Central limit theorem explained: Why use normal distribution? (Excel)
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- Опубликовано: 18 июл 2021
- Why is the normal distribution so frequently used in applied statistics, especially finance and economics? What is so special about it? And why sometimes the normality assumption is violated? Today we are investigating and illustrating a key concept in statistics - the central limit theorem (CLT) - that is at the heart of this conundrum. We are going to show how it works on a simple example of dice throws and also build some generalisations to the world of finance and economics.
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very helpful, tks teacher
Hi, thank you for the videos on determining the distribution of stock returns! I have a question: why is it, that the lognormal distribution implies constant volatility? Yes, it is clear, that in the geometric brownian motion and in deriving the Black Scholes option price of european call/put option it is assumed, that the volatility is constant, but why is that true for a lognormal distribution? And does a normal distribution have a constant volatility? Thank you for the answer!
Hi Elizabeta, and glad you liked the video! As for your question, the distributional assumption and the constant volatility assumption can be two separate issues. You can have a normally distributed return-generating process with non-constant volatility, for example (like in the standard GARCH model), or a non-normal distribution with constant volatility. Many models resort to both normality and constant volatility at the same time as it can be easier to derive closed-form solutions that way. Hope it helps!
@@NEDLeducation Hi, thank you for the answer! Could you please make a video on Breeden_litzenberger Formula for risk-neutral distribution from option prices, with application, no matter in excel, python, c++! there are always a lot of tutorils in u tube on common option topics. When the topics get more advanced, I am unfortunate in finding the explanation! It looks like you have a profound math and statistical background to explain the derivation and implementation of BL formula. For sure there will be people who are interested in this question. I am reading the John Hull book "Option, Futures ..", which is very commonly used as a studing material, and there is an explanation (however only as formula without application) on this formula. I will be very thankful, if you also make videos on implied volatility surface, risk neutral distribution, obtained from binomial tree modell and from BS Modell. I am not very sure, if in reality the implied volatility from BS modell is used for binomial trees, or if an implied binomial volatility is derived and then used. It will also be wonderful, if you could explain the steps, how the implied volatility surface is used, once it has been obtained for a certain option! Thank you! And I applogize for misspellings, I am just reading, listenig and preparing for FRM in a fast pace and don't really pay attention, when there are small misspelling errors in my text. Thank you!
Thank you for the video! Could you make a video about the Pareto distributions (aka power law)?
Hi Corrado, and glad you liked the video! Will definitely do one on power law distributions at some point in the future!