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Comment by Vincent Granville on November 25, 2018 at 2:47pm

Hi Zhongmin,

There is one thing in this chart that surprises me a lot. I have produced plenty of charts that look very similar to yours, but come from my number theory investigations. I am sure some of them can be found in my new book on stochastic processes. I came to the conclusion that there are many things in number theory (advanced probabilistic properties of numeration systems or prime numbers, in particular) that are very valuable for Fintech modeling. Indeed, my book, which is a book about number theory (in disguise), mentions many applications to stock market modeling, Brownian motions, and better stochastic processes (derived from the theory of numbers) to explain stock price fluctuations. For instance, the digits of some numbers (say Pi) behave in a such a way that they appear totally unpredictable -- indeed they can be used to build Brownian motions -- it just looks like those digits have the same amount of  "arbitraging" (or call it entropy) in their construction, as the stock market. Yet, you can derive significant value from them. Afterall, they are not random at all even if they appear to be so. Same with the stock market!

Vincent 

Comment by Zhongmin Luo on November 25, 2018 at 9:28am

Ok, please allow me to add a bit of descriptions to this picture presenting the daily CDS prices for Microsoft.

1. The line highlighted in Green color stands for 5-year CDS against the default of Microsoft, which is an insurance contract protecting the buyer, in this case, for 5 years, against default of an entity (which can be corporate or sovereign, yes, when people worried about Greek government bond's default, CDS for Greek govern't was popular).

2. The line highlighted in Brown color stands for 10-year CDS against the default of Microsoft.

3. The rest of dotted lines are the CDS of different maturities.

If you observed 5-year CDS (green) > 10-year (brown) or any short-term CDS > long-term CDS, it's called inverted CDS curve on a given day. Inverted yield curve is widely studied and economists cited inversion of yield curve as signal for economic stresses or evidence for potential upcoming economic crisis, but little systematic study done in terms of inverted CDS curve. 

However, no all inverted CDS curves imply arbitrage opportunities, which is why we mathematically derived in our study the exact mathematical conditions for such opportunities. If our conditions are violated, it permits <0 and >1 so-called default probabilities, which is nonsensical to probablistic theorists and allows arbitrage to financial economists.

My previous research paper titled ''CDS Rate Construction Methods by Machine Learning Techniques", awarded Risk's Quant Summit Europe Call for Paper 2018, has now been extended into two papers and forthcoming in a peer-review journal. I have been working on this research, unpaid for another year together with my PhD supervisor. Now I am glad to say, this second paper is done.

If possible, please show your support to my academic research by downloading the paper from here. I will give better summary of our research (now four papers) during my career break in future blogs.        

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