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1. Shard Calculation

Query:

Response:

Calculated Shard: 59 (from laksa151)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa059.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://quantnet.com/threads/realized-volatility-calculation.4914/\')), getAhrefsUnparsedNoserviceFromURL(\'https://quantnet.com/threads/realized-volatility-calculation.4914/\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/","crawl_time":1776291620,"first_indexed_time":1526114666,"http_code":200,"src_unparsed":"com,quantnet!\/threads\/realized-volatility-calculation.4914\/ s443","src_root_hash":"8281911274504672659","history_drop_reason":null,"meta_title":"Realized Volatility Calculation | QuantNet","meta_descriptions":["Hi, I am confused about the formula for calculating realized or historical volatility over a period of time. Paul Wilmott claims the formula in his book..."],"attrs_boilerpipe_text":"#2\nIn the case of common stocks, the expectation of daily log return is about zero.\n#3\nvariance is additive\ntherefore, number of trading days in a year * square of daily returns =annualized variance., you assume that the mean of these daily returns is zero.\nso annualized volatility = average daily return*(252)^.5.\nyou would change the trading days based on the product you are trading.\n#4\nThe trade 2 win calculation is correct, I am pretty sure that is what Wilmott must have meant also.\n#5\nThanks, I wasn't expecting that the mean was assumed to be zero.\n#6\nIn finance, we don't care about how the drift udt might vary over time, so it is good to have a volatility estimate independent of time drift estimate. True, you can use a R=udt+sdW to estimate s, but at the same time you assume u holds constant among your sample and estimate of s is based on that. Thus Wilmott's or Shreve's method derived from Ito's Calculus is preferable.\n#7\nHi,\nI am confused about the formula for calculating realized or historical volatility over a period of time.\nPaul Wilmott claims the formula in his book is:\nSQRT(252) * SQRT(AVERAGE_OF_LOG_RETURNS)\nBut in some other sources, it involves the average variance from the mean, for example\nhttp:\/\/www.trade2win.com\/boards\/att...498-volatility-historical-volatility-calc.doc\nWhich is right?\nThanks,\nwell, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat\/prob.\n#8\nHi,\nI am confused about the formula for calculating realized or historical volatility over a period of time.\nPaul Wilmott claims the formula in his book is:\nSQRT(252) * SQRT(AVERAGE_OF_LOG_RETURNS)\nit must be SQRT(252) * SQRT(AVERAGE_OF\n_SQUARED_\nLOG_RETURNS)\nbecause AVERAGE_OF_LOG_RETURNS is about zero\nnow this and the one in trade2win are the same\n#9\nwell, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat\/prob.\nSample var is calculated as\naverage\nof squared deviations from mean, not sum.\n#10\nso i think the question is coming down to the subtraction of mean returns.. technically when calculating this historical volatility, or standard deviation, you should subtract the mean return in the formula.. HOWEVER, it is market convention for the payout of volswaps and varswaps to NOT use this mean subtraction term, i.e. the payout is just calculated as the annualized average sum of squared log returns, which is not actually a proper standard deviation calculation, and so this is also of course what the pricing and risk management is based on .. maybe this is what's causing confusion? i'm not sure what context you pulled this reference out of\n#11\nSample var is calculated as\naverage\nof squared deviations from mean, not sum.\ni see, thanks. well average of returns is often missed just because of convenience. average is pretty small and it is assumed to be zero. when you calculate sample var you should divide by n-1, but again for convenience you divide just by N. After that you get average of squared returns. when you change N-1 to N you get some bias (as i remember), but any case difference is insignificantly small.","attrs_markdown":"[![QuantNet](https:\/\/quantnet.com\/styles\/default\/quantnet\/logo.svg)](https:\/\/quantnet.com\/)\n\n[![QuantNet](https:\/\/quantnet.com\/styles\/default\/quantnet\/logo.svg)](https:\/\/quantnet.com\/)\n\n- [Home](https:\/\/quantnet.com\/)\n- [Rankings](https:\/\/quantnet.com\/mfe-programs-rankings\/)\n  \n  [US Rankings](https:\/\/quantnet.com\/mfe-programs-rankings\/) [UK rankings](https:\/\/quantnet.com\/uk-rankings\/)\n- [Online Courses](https:\/\/quantnet.com\/courses\/)\n  \n  [C++ Programming for Financial Engineering](https:\/\/quantnet.com\/cpp\/) [Python for Finance with Intro to Data Science](https:\/\/quantnet.com\/python\/)\n- [Forums](https:\/\/quantnet.com\/forum\/)\n  \n  [New posts](https:\/\/quantnet.com\/whats-new\/posts\/) [Search forums](https:\/\/quantnet.com\/search\/?type=post)\n- [Resources](https:\/\/quantnet.com\/resources\/)\n  \n  [Latest reviews](https:\/\/quantnet.com\/resources\/latest-reviews) [Search resources](https:\/\/quantnet.com\/search\/?type=resource)\n- [Tracker](https:\/\/quantnet.com\/tracker\/)\n  \n  [United States](https:\/\/quantnet.com\/resources\/categories\/us.10\/) [United Kingdom & Europe](https:\/\/quantnet.com\/resources\/categories\/uk.11\/) [Canada](https:\/\/quantnet.com\/resources\/categories\/canada.12\/) [Asia & Australia](https:\/\/quantnet.com\/resources\/categories\/asia.13\/) [Rest of World](https:\/\/quantnet.com\/resources\/categories\/rest-of-world.14\/)\n- [What's new](https:\/\/quantnet.com\/whats-new\/)\n  \n  [Featured content](https:\/\/quantnet.com\/featured\/) [New posts](https:\/\/quantnet.com\/whats-new\/posts\/) [New media](https:\/\/quantnet.com\/whats-new\/media\/) [New media comments](https:\/\/quantnet.com\/whats-new\/media-comments\/) [New resources](https:\/\/quantnet.com\/whats-new\/resources\/) [New profile posts](https:\/\/quantnet.com\/whats-new\/profile-posts\/) [Latest activity](https:\/\/quantnet.com\/whats-new\/latest-activity)\n\n[Log in](https:\/\/quantnet.com\/login\/)   [Register](https:\/\/quantnet.com\/login\/register)\n\n[What's new](https:\/\/quantnet.com\/whats-new\/ \"What's new\")   [Search](https:\/\/quantnet.com\/search\/ \"Search\")\n\n- [New posts](https:\/\/quantnet.com\/whats-new\/posts\/)\n- [Search forums](https:\/\/quantnet.com\/search\/?type=post)\n\nMenu\n\n[Log in](https:\/\/quantnet.com\/login\/)\n***\n[Register](https:\/\/quantnet.com\/login\/register)\n***\n\nInstall the app\n\nInstall\n\n- [Forums](https:\/\/quantnet.com\/forum\/)\n- [🧠 Quant Skills & Prep](https:\/\/quantnet.com\/forum\/#%F0%9F%A7%A0-quant-skills-prep.84)\n- [Pricing, Modeling](https:\/\/quantnet.com\/forum\/pricing-modeling.40\/)\n\nJavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.\n\nYou are using an out of date browser. It may not display this or other websites correctly.  \nYou should upgrade or use an [alternative browser](https:\/\/www.google.com\/chrome\/).\n\n# Realized Volatility Calculation\n- Thread starter [kinderchocolate](https:\/\/quantnet.com\/members\/kinderchocolate.1882\/)\n- Start date\n  [11\/8\/10](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/)\n\n[K](https:\/\/quantnet.com\/members\/kinderchocolate.1882\/)\n\n#### [kinderchocolate](https:\/\/quantnet.com\/members\/kinderchocolate.1882\/)\nJoined\n\n5\/21\/09\n\nMessages\n\n13\n\nPoints\n\n11\n\n- [11\/8\/10](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40585)\n\n- [\\#1](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40585)\n\nHi,  \n   \n I am confused about the formula for calculating realized or historical volatility over a period of time.  \n   \n Paul Wilmott claims the formula in his book is:  \n   \n SQRT(252) \\* SQRT(AVERAGE\\_OF\\_LOG\\_RETURNS)  \n   \n But in some other sources, it involves the average variance from the mean, for example  \n   \n <http:\/\/www.trade2win.com\/boards\/attachments\/indicators\/8907d1090072498-volatility-historical-volatility-calc.doc>  \n   \n Which is right?  \n   \n Thanks,\n\n[Reply](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/reply?quote=40585 \"Reply, quoting this message\")\n\n[P](https:\/\/quantnet.com\/members\/pierrexu.4522\/)\n\n#### [PierreXu](https:\/\/quantnet.com\/members\/pierrexu.4522\/)\nJoined\n\n5\/16\/10\n\nMessages\n\n16\n\nPoints\n\n13\n\n- [11\/8\/10](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40586)\n\n- [\\#2](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40586)\n\nIn the case of common stocks, the expectation of daily log return is about zero.\n\n[Reply](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/reply?quote=40586 \"Reply, quoting this message\")\n\n[L](https:\/\/quantnet.com\/members\/latency.5493\/)\n\n#### [latency](https:\/\/quantnet.com\/members\/latency.5493\/)\nJoined\n\n7\/29\/10\n\nMessages\n\n88\n\nPoints\n\n18\n\n- [11\/8\/10](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40587)\n\n- [\\#3](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40587)\n\nvariance is additive  \n therefore, number of trading days in a year \\* square of daily returns =annualized variance., you assume that the mean of these daily returns is zero.  \n so annualized volatility = average daily return\\*(252)^.5.  \n   \n you would change the trading days based on the product you are trading.\n\n[Reply](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/reply?quote=40587 \"Reply, quoting this message\")\n\n[![iddqd](https:\/\/quantnet.com\/data\/avatars\/m\/2\/2075.jpg?1725322493)](https:\/\/quantnet.com\/members\/iddqd.2075\/)\n\n#### [iddqd](https:\/\/quantnet.com\/members\/iddqd.2075\/)\nJoined\n\n8\/3\/09\n\nMessages\n\n66\n\nResources\n\n[1](https:\/\/quantnet.com\/resources\/authors\/iddqd.2075\/)\n\nPoints\n\n18\n\n- [11\/8\/10](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40588)\n\n- [\\#4](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40588)\n\nThe trade 2 win calculation is correct, I am pretty sure that is what Wilmott must have meant also.\n\n[Reply](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/reply?quote=40588 \"Reply, quoting this message\")\n\n[K](https:\/\/quantnet.com\/members\/kinderchocolate.1882\/)\n\n#### [kinderchocolate](https:\/\/quantnet.com\/members\/kinderchocolate.1882\/)\nJoined\n\n5\/21\/09\n\nMessages\n\n13\n\nPoints\n\n11\n\n- [11\/8\/10](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40589)\n\n- [\\#5](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40589)\n\nThanks, I wasn't expecting that the mean was assumed to be zero.\n\n[Reply](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/reply?quote=40589 \"Reply, quoting this message\")\n\n[![quotes](https:\/\/quantnet.com\/data\/avatars\/m\/4\/4819.jpg?1725322493)](https:\/\/quantnet.com\/members\/quotes.4819\/)\n\n#### [quotes](https:\/\/quantnet.com\/members\/quotes.4819\/)\nJoined\n\n6\/11\/10\n\nMessages\n\n189\n\nPoints\n\n28\n\n- [12\/14\/11](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77249)\n\n- [\\#6](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77249)\n\nIn finance, we don't care about how the drift udt might vary over time, so it is good to have a volatility estimate independent of time drift estimate. True, you can use a R=udt+sdW to estimate s, but at the same time you assume u holds constant among your sample and estimate of s is based on that. Thus Wilmott's or Shreve's method derived from Ito's Calculus is preferable.\n\n[Reply](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/reply?quote=77249 \"Reply, quoting this message\")\n\n[D](https:\/\/quantnet.com\/members\/dvv.12415\/)\n\n#### [DVV](https:\/\/quantnet.com\/members\/dvv.12415\/)\nJoined\n\n11\/17\/11\n\nMessages\n\n9\n\nPoints\n\n11\n\n- [12\/14\/11](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77252)\n\n- [\\#7](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77252)\n\n> [kinderchocolate said:](https:\/\/quantnet.com\/goto\/post?id=40585)\n> \n> Hi,  \n>    \n>  I am confused about the formula for calculating realized or historical volatility over a period of time.  \n>    \n>  Paul Wilmott claims the formula in his book is:  \n>    \n>  SQRT(252) \\* SQRT(AVERAGE\\_OF\\_LOG\\_RETURNS)  \n>    \n>  But in some other sources, it involves the average variance from the mean, for example  \n>    \n>  [http:\/\/www.trade2win.com\/boards\/att...498-volatility-historical-volatility-calc.doc](http:\/\/www.trade2win.com\/boards\/attachments\/indicators\/8907d1090072498-volatility-historical-volatility-calc.doc)  \n>    \n>  Which is right?  \n>    \n>  Thanks,\n> \n> [Click to expand...]()\n\nwell, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat\/prob.\n\n[Reply](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/reply?quote=77252 \"Reply, quoting this message\")\n\n[![amir](https:\/\/quantnet.com\/data\/avatars\/m\/2\/2360.jpg?1725322493)](https:\/\/quantnet.com\/members\/amir.2360\/)\n\n#### [amir](https:\/\/quantnet.com\/members\/amir.2360\/)\nJoined\n\n11\/11\/09\n\nMessages\n\n52\n\nPoints\n\n18\n\n- [12\/15\/11](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77263)\n\n- [\\#8](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77263)\n\n> [kinderchocolate said:](https:\/\/quantnet.com\/goto\/post?id=40585)\n> \n> Hi,  \n>    \n>  I am confused about the formula for calculating realized or historical volatility over a period of time.  \n>    \n>  Paul Wilmott claims the formula in his book is:  \n>    \n>  SQRT(252) \\* SQRT(AVERAGE\\_OF\\_LOG\\_RETURNS)\n> \n> [Click to expand...]()\n\nit must be SQRT(252) \\* SQRT(AVERAGE\\_OF\\_SQUARED\\_LOG\\_RETURNS)  \n   \n because AVERAGE\\_OF\\_LOG\\_RETURNS is about zero  \n now this and the one in trade2win are the same\n\n[Reply](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/reply?quote=77263 \"Reply, quoting this message\")\n\n[![amir](https:\/\/quantnet.com\/data\/avatars\/m\/2\/2360.jpg?1725322493)](https:\/\/quantnet.com\/members\/amir.2360\/)\n\n#### [amir](https:\/\/quantnet.com\/members\/amir.2360\/)\nJoined\n\n11\/11\/09\n\nMessages\n\n52\n\nPoints\n\n18\n\n- [12\/15\/11](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77264)\n\n- [\\#9](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77264)\n\n> [DVV said:](https:\/\/quantnet.com\/goto\/post?id=77252)\n> \n> well, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat\/prob.\n> \n> [Click to expand...]()\n\nSample var is calculated as average of squared deviations from mean, not sum.\n\n[Reply](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/reply?quote=77264 \"Reply, quoting this message\")\n\n[F](https:\/\/quantnet.com\/members\/financeguy.1390\/)\n\n#### [financeguy](https:\/\/quantnet.com\/members\/financeguy.1390\/)\nJoined\n\n8\/28\/08\n\nMessages\n\n338\n\nPoints\n\n53\n\n- [12\/18\/11](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77439)\n\n- [\\#10](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77439)\n\nso i think the question is coming down to the subtraction of mean returns.. technically when calculating this historical volatility, or standard deviation, you should subtract the mean return in the formula.. HOWEVER, it is market convention for the payout of volswaps and varswaps to NOT use this mean subtraction term, i.e. the payout is just calculated as the annualized average sum of squared log returns, which is not actually a proper standard deviation calculation, and so this is also of course what the pricing and risk management is based on .. maybe this is what's causing confusion? i'm not sure what context you pulled this reference out of\n\n[Reply](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/reply?quote=77439 \"Reply, quoting this message\")\n\n[D](https:\/\/quantnet.com\/members\/dvv.12415\/)\n\n#### [DVV](https:\/\/quantnet.com\/members\/dvv.12415\/)\nJoined\n\n11\/17\/11\n\nMessages\n\n9\n\nPoints\n\n11\n\n- [12\/18\/11](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77453)\n\n- [\\#11](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77453)\n\n> [amir said:](https:\/\/quantnet.com\/goto\/post?id=77264)\n> \n> Sample var is calculated as average of squared deviations from mean, not sum.\n> \n> [Click to expand...]()\n\ni see, thanks. well average of returns is often missed just because of convenience. average is pretty small and it is assumed to be zero. when you calculate sample var you should divide by n-1, but again for convenience you divide just by N. After that you get average of squared returns. when you change N-1 to N you get some bias (as i remember), but any case difference is insignificantly small.\n\n[Reply](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/reply?quote=77453 \"Reply, quoting this message\")\n\n### Similar threads\n[Y](https:\/\/quantnet.com\/members\/youknowthething.48884\/)\n\n[Annualized Returns and Realized Volatility](https:\/\/quantnet.com\/threads\/annualized-returns-and-realized-volatility.52507\/)\n\n- [youknowthething](https:\/\/quantnet.com\/members\/youknowthething.48884\/)\n- [10\/3\/22](https:\/\/quantnet.com\/threads\/annualized-returns-and-realized-volatility.52507\/)\n- [Off 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[Advertise](https:\/\/quantnet.com\/advertise)\n- [Privacy policy](https:\/\/quantnet.com\/help\/privacy-policy\/)\n- [Help](https:\/\/quantnet.com\/help\/)\n- [Home](https:\/\/quantnet.com\/)\n- [RSS](https:\/\/quantnet.com\/forum\/-\/index.rss \"RSS\")\n\n© QUANTNET INC\n\n- This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.  \n   By continuing to use this site, you are consenting to our use of cookies.\n  \n  [Accept](https:\/\/quantnet.com\/account\/dismiss-notice) [Learn more…](https:\/\/quantnet.com\/help\/cookies)\n\n[Back]()\n\n[Top](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/#top) [Bottom](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/#footer)","attrs_readable_markdown":"- [\\#2](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40586)\n\nIn the case of common stocks, the expectation of daily log return is about zero.\n\n- [\\#3](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40587)\n\nvariance is additive  \n therefore, number of trading days in a year \\* square of daily returns =annualized variance., you assume that the mean of these daily returns is zero.  \n so annualized volatility = average daily return\\*(252)^.5.\n\nyou would change the trading days based on the product you are trading.\n\n- [\\#4](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40588)\n\nThe trade 2 win calculation is correct, I am pretty sure that is what Wilmott must have meant also.\n\n- [\\#5](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-40589)\n\nThanks, I wasn't expecting that the mean was assumed to be zero.\n\n- [\\#6](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77249)\n\nIn finance, we don't care about how the drift udt might vary over time, so it is good to have a volatility estimate independent of time drift estimate. True, you can use a R=udt+sdW to estimate s, but at the same time you assume u holds constant among your sample and estimate of s is based on that. Thus Wilmott's or Shreve's method derived from Ito's Calculus is preferable.\n\n- [\\#7](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77252)\n\n> Hi,\n> \n> I am confused about the formula for calculating realized or historical volatility over a period of time.\n> \n> Paul Wilmott claims the formula in his book is:\n> \n> SQRT(252) \\* SQRT(AVERAGE\\_OF\\_LOG\\_RETURNS)\n> \n> But in some other sources, it involves the average variance from the mean, for example\n> \n> [http:\/\/www.trade2win.com\/boards\/att...498-volatility-historical-volatility-calc.doc](http:\/\/www.trade2win.com\/boards\/attachments\/indicators\/8907d1090072498-volatility-historical-volatility-calc.doc)\n> \n> Which is right?\n> \n> Thanks,\n\nwell, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat\/prob.\n\n- [\\#8](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77263)\n\n> Hi,\n> \n> I am confused about the formula for calculating realized or historical volatility over a period of time.\n> \n> Paul Wilmott claims the formula in his book is:\n> \n> SQRT(252) \\* SQRT(AVERAGE\\_OF\\_LOG\\_RETURNS)\n\nit must be SQRT(252) \\* SQRT(AVERAGE\\_OF\\_SQUARED\\_LOG\\_RETURNS)\n\nbecause AVERAGE\\_OF\\_LOG\\_RETURNS is about zero  \n now this and the one in trade2win are the same\n\n- [\\#9](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77264)\n\n> well, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat\/prob.\n\nSample var is calculated as average of squared deviations from mean, not sum.\n\n- [\\#10](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77439)\n\nso i think the question is coming down to the subtraction of mean returns.. technically when calculating this historical volatility, or standard deviation, you should subtract the mean return in the formula.. HOWEVER, it is market convention for the payout of volswaps and varswaps to NOT use this mean subtraction term, i.e. the payout is just calculated as the annualized average sum of squared log returns, which is not actually a proper standard deviation calculation, and so this is also of course what the pricing and risk management is based on .. maybe this is what's causing confusion? i'm not sure what context you pulled this reference out of\n\n- [\\#11](https:\/\/quantnet.com\/threads\/realized-volatility-calculation.4914\/post-77453)\n\n> Sample var is calculated as average of squared deviations from mean, not sum.\n\ni see, thanks. well average of returns is often missed just because of convenience. average is pretty small and it is assumed to be zero. when you calculate sample var you should divide by n-1, but again for convenience you divide just by N. After that you get average of squared returns. when you change N-1 to N you get some bias (as i remember), but any case difference is insignificantly small.","meta_canonical":null}

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Boilerpipe Text	#2 In the case of common stocks, the expectation of daily log return is about zero. #3 variance is additive therefore, number of trading days in a year * square of daily returns =annualized variance., you assume that the mean of these daily returns is zero. so annualized volatility = average daily return(252)^.5. you would change the trading days based on the product you are trading. #4 The trade 2 win calculation is correct, I am pretty sure that is what Wilmott must have meant also. #5 Thanks, I wasn't expecting that the mean was assumed to be zero. #6 In finance, we don't care about how the drift udt might vary over time, so it is good to have a volatility estimate independent of time drift estimate. True, you can use a R=udt+sdW to estimate s, but at the same time you assume u holds constant among your sample and estimate of s is based on that. Thus Wilmott's or Shreve's method derived from Ito's Calculus is preferable. #7 Hi, I am confused about the formula for calculating realized or historical volatility over a period of time. Paul Wilmott claims the formula in his book is: SQRT(252) SQRT(AVERAGE_OF_LOG_RETURNS) But in some other sources, it involves the average variance from the mean, for example http://www.trade2win.com/boards/att...498-volatility-historical-volatility-calc.doc Which is right? Thanks, well, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat/prob. #8 Hi, I am confused about the formula for calculating realized or historical volatility over a period of time. Paul Wilmott claims the formula in his book is: SQRT(252) * SQRT(AVERAGE_OF_LOG_RETURNS) it must be SQRT(252) * SQRT(AVERAGE_OF _SQUARED_ LOG_RETURNS) because AVERAGE_OF_LOG_RETURNS is about zero now this and the one in trade2win are the same #9 well, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat/prob. Sample var is calculated as average of squared deviations from mean, not sum. #10 so i think the question is coming down to the subtraction of mean returns.. technically when calculating this historical volatility, or standard deviation, you should subtract the mean return in the formula.. HOWEVER, it is market convention for the payout of volswaps and varswaps to NOT use this mean subtraction term, i.e. the payout is just calculated as the annualized average sum of squared log returns, which is not actually a proper standard deviation calculation, and so this is also of course what the pricing and risk management is based on .. maybe this is what's causing confusion? i'm not sure what context you pulled this reference out of #11 Sample var is calculated as average of squared deviations from mean, not sum. i see, thanks. well average of returns is often missed just because of convenience. average is pretty small and it is assumed to be zero. when you calculate sample var you should divide by n-1, but again for convenience you divide just by N. After that you get average of squared returns. when you change N-1 to N you get some bias (as i remember), but any case difference is insignificantly small.
Markdown	[![QuantNet](https://quantnet.com/styles/default/quantnet/logo.svg)](https://quantnet.com/) [![QuantNet](https://quantnet.com/styles/default/quantnet/logo.svg)](https://quantnet.com/) - [Home](https://quantnet.com/) - [Rankings](https://quantnet.com/mfe-programs-rankings/) [US Rankings](https://quantnet.com/mfe-programs-rankings/) [UK rankings](https://quantnet.com/uk-rankings/) - [Online Courses](https://quantnet.com/courses/) [C++ Programming for Financial Engineering](https://quantnet.com/cpp/) [Python for Finance with Intro to Data Science](https://quantnet.com/python/) - [Forums](https://quantnet.com/forum/) [New posts](https://quantnet.com/whats-new/posts/) [Search forums](https://quantnet.com/search/?type=post) - [Resources](https://quantnet.com/resources/) [Latest reviews](https://quantnet.com/resources/latest-reviews) [Search resources](https://quantnet.com/search/?type=resource) - [Tracker](https://quantnet.com/tracker/) [United States](https://quantnet.com/resources/categories/us.10/) [United Kingdom & Europe](https://quantnet.com/resources/categories/uk.11/) [Canada](https://quantnet.com/resources/categories/canada.12/) [Asia & Australia](https://quantnet.com/resources/categories/asia.13/) [Rest of World](https://quantnet.com/resources/categories/rest-of-world.14/) - [What's new](https://quantnet.com/whats-new/) [Featured content](https://quantnet.com/featured/) [New posts](https://quantnet.com/whats-new/posts/) [New media](https://quantnet.com/whats-new/media/) [New media comments](https://quantnet.com/whats-new/media-comments/) [New resources](https://quantnet.com/whats-new/resources/) [New profile posts](https://quantnet.com/whats-new/profile-posts/) [Latest activity](https://quantnet.com/whats-new/latest-activity) [Log in](https://quantnet.com/login/) [Register](https://quantnet.com/login/register) [What's new](https://quantnet.com/whats-new/ "What's new") [Search](https://quantnet.com/search/ "Search") - [New posts](https://quantnet.com/whats-new/posts/) - [Search forums](https://quantnet.com/search/?type=post) Menu [Log in](https://quantnet.com/login/) * [Register](https://quantnet.com/login/register) * Install the app Install - [Forums](https://quantnet.com/forum/) - [🧠 Quant Skills & Prep](https://quantnet.com/forum/#%F0%9F%A7%A0-quant-skills-prep.84) - [Pricing, Modeling](https://quantnet.com/forum/pricing-modeling.40/) JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. You are using an out of date browser. It may not display this or other websites correctly. You should upgrade or use an [alternative browser](https://www.google.com/chrome/). # Realized Volatility Calculation - Thread starter [kinderchocolate](https://quantnet.com/members/kinderchocolate.1882/) - Start date [11/8/10](https://quantnet.com/threads/realized-volatility-calculation.4914/) [K](https://quantnet.com/members/kinderchocolate.1882/) #### [kinderchocolate](https://quantnet.com/members/kinderchocolate.1882/) Joined 5/21/09 Messages 13 Points 11 - [11/8/10](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40585) - [\#1](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40585) Hi, I am confused about the formula for calculating realized or historical volatility over a period of time. Paul Wilmott claims the formula in his book is: SQRT(252) \* SQRT(AVERAGE\_OF\_LOG\_RETURNS) But in some other sources, it involves the average variance from the mean, for example <http://www.trade2win.com/boards/attachments/indicators/8907d1090072498-volatility-historical-volatility-calc.doc> Which is right? Thanks, [Reply](https://quantnet.com/threads/realized-volatility-calculation.4914/reply?quote=40585 "Reply, quoting this message") [P](https://quantnet.com/members/pierrexu.4522/) #### [PierreXu](https://quantnet.com/members/pierrexu.4522/) Joined 5/16/10 Messages 16 Points 13 - [11/8/10](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40586) - [\#2](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40586) In the case of common stocks, the expectation of daily log return is about zero. [Reply](https://quantnet.com/threads/realized-volatility-calculation.4914/reply?quote=40586 "Reply, quoting this message") [L](https://quantnet.com/members/latency.5493/) #### [latency](https://quantnet.com/members/latency.5493/) Joined 7/29/10 Messages 88 Points 18 - [11/8/10](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40587) - [\#3](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40587) variance is additive therefore, number of trading days in a year \* square of daily returns =annualized variance., you assume that the mean of these daily returns is zero. so annualized volatility = average daily return\(252)^.5. you would change the trading days based on the product you are trading. [Reply](https://quantnet.com/threads/realized-volatility-calculation.4914/reply?quote=40587 "Reply, quoting this message") [![iddqd](https://quantnet.com/data/avatars/m/2/2075.jpg?1725322493)](https://quantnet.com/members/iddqd.2075/) #### [iddqd](https://quantnet.com/members/iddqd.2075/) Joined 8/3/09 Messages 66 Resources [1](https://quantnet.com/resources/authors/iddqd.2075/) Points 18 - [11/8/10](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40588) - [\#4](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40588) The trade 2 win calculation is correct, I am pretty sure that is what Wilmott must have meant also. [Reply](https://quantnet.com/threads/realized-volatility-calculation.4914/reply?quote=40588 "Reply, quoting this message") [K](https://quantnet.com/members/kinderchocolate.1882/) #### [kinderchocolate](https://quantnet.com/members/kinderchocolate.1882/) Joined 5/21/09 Messages 13 Points 11 - [11/8/10](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40589) - [\#5](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40589) Thanks, I wasn't expecting that the mean was assumed to be zero. [Reply](https://quantnet.com/threads/realized-volatility-calculation.4914/reply?quote=40589 "Reply, quoting this message") [![quotes](https://quantnet.com/data/avatars/m/4/4819.jpg?1725322493)](https://quantnet.com/members/quotes.4819/) #### [quotes](https://quantnet.com/members/quotes.4819/) Joined 6/11/10 Messages 189 Points 28 - [12/14/11](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77249) - [\#6](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77249) In finance, we don't care about how the drift udt might vary over time, so it is good to have a volatility estimate independent of time drift estimate. True, you can use a R=udt+sdW to estimate s, but at the same time you assume u holds constant among your sample and estimate of s is based on that. Thus Wilmott's or Shreve's method derived from Ito's Calculus is preferable. [Reply](https://quantnet.com/threads/realized-volatility-calculation.4914/reply?quote=77249 "Reply, quoting this message") [D](https://quantnet.com/members/dvv.12415/) #### [DVV](https://quantnet.com/members/dvv.12415/) Joined 11/17/11 Messages 9 Points 11 - [12/14/11](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77252) - [\#7](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77252) > [kinderchocolate said:](https://quantnet.com/goto/post?id=40585) > > Hi, > > I am confused about the formula for calculating realized or historical volatility over a period of time. > > Paul Wilmott claims the formula in his book is: > > SQRT(252) \ SQRT(AVERAGE\_OF\_LOG\_RETURNS) > > But in some other sources, it involves the average variance from the mean, for example > > [http://www.trade2win.com/boards/att...498-volatility-historical-volatility-calc.doc](http://www.trade2win.com/boards/attachments/indicators/8907d1090072498-volatility-historical-volatility-calc.doc) > > Which is right? > > Thanks, > > [Click to expand...]() well, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat/prob. [Reply](https://quantnet.com/threads/realized-volatility-calculation.4914/reply?quote=77252 "Reply, quoting this message") [![amir](https://quantnet.com/data/avatars/m/2/2360.jpg?1725322493)](https://quantnet.com/members/amir.2360/) #### [amir](https://quantnet.com/members/amir.2360/) Joined 11/11/09 Messages 52 Points 18 - [12/15/11](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77263) - [\#8](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77263) > [kinderchocolate said:](https://quantnet.com/goto/post?id=40585) > > Hi, > > I am confused about the formula for calculating realized or historical volatility over a period of time. > > Paul Wilmott claims the formula in his book is: > > SQRT(252) \* SQRT(AVERAGE\_OF\_LOG\_RETURNS) > > [Click to expand...]() it must be SQRT(252) \* SQRT(AVERAGE\_OF\_SQUARED\_LOG\_RETURNS) because AVERAGE\_OF\_LOG\_RETURNS is about zero now this and the one in trade2win are the same [Reply](https://quantnet.com/threads/realized-volatility-calculation.4914/reply?quote=77263 "Reply, quoting this message") [![amir](https://quantnet.com/data/avatars/m/2/2360.jpg?1725322493)](https://quantnet.com/members/amir.2360/) #### [amir](https://quantnet.com/members/amir.2360/) Joined 11/11/09 Messages 52 Points 18 - [12/15/11](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77264) - [\#9](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77264) > [DVV said:](https://quantnet.com/goto/post?id=77252) > > well, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat/prob. > > [Click to expand...]() Sample var is calculated as average of squared deviations from mean, not sum. [Reply](https://quantnet.com/threads/realized-volatility-calculation.4914/reply?quote=77264 "Reply, quoting this message") [F](https://quantnet.com/members/financeguy.1390/) #### [financeguy](https://quantnet.com/members/financeguy.1390/) Joined 8/28/08 Messages 338 Points 53 - [12/18/11](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77439) - [\#10](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77439) so i think the question is coming down to the subtraction of mean returns.. technically when calculating this historical volatility, or standard deviation, you should subtract the mean return in the formula.. HOWEVER, it is market convention for the payout of volswaps and varswaps to NOT use this mean subtraction term, i.e. the payout is just calculated as the annualized average sum of squared log returns, which is not actually a proper standard deviation calculation, and so this is also of course what the pricing and risk management is based on .. maybe this is what's causing confusion? i'm not sure what context you pulled this reference out of [Reply](https://quantnet.com/threads/realized-volatility-calculation.4914/reply?quote=77439 "Reply, quoting this message") [D](https://quantnet.com/members/dvv.12415/) #### [DVV](https://quantnet.com/members/dvv.12415/) Joined 11/17/11 Messages 9 Points 11 - [12/18/11](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77453) - [\#11](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77453) > [amir said:](https://quantnet.com/goto/post?id=77264) > > Sample var is calculated as average of squared deviations from mean, not sum. > > [Click to expand...]() i see, thanks. well average of returns is often missed just because of convenience. average is pretty small and it is assumed to be zero. when you calculate sample var you should divide by n-1, but again for convenience you divide just by N. After that you get average of squared returns. when you change N-1 to N you get some bias (as i remember), but any case difference is insignificantly small. 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Readable Markdown	- [\#2](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40586) In the case of common stocks, the expectation of daily log return is about zero. - [\#3](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40587) variance is additive therefore, number of trading days in a year \* square of daily returns =annualized variance., you assume that the mean of these daily returns is zero. so annualized volatility = average daily return\(252)^.5. you would change the trading days based on the product you are trading. - [\#4](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40588) The trade 2 win calculation is correct, I am pretty sure that is what Wilmott must have meant also. - [\#5](https://quantnet.com/threads/realized-volatility-calculation.4914/post-40589) Thanks, I wasn't expecting that the mean was assumed to be zero. - [\#6](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77249) In finance, we don't care about how the drift udt might vary over time, so it is good to have a volatility estimate independent of time drift estimate. True, you can use a R=udt+sdW to estimate s, but at the same time you assume u holds constant among your sample and estimate of s is based on that. Thus Wilmott's or Shreve's method derived from Ito's Calculus is preferable. - [\#7](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77252) > Hi, > > I am confused about the formula for calculating realized or historical volatility over a period of time. > > Paul Wilmott claims the formula in his book is: > > SQRT(252) \ SQRT(AVERAGE\_OF\_LOG\_RETURNS) > > But in some other sources, it involves the average variance from the mean, for example > > [http://www.trade2win.com/boards/att...498-volatility-historical-volatility-calc.doc](http://www.trade2win.com/boards/attachments/indicators/8907d1090072498-volatility-historical-volatility-calc.doc) > > Which is right? > > Thanks, well, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat/prob. - [\#8](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77263) > Hi, > > I am confused about the formula for calculating realized or historical volatility over a period of time. > > Paul Wilmott claims the formula in his book is: > > SQRT(252) \* SQRT(AVERAGE\_OF\_LOG\_RETURNS) it must be SQRT(252) \* SQRT(AVERAGE\_OF\_SQUARED\_LOG\_RETURNS) because AVERAGE\_OF\_LOG\_RETURNS is about zero now this and the one in trade2win are the same - [\#9](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77264) > well, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat/prob. Sample var is calculated as average of squared deviations from mean, not sum. - [\#10](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77439) so i think the question is coming down to the subtraction of mean returns.. technically when calculating this historical volatility, or standard deviation, you should subtract the mean return in the formula.. HOWEVER, it is market convention for the payout of volswaps and varswaps to NOT use this mean subtraction term, i.e. the payout is just calculated as the annualized average sum of squared log returns, which is not actually a proper standard deviation calculation, and so this is also of course what the pricing and risk management is based on .. maybe this is what's causing confusion? i'm not sure what context you pulled this reference out of - [\#11](https://quantnet.com/threads/realized-volatility-calculation.4914/post-77453) > Sample var is calculated as average of squared deviations from mean, not sum. i see, thanks. well average of returns is often missed just because of convenience. average is pretty small and it is assumed to be zero. when you calculate sample var you should divide by n-1, but again for convenience you divide just by N. After that you get average of squared returns. when you change N-1 to N you get some bias (as i remember), but any case difference is insignificantly small.
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