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Modelling stock returns - the Laplace distribution (Excel) (SUB)

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What else can you do to model fat-tailed distributions so prominent on financial markets? Laplace distribution glues two exponential functions together and, being a conceptually simple distribution, sometimes achieves a remarkably good fit. We will learn how to estimate the parameters for the Laplace distribution using maximum likelihood and apply it to real-world financial data.
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Опубликовано:

5 сен 2024

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Комментарии : 11

@NEDLeducation 4 года назад

You can find the spreadsheets for this video and some additional materials here: drive.google.com/drive/folders/1sP40IW0p0w5IETCgo464uhDFfdyR6rh7 Please consider supporting NEDL on Patreon: www.patreon.com/NEDLeducation

@troyc4487 4 года назад

This is simply one of the best videos for bridging statistics and financial instruments. Thank you.

@NEDLeducation 4 года назад

Hi Troy, thanks so much for your feedback! Glad that you liked the content. Please check our Mathematical Finance playlist to find more videos on similar topics if you are interested.

@RustuYucel 4 года назад

Very good explaination. Pls keep this format. Looking fwd to watch similar Distribuiton tuts on excel esp. power law dist and forecasts. Thnx

@NEDLeducation 4 года назад

Hi Rustu, many thanks for the feedback and glad you liked the video. Please check the mathematical finance playlist for more videos on distributions. Applying power laws to stock returns is less straightforward than it seems though (you cannot model the whole distribution as a power law distribution has a lower bound so you have to glue together a power law tail and a "hump" that is defined using some other function), but we will surely make a video on it at some point :)

@gustavocardoso6348 4 года назад

Hi NEDL. Thank you for sharing your videos with us! As a suggestion, I would like to see an example of a sum of two correlated laplace-distributed random variables. The idea is to have a portfolio VaR using Laplace instead of Normal distribution. Best.

@NEDLeducation 4 года назад

Hi Gustavo and many thanks for your feedback! The video on parametric VaR with various distributional assumptions (Laplace VaR included!) is on the way! As for the sum of the two Laplace-distributed random variables, the issue is actually very tricky :) A sum of two Laplace distributions need not follow a Laplace distribution itself. Therefore, most commonly you just test for the distribution of portfolio returns without looking at individual stock return distributions.

@maynardvargas6898 4 года назад

Well done! :D

@Hachann 3 года назад

Thanks alot for your videos ! In the Excel file you made, you show a way to approximate the asymmetric laplace parameters using calculous on (normal distribution) excess kurtosis and (normal distribution) std dev, please correct me if I'm wrong. Looking at Supremum scores, one can think that the "MM" approximation performs poorer than the "MLE" method. If we can't use an MLE method (because of software limitation for exemple), do you think it's still useful to use the MM approx ? Or go back to symmetrical Laplace ? Thank you for your lights ! EDIT : Sorry I thought I did comment under the asymmetric laplace video

@NEDLeducation 3 года назад

Hi Hachann, and glad you liked the video! Also, thanks for such a profound question! Yes, indeed, if MLE is unavailable, MM can be used, for example, use sample skewness to retrieve the shape parameter for asymmetric Laplace, and then do median and average absolute deviation for location and scale. MM estimates are less robust and most of the time produce poorer fit than MLE, but are still feasible to use. Hope it helps!