vlsKfyI0\/rv2.png)\n\nwhere, **Vol = Realized volatility**\n\n**252 = approximate number of trading days in a year**\n\n**t = a counter representing each trading day**\n\n**n = number of trading days in the specific time frame**\n\n**Rt = continuously compounded daily returns**\n\nAll the concepts covered in this post are taken from the Quantra course on **[Options Volatility Strategies: Greeks, GARCH & Python Backtesting](https:\/\/quantra.quantinsti.com\/course\/options-volatility-trading)**. You can preview the concepts taught in this course by clicking on the free preview button.\n\n**Note:** The links in this tutorial will be accessible only after logging into [quantra.quantinsti.com](https:\/\/quantra.quantinsti.com\/) and enrolling for the free preview of the course.\n\n[![Start Free Preview](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/MediaContent\/Wkz2PGU0\/Group-3246.png)](https:\/\/quantra.quantinsti.com\/startCourseDetails?cid=290&section_no=1&unit_no=1&preview=true&course_type=paid&unit_type=Video) [![View Course](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/MediaContent\/rt2enKhG\/Group-3244.png)](https:\/\/quantra.quantinsti.com\/course\/options-volatility-trading)\n***\n##\n## Advantages\n- The realized volatility is the measure of the historical performance of an asset which implies that one comes to know if the asset’s price has been fluctuating a lot or not. Hence, the asset’s volatility is predicted by the historical performance.\n- The realized volatility also concentrates on the time period and hence you can analyse a particular time period in this manner.\n- For measuring the implied volatility (future volatility), an analysis of historical performance is always helpful. Hence, realized volatility is the base of implied volatility.\n***\n##\n## Disadvantages\nThe only disadvantage of the realized volatility is that it does not take into account the current price and also does not look into the future volatility, unlike implied volatility. Hence, realized volatility is actually directionless and simply chases the upward and downward trends of the historical data.\n\nLet us find out realized volatility with the help of Python. We begin with extracting the data from yahoo finance. We will take Amazon’s data here.\n```\n# For data manipulation\n\nimport pandas as pd import numpy as np\n\n# To fetch financial data\n\nimport yfinance as yf\n # Download the price data of Apple from Jan 2019 to Dec 2019 # Set the ticker as 'AAPL' and specify the start and end dates\n price_data_AMZN= yf.download('AMZN', start='2020-11-06', end='2023-1-3', auto_adjust = True) price_data_AMZN \n\nOutput:\n```\n\\[\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*100%\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\] 1 of 1 completed\n\n**Output:**\n\n|   |   |   |   |   |   |\n|---|---|---|---|---|---|\n|   | **Open** | **High** | **Low** | **Close** | **Volume** |\n| **Date** |   |   |   |   |   |\n| **2020-11-05** | 165\\.998505 | 168\\.339996 | 164\\.444000 | 166\\.100006 | 115786000 |\n| **2020-11-06** | 165\\.231995 | 166\\.100006 | 161\\.600006 | 165\\.568497 | 92946000 |\n| **2020-11-09** | 161\\.551498 | 164\\.449997 | 155\\.605499 | 157\\.186996 | 143808000 |\n| **2020-11-10** | 154\\.751007 | 155\\.699997 | 150\\.973999 | 151\\.751007 | 131820000 |\n| **2020-11-11** | 153\\.089005 | 156\\.957504 | 152\\.500000 | 156\\.869507 | 87338000 |\n| **...** | ... | ... | ... | ... | ... |\n| **2022-12-23** | 83\\.250000 | 85\\.779999 | 82\\.930000 | 85\\.250000 | 57433700 |\n| **2022-12-27** | 84\\.970001 | 85\\.349998 | 83\\.000000 | 83\\.040001 | 57284000 |\n| **2022-12-28** | 82\\.800003 | 83\\.480003 | 81\\.690002 | 81\\.820000 | 58228600 |\n| **2022-12-29** | 82\\.870003 | 84\\.550003 | 82\\.550003 | 84\\.180000 | 54995900 |\n| **2022-12-30** | 83\\.120003 | 84\\.050003 | 82\\.470001 | 84\\.000000 | 62401200 |\n\n542 rows × 5 columns\n\nNow, let us plot the data.\n```\nimport matplotlib.pyplot as plt %matplotlib inline\n\n# Compute the logarithmic returns using the Closing price\n\nprice_data_AMZN['Log_Ret'] = np.log(price_data_AMZN['Close'] \/ price_data_AMZN['Close'].shift(1)) \n \n# Compute Volatility using the pandas rolling standard deviation function \nprice_data_AMZN['Realized Volatility'] = price_data_AMZN['Log_Ret'].rolling(window=252).std() * np.sqrt(252) \n \n# Plot the AMZN Price series and the Volatility \nprice_data_AMZN[['Close']].plot(subplots=True, color='blue',figsize=(8, 6)) \nplt.title('Close price', color='purple', size=15) \n  # Setting axes labels for close prices plot\n\nplt.xlabel('Dates', {'color': 'orange', 'fontsize':15}) plt.ylabel('Prices', {'color': 'orange', 'fontsize':15})\n\n \nprice_data_AMZN[['Realized Volatility']].plot(subplots=True, color='blue',figsize=(8, 6)) plt.title('Realized Volatility', color='purple', size=15)\n\n \n# Setting axes labels for realized volatility plot\n\nplt.xlabel('Dates', {'color': 'orange', 'fontsize':15}) \nplt.ylabel('Realized volatility', {'color': 'orange', 'fontsize':15}) \n\n# Rotating the values along x-axis to 45 degrees \nplt.xticks(rotation=45)\n```\n**Output:**\n\n![](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/ZoouET7N\/Screen-Shot-2023-04-24-at-10.46.04-AM.png)  \n The output above shows a steep rise in the realized volatility between November 2021 and January 2023.\n\n## **What to do next?**\n- Go to [this](https:\/\/quantra.quantinsti.com\/course\/options-volatility-trading) course\n- Click on '**[Free Preview](https:\/\/quantra.quantinsti.com\/startCourseDetails?cid=290&section_no=1&unit_no=1&course_type=paid&unit_type=Video)**'\n- Go through 10-15% of course content\n- Drop us your comments, queries on [community](https:\/\/quantra.quantinsti.com\/community)\n\n[![Start Free Preview](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/MediaContent\/Wkz2PGU0\/Group-3246.png)](https:\/\/quantra.quantinsti.com\/startCourseDetails?cid=290&section_no=1&unit_no=1&preview=true&course_type=paid&unit_type=Video)\n\n### **About the Course Author**\n![](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/MediaContent\/dIfDJES4\/Group-113.png)\n***\nIMPORTANT DISCLAIMER: *This post is for educational purposes only and is not a solicitation or recommendation to buy or sell any securities. Investing in financial markets involves risks and you should seek the advice of a licensed financial advisor before making any investment decisions. Your investment decisions are solely your responsibility. The information provided is based on publicly available data and our own analysis, and we do not guarantee its accuracy or completeness. By no means is this communication sent as the licensed equity analysts or financial advisors and it should not be construed as professional advice or a recommendation to buy or sell any securities or any other kind of asset.*\n\nRELATED KEYWORDS\n\n- [Dispersion Trading](https:\/\/quantra.quantinsti.com\/glossary\/Dispersion-Trading)\n- [Implied Volatility](https:\/\/quantra.quantinsti.com\/glossary\/Implied-Volatility)\n- [Standard Deviation](https:\/\/quantra.quantinsti.com\/glossary\/Standard-Deviation)\n- [Volatility](https:\/\/quantra.quantinsti.com\/glossary\/Volatility)\n- [Volatility Arbitrage](https:\/\/quantra.quantinsti.com\/glossary\/Volatility-Arbitrage)\n- [Volatility Skew](https:\/\/quantra.quantinsti.com\/glossary\/Volatility-Skew)\n- [Volatility Smile](https:\/\/quantra.quantinsti.com\/glossary\/Volatility-Smile)\n- [Volatility Surface](https:\/\/quantra.quantinsti.com\/glossary\/Volatility-Surface)\n- [VWAP](https:\/\/quantra.quantinsti.com\/glossary\/VWAP)\n\n- [About Us](https:\/\/www.quantinsti.com\/about-us)\n- [QuantInsti](https:\/\/www.quantinsti.com\/)\n- [Blueshift](https:\/\/blueshift.quantinsti.com\/)\n- [Associates](https:\/\/www.quantinsti.com\/associates)\n- [Contact Us](https:\/\/www.quantinsti.com\/contact-us\/#inquiry=quantra)\n- [Affiliate Program](https:\/\/quantinsti.tapfiliate.com\/)\n- [Privacy Policy](https:\/\/www.quantinsti.com\/privacy-policy\/)\n\n- [FAQs](https:\/\/quantra.quantinsti.com\/docs\/)\n- [Courses](https:\/\/quantra.quantinsti.com\/courses)\n- [Blog](https:\/\/blog.quantinsti.com\/)\n- [For Business](https:\/\/quantra.quantinsti.com\/corporate)\n- [Success Stories](https:\/\/quantra.quantinsti.com\/successful-quants)\n- [Community](https:\/\/quantra.quantinsti.com\/community)\n- [Glossary](https:\/\/quantra.quantinsti.com\/glossary)\n\n- [![X](https:\/\/d37y0qrjxmff6w.cloudfront.net\/production-new\/static\/images\/social-icons\/X.954552b1a485c079.svg)](https:\/\/x.com\/quantinsti\/)\n- [![Facebook](https:\/\/d37y0qrjxmff6w.cloudfront.net\/production-new\/static\/images\/social-icons\/FB.eebd059a1b20a291.svg)](https:\/\/www.facebook.com\/quantinsti)\n- [![LinkedIn](https:\/\/d37y0qrjxmff6w.cloudfront.net\/production-new\/static\/images\/social-icons\/Linkedin.44d73acf4f25701e.svg)](https:\/\/www.linkedin.com\/school\/1229089)\n- [![Youtube](https:\/\/d37y0qrjxmff6w.cloudfront.net\/production-new\/static\/images\/social-icons\/YT.3a414f2705f0bdec.svg)](https:\/\/www.youtube.com\/c\/Quantra)\n- [![Instagram](https:\/\/d37y0qrjxmff6w.cloudfront.net\/production-new\/static\/images\/social-icons\/IG.224eb7351902f1ac.svg)](https:\/\/www.instagram.com\/quantinstian\/)\n- [![Github](https:\/\/d37y0qrjxmff6w.cloudfront.net\/production-new\/static\/images\/social-icons\/Github.3570b93d70878364.svg)](https:\/\/github.com\/quantinsti)\n\n[![Quantinsti](https:\/\/d37y0qrjxmff6w.cloudfront.net\/production-new\/static\/images\/quantinsti-logo.2c0a345f6f588ab6.png)](https:\/\/www.quantinsti.com\/)\n\n©2026 QuantInsti® - Quantra® is a trademark property of QuantInsti®\n\n#### Our Cookie Policy\nTo give you the best user experience, through analytics, and to show you tailored & most relevant content on our website, we use cookies. Please note that by closing this banner, scrolling this page, clicking a link or continuing to use our site, you consent to our use of cookies. You can read more about our privacy policy  [here](https:\/\/www.quantinsti.com\/privacy-policy\/)\n\nAccept all cookies","attrs_readable_markdown":"## Introduction\nRealized volatility refers to the measure of daily changes in the price of a security over a particular period of time. It assumes the daily mean price to be zero in order to provide movement regardless of direction. It is different from Implied volatility in the sense that realized volatility is the actual change in historical prices, while implied volatility predicts future price volatility. Realized volatility can be calculated by firstly calculating continuously compounded daily returns using the following formula:\n\n![](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/XWeZ5dIY\/rv1.png)\n\nwhere, **Ln = natural logarithm**\n\n**Pt = Underlying Reference Price (“closing price”) at day t**\n\n**Pt–1 = Underlying Reference Price at day immediately preceding day t**\n\nThen, by plugging the value of Rt in the formula below:\n\n![](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/vlsKfyI0\/rv2.png)\n\nwhere, **Vol = Realized volatility**\n\n**252 = approximate number of trading days in a year**\n\n**t = a counter representing each trading day**\n\n**n = number of trading days in the specific time frame**\n\n**Rt = continuously compounded daily returns**\n\nAll the concepts covered in this post are taken from the Quantra course on **[Options Volatility Strategies: Greeks, GARCH & Python Backtesting](https:\/\/quantra.quantinsti.com\/course\/options-volatility-trading)**. You can preview the concepts taught in this course by clicking on the free preview button.\n\n**Note:** The links in this tutorial will be accessible only after logging into [quantra.quantinsti.com](https:\/\/quantra.quantinsti.com\/) and enrolling for the free preview of the course.\n\n[![Start Free Preview](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/MediaContent\/Wkz2PGU0\/Group-3246.png)](https:\/\/quantra.quantinsti.com\/startCourseDetails?cid=290&section_no=1&unit_no=1&preview=true&course_type=paid&unit_type=Video) [![View Course](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/MediaContent\/rt2enKhG\/Group-3244.png)](https:\/\/quantra.quantinsti.com\/course\/options-volatility-trading)\n***\n## Advantages\n- The realized volatility is the measure of the historical performance of an asset which implies that one comes to know if the asset’s price has been fluctuating a lot or not. Hence, the asset’s volatility is predicted by the historical performance.\n- The realized volatility also concentrates on the time period and hence you can analyse a particular time period in this manner.\n- For measuring the implied volatility (future volatility), an analysis of historical performance is always helpful. Hence, realized volatility is the base of implied volatility.\n***\n## Disadvantages\nThe only disadvantage of the realized volatility is that it does not take into account the current price and also does not look into the future volatility, unlike implied volatility. Hence, realized volatility is actually directionless and simply chases the upward and downward trends of the historical data.\n\nLet us find out realized volatility with the help of Python. We begin with extracting the data from yahoo finance. We will take Amazon’s data here.\n```\n# For data manipulation\n\nimport pandas as pd import numpy as np\n\n# To fetch financial data\n\nimport yfinance as yf\n # Download the price data of Apple from Jan 2019 to Dec 2019 # Set the ticker as 'AAPL' and specify the start and end dates\n price_data_AMZN= yf.download('AMZN', start='2020-11-06', end='2023-1-3', auto_adjust = True) price_data_AMZN \n\nOutput:\n```\n\\[\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*100%\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\*\\] 1 of 1 completed\n\n**Output:**\n\n|   |   |   |   |   |   |\n|---|---|---|---|---|---|\n|   | **Open** | **High** | **Low** | **Close** | **Volume** |\n| **Date** |   |   |   |   |   |\n| **2020-11-05** | 165\\.998505 | 168\\.339996 | 164\\.444000 | 166\\.100006 | 115786000 |\n| **2020-11-06** | 165\\.231995 | 166\\.100006 | 161\\.600006 | 165\\.568497 | 92946000 |\n| **2020-11-09** | 161\\.551498 | 164\\.449997 | 155\\.605499 | 157\\.186996 | 143808000 |\n| **2020-11-10** | 154\\.751007 | 155\\.699997 | 150\\.973999 | 151\\.751007 | 131820000 |\n| **2020-11-11** | 153\\.089005 | 156\\.957504 | 152\\.500000 | 156\\.869507 | 87338000 |\n| **...** | ... | ... | ... | ... | ... |\n| **2022-12-23** | 83\\.250000 | 85\\.779999 | 82\\.930000 | 85\\.250000 | 57433700 |\n| **2022-12-27** | 84\\.970001 | 85\\.349998 | 83\\.000000 | 83\\.040001 | 57284000 |\n| **2022-12-28** | 82\\.800003 | 83\\.480003 | 81\\.690002 | 81\\.820000 | 58228600 |\n| **2022-12-29** | 82\\.870003 | 84\\.550003 | 82\\.550003 | 84\\.180000 | 54995900 |\n| **2022-12-30** | 83\\.120003 | 84\\.050003 | 82\\.470001 | 84\\.000000 | 62401200 |\n\n542 rows × 5 columns\n\nNow, let us plot the data.\n```\nimport matplotlib.pyplot as plt %matplotlib inline\n\n# Compute the logarithmic returns using the Closing price\n\nprice_data_AMZN['Log_Ret'] = np.log(price_data_AMZN['Close'] \/ price_data_AMZN['Close'].shift(1)) \n \n# Compute Volatility using the pandas rolling standard deviation function \nprice_data_AMZN['Realized Volatility'] = price_data_AMZN['Log_Ret'].rolling(window=252).std() * np.sqrt(252) \n \n# Plot the AMZN Price series and the Volatility \nprice_data_AMZN[['Close']].plot(subplots=True, color='blue',figsize=(8, 6)) \nplt.title('Close price', color='purple', size=15) \n  # Setting axes labels for close prices plot\n\nplt.xlabel('Dates', {'color': 'orange', 'fontsize':15}) plt.ylabel('Prices', {'color': 'orange', 'fontsize':15})\n\n \nprice_data_AMZN[['Realized Volatility']].plot(subplots=True, color='blue',figsize=(8, 6)) plt.title('Realized Volatility', color='purple', size=15)\n\n \n# Setting axes labels for realized volatility plot\n\nplt.xlabel('Dates', {'color': 'orange', 'fontsize':15}) \nplt.ylabel('Realized volatility', {'color': 'orange', 'fontsize':15}) \n\n# Rotating the values along x-axis to 45 degrees \nplt.xticks(rotation=45)\n```\n**Output:**\n\n![](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/ZoouET7N\/Screen-Shot-2023-04-24-at-10.46.04-AM.png)  \n The output above shows a steep rise in the realized volatility between November 2021 and January 2023.\n\n## **What to do next?**\n- Go to [this](https:\/\/quantra.quantinsti.com\/course\/options-volatility-trading) course\n- Click on '**[Free Preview](https:\/\/quantra.quantinsti.com\/startCourseDetails?cid=290&section_no=1&unit_no=1&course_type=paid&unit_type=Video)**'\n- Go through 10-15% of course content\n- Drop us your comments, queries on [community](https:\/\/quantra.quantinsti.com\/community)\n\n[![Start Free Preview](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/MediaContent\/Wkz2PGU0\/Group-3246.png)](https:\/\/quantra.quantinsti.com\/startCourseDetails?cid=290&section_no=1&unit_no=1&preview=true&course_type=paid&unit_type=Video)\n\n### **About the Course Author**\n![](https:\/\/d2a032ejo53cab.cloudfront.net\/Glossary\/MediaContent\/dIfDJES4\/Group-113.png)\n***\nIMPORTANT DISCLAIMER: *This post is for educational purposes only and is not a solicitation or recommendation to buy or sell any securities. Investing in financial markets involves risks and you should seek the advice of a licensed financial advisor before making any investment decisions. Your investment decisions are solely your responsibility. The information provided is based on publicly available data and our own analysis, and we do not guarantee its accuracy or completeness. By no means is this communication sent as the licensed equity analysts or financial advisors and it should not be construed as professional advice or a recommendation to buy or sell any securities or any other kind of asset.*","meta_canonical":null}

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Boilerpipe Text	Introduction Realized volatility refers to the measure of daily changes in the price of a security over a particular period of time. It assumes the daily mean price to be zero in order to provide movement regardless of direction. It is different from Implied volatility in the sense that realized volatility is the actual change in historical prices, while implied volatility predicts future price volatility. Realized volatility can be calculated by firstly calculating continuously compounded daily returns using the following formula: where, Ln = natural logarithm Pt = Underlying Reference Price (“closing price”) at day t Pt–1 = Underlying Reference Price at day immediately preceding day t Then, by plugging the value of Rt in the formula below: where, Vol = Realized volatility 252 = approximate number of trading days in a year t = a counter representing each trading day n = number of trading days in the specific time frame Rt = continuously compounded daily returns All the concepts covered in this post are taken from the Quantra course on Options Volatility Strategies: Greeks, GARCH & Python Backtesting . You can preview the concepts taught in this course by clicking on the free preview button. Note: The links in this tutorial will be accessible only after logging into quantra.quantinsti.com and enrolling for the free preview of the course. Advantages The realized volatility is the measure of the historical performance of an asset which implies that one comes to know if the asset’s price has been fluctuating a lot or not. Hence, the asset’s volatility is predicted by the historical performance. The realized volatility also concentrates on the time period and hence you can analyse a particular time period in this manner. For measuring the implied volatility (future volatility), an analysis of historical performance is always helpful. Hence, realized volatility is the base of implied volatility. Disadvantages The only disadvantage of the realized volatility is that it does not take into account the current price and also does not look into the future volatility, unlike implied volatility. Hence, realized volatility is actually directionless and simply chases the upward and downward trends of the historical data. Let us find out realized volatility with the help of Python. We begin with extracting the data from yahoo finance. We will take Amazon’s data here. # For data manipulation import pandas as pd import numpy as np # To fetch financial data import yfinance as yf # Download the price data of Apple from Jan 2019 to Dec 2019 # Set the ticker as 'AAPL' and specify the start and end dates price_data_AMZN= yf.download('AMZN', start='2020-11-06', end='2023-1-3', auto_adjust = True) price_data_AMZN Output: [*******************100%********************] 1 of 1 completed Output: Open High Low Close Volume Date 2020-11-05 165.998505 168.339996 164.444000 166.100006 115786000 2020-11-06 165.231995 166.100006 161.600006 165.568497 92946000 2020-11-09 161.551498 164.449997 155.605499 157.186996 143808000 2020-11-10 154.751007 155.699997 150.973999 151.751007 131820000 2020-11-11 153.089005 156.957504 152.500000 156.869507 87338000 ... ... ... ... ... ... 2022-12-23 83.250000 85.779999 82.930000 85.250000 57433700 2022-12-27 84.970001 85.349998 83.000000 83.040001 57284000 2022-12-28 82.800003 83.480003 81.690002 81.820000 58228600 2022-12-29 82.870003 84.550003 82.550003 84.180000 54995900 2022-12-30 83.120003 84.050003 82.470001 84.000000 62401200 542 rows × 5 columns Now, let us plot the data. import matplotlib.pyplot as plt %matplotlib inline # Compute the logarithmic returns using the Closing price price_data_AMZN['Log_Ret'] = np.log(price_data_AMZN['Close'] / price_data_AMZN['Close'].shift(1)) # Compute Volatility using the pandas rolling standard deviation function price_data_AMZN['Realized Volatility'] = price_data_AMZN['Log_Ret'].rolling(window=252).std() np.sqrt(252) # Plot the AMZN Price series and the Volatility price_data_AMZN[['Close']].plot(subplots=True, color='blue',figsize=(8, 6)) plt.title('Close price', color='purple', size=15) # Setting axes labels for close prices plot plt.xlabel('Dates', {'color': 'orange', 'fontsize':15}) plt.ylabel('Prices', {'color': 'orange', 'fontsize':15}) price_data_AMZN[['Realized Volatility']].plot(subplots=True, color='blue',figsize=(8, 6)) plt.title('Realized Volatility', color='purple', size=15) # Setting axes labels for realized volatility plot plt.xlabel('Dates', {'color': 'orange', 'fontsize':15}) plt.ylabel('Realized volatility', {'color': 'orange', 'fontsize':15}) # Rotating the values along x-axis to 45 degrees plt.xticks(rotation=45) Output: The output above shows a steep rise in the realized volatility between November 2021 and January 2023. What to do next? Go to this course Click on ' Free Preview ' Go through 10-15% of course content Drop us your comments, queries on community About the Course Author IMPORTANT DISCLAIMER: This post is for educational purposes only and is not a solicitation or recommendation to buy or sell any securities. Investing in financial markets involves risks and you should seek the advice of a licensed financial advisor before making any investment decisions. Your investment decisions are solely your responsibility. The information provided is based on publicly available data and our own analysis, and we do not guarantee its accuracy or completeness. By no means is this communication sent as the licensed equity analysts or financial advisors and it should not be construed as professional advice or a recommendation to buy or sell any securities or any other kind of asset.
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It assumes the daily mean price to be zero in order to provide movement regardless of direction. It is different from Implied volatility in the sense that realized volatility is the actual change in historical prices, while implied volatility predicts future price volatility. Realized volatility can be calculated by firstly calculating continuously compounded daily returns using the following formula: ![](https://d2a032ejo53cab.cloudfront.net/Glossary/XWeZ5dIY/rv1.png) where, Ln = natural logarithm Pt = Underlying Reference Price (“closing price”) at day t Pt–1 = Underlying Reference Price at day immediately preceding day t Then, by plugging the value of Rt in the formula below: ![](https://d2a032ejo53cab.cloudfront.net/Glossary/vlsKfyI0/rv2.png) where, Vol = Realized volatility 252 = approximate number of trading days in a year t = a counter representing each trading day n = number of trading days in the specific time frame Rt = continuously compounded daily returns All the concepts covered in this post are taken from the Quantra course on [Options Volatility Strategies: Greeks, GARCH & Python Backtesting](https://quantra.quantinsti.com/course/options-volatility-trading). You can preview the concepts taught in this course by clicking on the free preview button. Note: The links in this tutorial will be accessible only after logging into [quantra.quantinsti.com](https://quantra.quantinsti.com/) and enrolling for the free preview of the course. [![Start Free Preview](https://d2a032ejo53cab.cloudfront.net/Glossary/MediaContent/Wkz2PGU0/Group-3246.png)](https://quantra.quantinsti.com/startCourseDetails?cid=290&section_no=1&unit_no=1&preview=true&course_type=paid&unit_type=Video) [![View Course](https://d2a032ejo53cab.cloudfront.net/Glossary/MediaContent/rt2enKhG/Group-3244.png)](https://quantra.quantinsti.com/course/options-volatility-trading) * ## ## Advantages - The realized volatility is the measure of the historical performance of an asset which implies that one comes to know if the asset’s price has been fluctuating a lot or not. Hence, the asset’s volatility is predicted by the historical performance. - The realized volatility also concentrates on the time period and hence you can analyse a particular time period in this manner. - For measuring the implied volatility (future volatility), an analysis of historical performance is always helpful. Hence, realized volatility is the base of implied volatility. * ## ## Disadvantages The only disadvantage of the realized volatility is that it does not take into account the current price and also does not look into the future volatility, unlike implied volatility. Hence, realized volatility is actually directionless and simply chases the upward and downward trends of the historical data. Let us find out realized volatility with the help of Python. We begin with extracting the data from yahoo finance. We will take Amazon’s data here. ``` # For data manipulation import pandas as pd import numpy as np # To fetch financial data import yfinance as yf # Download the price data of Apple from Jan 2019 to Dec 2019 # Set the ticker as 'AAPL' and specify the start and end dates price_data_AMZN= yf.download('AMZN', start='2020-11-06', end='2023-1-3', auto_adjust = True) price_data_AMZN Output: ``` \[\\\\\\\\\\\\\\\\\\\\\100%\\\\\\\\\\\\\\\\\\\\\\\\] 1 of 1 completed Output: \| \| \| \| \| \| \| \|---\|---\|---\|---\|---\|---\| \| \| Open \| High \| Low \| Close \| Volume \| \| Date \| \| \| \| \| \| \| 2020-11-05 \| 165\.998505 \| 168\.339996 \| 164\.444000 \| 166\.100006 \| 115786000 \| \| 2020-11-06 \| 165\.231995 \| 166\.100006 \| 161\.600006 \| 165\.568497 \| 92946000 \| \| 2020-11-09 \| 161\.551498 \| 164\.449997 \| 155\.605499 \| 157\.186996 \| 143808000 \| \| 2020-11-10 \| 154\.751007 \| 155\.699997 \| 150\.973999 \| 151\.751007 \| 131820000 \| \| 2020-11-11 \| 153\.089005 \| 156\.957504 \| 152\.500000 \| 156\.869507 \| 87338000 \| \| ... \| ... \| ... \| ... \| ... \| ... \| \| 2022-12-23 \| 83\.250000 \| 85\.779999 \| 82\.930000 \| 85\.250000 \| 57433700 \| \| 2022-12-27 \| 84\.970001 \| 85\.349998 \| 83\.000000 \| 83\.040001 \| 57284000 \| \| 2022-12-28 \| 82\.800003 \| 83\.480003 \| 81\.690002 \| 81\.820000 \| 58228600 \| \| 2022-12-29 \| 82\.870003 \| 84\.550003 \| 82\.550003 \| 84\.180000 \| 54995900 \| \| 2022-12-30 \| 83\.120003 \| 84\.050003 \| 82\.470001 \| 84\.000000 \| 62401200 \| 542 rows × 5 columns Now, let us plot the data. ``` import matplotlib.pyplot as plt %matplotlib inline # Compute the logarithmic returns using the Closing price price_data_AMZN['Log_Ret'] = np.log(price_data_AMZN['Close'] / price_data_AMZN['Close'].shift(1)) # Compute Volatility using the pandas rolling standard deviation function price_data_AMZN['Realized Volatility'] = price_data_AMZN['Log_Ret'].rolling(window=252).std() * np.sqrt(252) # Plot the AMZN Price series and the Volatility price_data_AMZN[['Close']].plot(subplots=True, color='blue',figsize=(8, 6)) plt.title('Close price', color='purple', size=15) # Setting axes labels for close prices plot plt.xlabel('Dates', {'color': 'orange', 'fontsize':15}) plt.ylabel('Prices', {'color': 'orange', 'fontsize':15}) price_data_AMZN[['Realized Volatility']].plot(subplots=True, color='blue',figsize=(8, 6)) plt.title('Realized Volatility', color='purple', size=15) # Setting axes labels for realized volatility plot plt.xlabel('Dates', {'color': 'orange', 'fontsize':15}) plt.ylabel('Realized volatility', {'color': 'orange', 'fontsize':15}) # Rotating the values along x-axis to 45 degrees plt.xticks(rotation=45) ``` Output: ![](https://d2a032ejo53cab.cloudfront.net/Glossary/ZoouET7N/Screen-Shot-2023-04-24-at-10.46.04-AM.png) The output above shows a steep rise in the realized volatility between November 2021 and January 2023. ## What to do next? - Go to [this](https://quantra.quantinsti.com/course/options-volatility-trading) course - Click on '[Free Preview](https://quantra.quantinsti.com/startCourseDetails?cid=290&section_no=1&unit_no=1&course_type=paid&unit_type=Video)' - Go through 10-15% of course content - Drop us your comments, queries on [community](https://quantra.quantinsti.com/community) [![Start Free Preview](https://d2a032ejo53cab.cloudfront.net/Glossary/MediaContent/Wkz2PGU0/Group-3246.png)](https://quantra.quantinsti.com/startCourseDetails?cid=290&section_no=1&unit_no=1&preview=true&course_type=paid&unit_type=Video) ### About the Course Author ![](https://d2a032ejo53cab.cloudfront.net/Glossary/MediaContent/dIfDJES4/Group-113.png) *** IMPORTANT DISCLAIMER: This post is for educational purposes only and is not a solicitation or recommendation to buy or sell any securities. Investing in financial markets involves risks and you should seek the advice of a licensed financial advisor before making any investment decisions. Your investment decisions are solely your responsibility. The information provided is based on publicly available data and our own analysis, and we do not guarantee its accuracy or completeness. By no means is this communication sent as the licensed equity analysts or financial advisors and it should not be construed as professional advice or a recommendation to buy or sell any securities or any other kind of asset. RELATED KEYWORDS - [Dispersion Trading](https://quantra.quantinsti.com/glossary/Dispersion-Trading) - [Implied Volatility](https://quantra.quantinsti.com/glossary/Implied-Volatility) - [Standard Deviation](https://quantra.quantinsti.com/glossary/Standard-Deviation) - [Volatility](https://quantra.quantinsti.com/glossary/Volatility) - [Volatility Arbitrage](https://quantra.quantinsti.com/glossary/Volatility-Arbitrage) - [Volatility Skew](https://quantra.quantinsti.com/glossary/Volatility-Skew) - [Volatility Smile](https://quantra.quantinsti.com/glossary/Volatility-Smile) - [Volatility Surface](https://quantra.quantinsti.com/glossary/Volatility-Surface) - [VWAP](https://quantra.quantinsti.com/glossary/VWAP) - [About Us](https://www.quantinsti.com/about-us) - [QuantInsti](https://www.quantinsti.com/) - [Blueshift](https://blueshift.quantinsti.com/) - [Associates](https://www.quantinsti.com/associates) - [Contact Us](https://www.quantinsti.com/contact-us/#inquiry=quantra) - [Affiliate Program](https://quantinsti.tapfiliate.com/) - [Privacy Policy](https://www.quantinsti.com/privacy-policy/) - [FAQs](https://quantra.quantinsti.com/docs/) - [Courses](https://quantra.quantinsti.com/courses) - [Blog](https://blog.quantinsti.com/) - [For Business](https://quantra.quantinsti.com/corporate) - [Success Stories](https://quantra.quantinsti.com/successful-quants) - [Community](https://quantra.quantinsti.com/community) - [Glossary](https://quantra.quantinsti.com/glossary) - [![X](https://d37y0qrjxmff6w.cloudfront.net/production-new/static/images/social-icons/X.954552b1a485c079.svg)](https://x.com/quantinsti/) - [![Facebook](https://d37y0qrjxmff6w.cloudfront.net/production-new/static/images/social-icons/FB.eebd059a1b20a291.svg)](https://www.facebook.com/quantinsti) - [![LinkedIn](https://d37y0qrjxmff6w.cloudfront.net/production-new/static/images/social-icons/Linkedin.44d73acf4f25701e.svg)](https://www.linkedin.com/school/1229089) - [![Youtube](https://d37y0qrjxmff6w.cloudfront.net/production-new/static/images/social-icons/YT.3a414f2705f0bdec.svg)](https://www.youtube.com/c/Quantra) - [![Instagram](https://d37y0qrjxmff6w.cloudfront.net/production-new/static/images/social-icons/IG.224eb7351902f1ac.svg)](https://www.instagram.com/quantinstian/) - [![Github](https://d37y0qrjxmff6w.cloudfront.net/production-new/static/images/social-icons/Github.3570b93d70878364.svg)](https://github.com/quantinsti) [![Quantinsti](https://d37y0qrjxmff6w.cloudfront.net/production-new/static/images/quantinsti-logo.2c0a345f6f588ab6.png)](https://www.quantinsti.com/) ©2026 QuantInsti® - Quantra® is a trademark property of QuantInsti® #### Our Cookie Policy To give you the best user experience, through analytics, and to show you tailored & most relevant content on our website, we use cookies. 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Readable Markdown	## Introduction Realized volatility refers to the measure of daily changes in the price of a security over a particular period of time. It assumes the daily mean price to be zero in order to provide movement regardless of direction. It is different from Implied volatility in the sense that realized volatility is the actual change in historical prices, while implied volatility predicts future price volatility. Realized volatility can be calculated by firstly calculating continuously compounded daily returns using the following formula: ![](https://d2a032ejo53cab.cloudfront.net/Glossary/XWeZ5dIY/rv1.png) where, Ln = natural logarithm Pt = Underlying Reference Price (“closing price”) at day t Pt–1 = Underlying Reference Price at day immediately preceding day t Then, by plugging the value of Rt in the formula below: ![](https://d2a032ejo53cab.cloudfront.net/Glossary/vlsKfyI0/rv2.png) where, Vol = Realized volatility 252 = approximate number of trading days in a year t = a counter representing each trading day n = number of trading days in the specific time frame Rt = continuously compounded daily returns All the concepts covered in this post are taken from the Quantra course on [Options Volatility Strategies: Greeks, GARCH & Python Backtesting](https://quantra.quantinsti.com/course/options-volatility-trading). You can preview the concepts taught in this course by clicking on the free preview button. Note: The links in this tutorial will be accessible only after logging into [quantra.quantinsti.com](https://quantra.quantinsti.com/) and enrolling for the free preview of the course. [![Start Free Preview](https://d2a032ejo53cab.cloudfront.net/Glossary/MediaContent/Wkz2PGU0/Group-3246.png)](https://quantra.quantinsti.com/startCourseDetails?cid=290&section_no=1&unit_no=1&preview=true&course_type=paid&unit_type=Video) [![View Course](https://d2a032ejo53cab.cloudfront.net/Glossary/MediaContent/rt2enKhG/Group-3244.png)](https://quantra.quantinsti.com/course/options-volatility-trading) * ## Advantages - The realized volatility is the measure of the historical performance of an asset which implies that one comes to know if the asset’s price has been fluctuating a lot or not. Hence, the asset’s volatility is predicted by the historical performance. - The realized volatility also concentrates on the time period and hence you can analyse a particular time period in this manner. - For measuring the implied volatility (future volatility), an analysis of historical performance is always helpful. Hence, realized volatility is the base of implied volatility. * ## Disadvantages The only disadvantage of the realized volatility is that it does not take into account the current price and also does not look into the future volatility, unlike implied volatility. Hence, realized volatility is actually directionless and simply chases the upward and downward trends of the historical data. Let us find out realized volatility with the help of Python. We begin with extracting the data from yahoo finance. We will take Amazon’s data here. ``` # For data manipulation import pandas as pd import numpy as np # To fetch financial data import yfinance as yf # Download the price data of Apple from Jan 2019 to Dec 2019 # Set the ticker as 'AAPL' and specify the start and end dates price_data_AMZN= yf.download('AMZN', start='2020-11-06', end='2023-1-3', auto_adjust = True) price_data_AMZN Output: ``` \[\\\\\\\\\\\\\\\\\\\\\100%\\\\\\\\\\\\\\\\\\\\\\\\] 1 of 1 completed Output: \| \| \| \| \| \| \| \|---\|---\|---\|---\|---\|---\| \| \| Open \| High \| Low \| Close \| Volume \| \| Date \| \| \| \| \| \| \| 2020-11-05 \| 165\.998505 \| 168\.339996 \| 164\.444000 \| 166\.100006 \| 115786000 \| \| 2020-11-06 \| 165\.231995 \| 166\.100006 \| 161\.600006 \| 165\.568497 \| 92946000 \| \| 2020-11-09 \| 161\.551498 \| 164\.449997 \| 155\.605499 \| 157\.186996 \| 143808000 \| \| 2020-11-10 \| 154\.751007 \| 155\.699997 \| 150\.973999 \| 151\.751007 \| 131820000 \| \| 2020-11-11 \| 153\.089005 \| 156\.957504 \| 152\.500000 \| 156\.869507 \| 87338000 \| \| ... \| ... \| ... \| ... \| ... \| ... \| \| 2022-12-23 \| 83\.250000 \| 85\.779999 \| 82\.930000 \| 85\.250000 \| 57433700 \| \| 2022-12-27 \| 84\.970001 \| 85\.349998 \| 83\.000000 \| 83\.040001 \| 57284000 \| \| 2022-12-28 \| 82\.800003 \| 83\.480003 \| 81\.690002 \| 81\.820000 \| 58228600 \| \| 2022-12-29 \| 82\.870003 \| 84\.550003 \| 82\.550003 \| 84\.180000 \| 54995900 \| \| 2022-12-30 \| 83\.120003 \| 84\.050003 \| 82\.470001 \| 84\.000000 \| 62401200 \| 542 rows × 5 columns Now, let us plot the data. ``` import matplotlib.pyplot as plt %matplotlib inline # Compute the logarithmic returns using the Closing price price_data_AMZN['Log_Ret'] = np.log(price_data_AMZN['Close'] / price_data_AMZN['Close'].shift(1)) # Compute Volatility using the pandas rolling standard deviation function price_data_AMZN['Realized Volatility'] = price_data_AMZN['Log_Ret'].rolling(window=252).std() * np.sqrt(252) # Plot the AMZN Price series and the Volatility price_data_AMZN[['Close']].plot(subplots=True, color='blue',figsize=(8, 6)) plt.title('Close price', color='purple', size=15) # Setting axes labels for close prices plot plt.xlabel('Dates', {'color': 'orange', 'fontsize':15}) plt.ylabel('Prices', {'color': 'orange', 'fontsize':15}) price_data_AMZN[['Realized Volatility']].plot(subplots=True, color='blue',figsize=(8, 6)) plt.title('Realized Volatility', color='purple', size=15) # Setting axes labels for realized volatility plot plt.xlabel('Dates', {'color': 'orange', 'fontsize':15}) plt.ylabel('Realized volatility', {'color': 'orange', 'fontsize':15}) # Rotating the values along x-axis to 45 degrees plt.xticks(rotation=45) ``` Output: ![](https://d2a032ejo53cab.cloudfront.net/Glossary/ZoouET7N/Screen-Shot-2023-04-24-at-10.46.04-AM.png) The output above shows a steep rise in the realized volatility between November 2021 and January 2023. ## What to do next? - Go to [this](https://quantra.quantinsti.com/course/options-volatility-trading) course - Click on '[Free Preview](https://quantra.quantinsti.com/startCourseDetails?cid=290&section_no=1&unit_no=1&course_type=paid&unit_type=Video)' - Go through 10-15% of course content - Drop us your comments, queries on [community](https://quantra.quantinsti.com/community) [![Start Free Preview](https://d2a032ejo53cab.cloudfront.net/Glossary/MediaContent/Wkz2PGU0/Group-3246.png)](https://quantra.quantinsti.com/startCourseDetails?cid=290&section_no=1&unit_no=1&preview=true&course_type=paid&unit_type=Video) ### About the Course Author ![](https://d2a032ejo53cab.cloudfront.net/Glossary/MediaContent/dIfDJES4/Group-113.png) *** IMPORTANT DISCLAIMER: This post is for educational purposes only and is not a solicitation or recommendation to buy or sell any securities. Investing in financial markets involves risks and you should seek the advice of a licensed financial advisor before making any investment decisions. Your investment decisions are solely your responsibility. The information provided is based on publicly available data and our own analysis, and we do not guarantee its accuracy or completeness. By no means is this communication sent as the licensed equity analysts or financial advisors and it should not be construed as professional advice or a recommendation to buy or sell any securities or any other kind of asset.
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