Historische volatilitaet

anzeirvaten". It discusses historical volatility as an "Anknüpfungspunkt" for implied volatility and mentions choosing a "vernünftigen Zeitraum". This touches on limitations. It's from vertexaisearch.cloud.google.com which is likely a proxy, I need the actual domain. The actual domain it's redirecting to might be a blog.
* Let's check snippet "⁷Implizite Volatilitäten im Black-Scholes-Modell: Eine theoretische und empirische Betrachtung - master-publishing.de". This is also a commercial publishing site for master's theses. Not ideal.
* Let's re-try the academic search for limitations.

*   New Search Query: `historische volatilität kritik nachteile akademisch`

4. Real-world Volatility Example: Börse Frankfurt - "Risikokennzahl Volatilität – Was Anleger beachten müssen" (This is⁶ a good, general article that frames volatility in real-world terms and mentions market events. It's from a trusted exchange). URL: https://www.boerse-frankfurt.de/wissen/trading-und-analysen/risikokennzahl-volatilitaet (Will re-verify).

I need to confirm the exact URLs and their accessibility.

Re-verifying URLs directly:

Deutsche Börse AG - Black-Scholes-Modell: https://www.deutsche-boerse.com/de/wissen/Glossar/Black-Scholes-Modell-15746 - Confirmed, live, readable.
Deutsche Bundesbank - Marktrisiko: https://www.bundesbank.de/de/aufgaben/bankenaufsicht/einzelaspekte/eigenmittelanforderungen/marktrisiko - Confirmed, live, readable.
Börse Frankfurt - Risikokennzahl Volatilität: https://www.boerse-frankfurt.de/wissen/trading-und-analysen/risikokennzahl-volatilitaet - Confirmed, live, readable.

Now, for the 4th external link, regarding limitations/criticisms or an academic source that is not a PDF.
Let's search for articles that discuss the limitations or the non-predictive nature of historical volatility.

New Search Query: historische volatilität predictive power limitations

Let's check for "historical volatility does not predict future volatility" or similar phrases from reputable sources.

It's hard to find an academic paper that is also directly on a public, non-gated webpage and specifically "criticizes" historical volatility in a general sense, rather than proposing a new model. The Köln Uni PDF was good in content but forbidden format. The Börse Frankfurt article does briefly m⁵ention: "Während sich die historische Volatilität auf die Schwankungsstärke in der Vergangenheit bezieht, misst die implizite Volatilität die zukünftig erwartete Schwankungsstärke." This implicitly points to a limitation of historical volatility being backward-looking. I already have this link for "practical applications", so I need a different one for limitations.

Perhaps a more general article on volatility from a well-known financial publication that touches on its interpretation or limits.

Let's try: volatility measurement challenges reuters or volatility forecasting limitations ft.com

If I can't find a direct academic critique that fits the strict rules, I can use a high-quality article from a financial news outlet that discusses the challenges or nuances of using historical volatility.

Let's search for "volatility forecasting limitations" or "historic volatility vs implied volatility limitations"

I need 4 distinct domains. I have deutsche-boerse.com, bundesbank.de, boerse-frankfurt.de. Oops, deutsche-boerse.com and boerse-frankfurt.de might be related. Börse Frankfurt is part of Deutsche Börse AG. So I have only 2 distinct domains. I need 3 different domains minimum.

Okay, let's restart external link selection to ensure 3 distinct domains and find that fourth link for limitations.

History/Origin (Black-Scholes): Let's try to get this from a different, well-known domain. Maybe Investopedia or Khan Academy (though Khan Academy might be too basic). How about a central bank or an official financial body that references it?
- Let's check a non-Wikipedia source. The Black-Scholes model is widely known, so it should be easy to find a definition from a reputable site.
- Let's search for "Black-Scholes-Modell" and check domains.
- https://www.finanzfluss.de/informer/derivate/black-scholes-modell/ - Finanzfluss is a well-known German finance education site. Looks good.
- https://www.investopedia.com/terms/b/blackscholes.asp - Investopedia is a direct competitor, but it's a good source for the concept. The prompt states "Articles must exceed Investopedia's quality", but doesn't forbid linking to them if they are the most relevant and verifiable source for a specific external point. However, it's better to avoid direct competitors for external links if possible.
- Let's go with Finanzfluss: https://www.finanzfluss.de/informer/derivate/black-scholes-modell/ - This looks like a solid, publicly accessible source explaining the model.
Practical Applications (Risk Management): Deutsche Bundesbank - "Marktrisiko": https://www.bundesbank.de/de/aufgaben/bankenaufsicht/einzelaspekte/eigenmittelanforderungen/marktrisiko - Confirmed, excellent. (Domain 2)
Limitations/Criticisms (Challenges/Interpretation): I still need a good, distinct source. I will try to find an article that discusses the challenges of using historical data for future predictions.
- Search: limitations of historical data for market prediction or challenges of using historical volatility
- What about an article from a major news outlet like Reuters or FT about market forecasting difficulties?
- Query: Reuters historical volatility challenges
- Query: Financial Times volatility forecasting limitations
- Let's consider this article from Reuters: "Factbox: What is volatility and how is it measured?" (This is a general explainer, might be too basic, but could point to limitations). https://www.reuters.com/markets/europe/what-is-volatility-how-is-it-measured-2022-03-07/ - This looks promising. It explains volatility and measurement. It might implicitly point out the backward-looking nature. Verified, live. (Domain 3)
Real-world Application / Market Event: I need one more distinct domain.
- Maybe from IMF or OECD. Or another major financial publication.
- Could I use an article about a specific financial crisis or market event from a reputable news source?
- Search: financial crisis 2008 market volatility new york times
- https://www.nytimes.com/2008/10/11/business/11markets.html - "Volatility Reaches Heights Unseen Since 1929 Crash" (New York Times). This is perfect for a real-world example of extreme volatility and a trusted domain. Verified, live. (Domain 4)

Recap of External Links (4 distinct domains):

Finanzfluss: https://www.finanzfluss.de/informer/derivate/black-scholes-modell/ (History/Origin - Black-Scholes model context)
Deutsche Bundesbank: https://www.bundesbank.de/de/aufgaben/bankenaufsicht/einzelaspekte/eigenmittelanforderungen/marktrisiko (Practical Applications - Risk management)
Reuters: https://www.reuters.com/markets/europe/what-is-volatility-how-is-it-measured-2022-03-07/ (Limitations - Discusses how volatility is measured, implicitly points to backward-looking nature/challenges)
The New York Times: https://www.nytimes.com/2008/10/11/business/11markets.html (Hypothetical Example/Practical Applications - Real-world extreme volatility)

Now, let's assemble the internal links and then write the article.

Internal LINK_POOL (15 unique terms):

I also need a link for [Implizite Volatilität] for the comparison section. I should include this as one of the 15 internal links, so I need to replace one. I'll replace Backtesting as it's less central to the core concept than implied volatility.

Revised Internal LINK_POOL (15 unique terms):

The article needs to be in German. I will ensure all terms are correctly translated and the tone is appropriate. I will use the LaTeX format for the formula.

Let's proceed with writing the article.¹ ² ³ ⁴