How to Catch a Thief: Unmasking Madoff’s Ponzi Scheme with Benford’s Law

One of my starting points into quantitive finance was Bernie Madoff’s fund. Back then because Bernie was in desperate need of money to keep his Ponzi scheme running there existed several so-called feeder funds.

One of them happened to approach me to offer me a once in a lifetime investment opportunity. Or so it seemed. Now, there is this old saying that when something seems too good to be true it probably is. If you want to learn what Benford’s law is and how to apply it to uncover fraud, read on!
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Create Bart Simpson Blackboard Memes with R


Everybody knows the Simpsons, everybody loves the Simpsons and everybody can laugh about Bart Simpson writing funny lines on the blackboard! If you want to create your own Bart Simpson Blackboard Meme Generator with R read on!
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Financial Engineering: Static Replication of any Payoff Function


In the area of option strategy trading, it has always been a dream of mine to have a universal tool that is able to replicate any payoff function statically by combining plain vanilla products like calls, puts, and zerobonds.

Many years ago there was such a tool online but it has long gone since and the domain is inactive. So, based on the old project paper from that website I decided to program it in R and make it available for free here!
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The Central Limit Theorem (CLT): From Perfect Symmetry to the Normal Distribution


How can the Normal Distribution arise out of a completely symmetric set-up? The so-called Central Limit Theorem (CLT) is a fascinating example that demonstrates such behaviour. If you want to get some intuition on what lies at the core of many statistical tests, read on!
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“You Are Here”: Understanding How GPS Works


Last week, I showed you a method of how to find the fastest path from A to B: Finding the Shortest Path with Dijkstra’s Algorithm. To make use of that, we need a method to determine our position at any point in time.

For that matter, many devices use the so-called Global Positioning System (GPS). If you want to understand how it works and do some simple calculations in R, read on!
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Finding the Shortest Path with Dijkstra’s Algorithm


I have to make a confession: when it comes to my sense of orientation I am a total failure… sometimes it feels like GPS and Google maps were actually invented for me!

Well, nowadays anybody uses those practical little helpers. But how do they actually manage to find the shortest path from A to B?

If you want to understand the father of all routing algorithms, Dijkstra’s algorithm, and want to know how to program it in R read on!
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3.84 or: How to Detect BS (Fast)

In From Coin Tosses to p-Hacking: Make Statistics Significant Again! I explained the general principles behind statistical testing, here I will give you a simple method that you could use for quick calculations to check whether something fishy is going on (i.e. a fast statistical BS detector), so read on!
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Network Analysis: Who is the Most Important Influencer?

Networks are everywhere: traffic infrastructure and the internet come to mind, but networks are also in nature: food chains, protein-interaction networks, genetic interaction networks and of course neural networks which are being modelled by Artificial Neural Networks.

In this post, we will create a small network (also called graph mathematically) and ask some question about which is the “most important” node (also called vertex, pl. vertices). If you want to understand important concepts of network centrality and how to calculate those in R, read on!
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Local Differential Privacy: Getting Honest Answers on Embarrassing Questions

Do you cheat on your partner? Do you take drugs? Are you gay? Are you an atheist? Did you have an abortion? Will you vote for the right-wing candidate? Not all people feel comfortable answering those kinds of questions in every situation honestly.

So, is there a method to find the respective proportion of people without putting them on the spot? Actually, there is! If you want to learn about randomized response (and how to create flowcharts in R along the way) read on!
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Doing Maths Symbolically: R as a Computer Algebra System (CAS)


When I first saw the Computer Algebra System Mathematica in the nineties I was instantly fascinated by it: you could not just calculate things with it but solve equations, simplify, differentiate and integrate expressions and even solve simple differential equations… not just numerically but symbolically! It helped me a lot during my studies at the university back then. Normally you cannot do this kind of stuff with R but fear not, there is, of course, a package for that!
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