As I have already told you in the post 3rd Day in Stuttgart and Cryptography, we had some of the financial math in the same day as Cryptography, but we also had another day especially dedicated to this subject and I thought that it would be better to present you everything in one go. I hope this makes sense for everyone.
First of all I will start with a small thing about me: I don’t really like Probability. This is really important when it comes to Financial Math because a lot of theory is just principles form probability and the study of chance. I remember I had an Introduction to Probability course in my 1st year at university, but I never loved it. I believe it is really very important, but never went in deep with it. I like to read easy articles about it and how it can be applied to our society, but I never went deeper. So, if you have any recommendations let me know in the comment box, they will be way helpful. So lets go to the thing I wanted to tell you:
I will start with the Credit Risk presentation. In case you do not know, credit risk is the risk that an obligor does not honor his payments ( a good example is a company that has borrowed money form bank, and in this case the default might be the company goes bankrupt). We started with the binomial model for independent defaults, where we need to consider a homogeneous credit portfolio model with m obligors. And here the probability theory appears in full, because I remember doing a lot of examples with binomial probability. To fully understand it, you need to think about the random variables and the fact that they are all independent with identical distribution. And after this a lot of formulas and definitions came that are purely theory, so I believe it will just be easier for you to check the following Wikipedia article: Binomial Distribution (it explains things way better than me). Considering all this, we concluded that the independent identical distribution assumption for the individual default indicators (or variables) implies that the average number of defaults in the portfolio converges to the constant p. It seems that given the recent credit crisis, the assumption of independent defaults is somehow ridiculous. Hence, the fraction of defaults in the portfolio will often have values much bigger than the constant p. But, in fact the binomial model is just the starting point for more sophisticated models (for example, the mixed binomial model which randomizes the default probability in the standard binomial model, allowing the stronger dependence). This mixed binomial model will then imply more realistic probabilities for extreme loss scenarios, compared with the standard binomial loss distribution. You can see this in the following picture (witch is in fact a Print Screen from the lecture notes):
The next lecture was about mathematics of insurance. He started with an interesting insight into the European insurance market, and this was full of a lot of graphs and explanations. Again, here is a Print Screen form the lecture notes:
After this we got a nice explanation of the tasks a mathematician has in an insurance company. They involve evaluating statistical data with respect to risks such as death, sickness, injury, disability and loss of property; analyzing investment strategies with respect to performance, risks, liquidity and diversification; calculating insurance premiums for term life, annuities, total and permanent disability, permanent health, accidental death, transport risks and public liability; calculating reserves for unearned premiums, annuities, outstanding claims in liability insurance and unexpected contingencies. But he also talked about calculating premium, which involved again a little probability. Also this is extremely important because a good and appropriate premium calculation principle reflects the real risk connected with the business. (in case you are thinking what part of probability is used here, I can give you a small hint: expectation and variance).
Before I finish, in case this is way to old for some of you and don’t really know what is it about check this post: Visiting Stuttgart. Also, you can check the posts made for the first 3 days of the project with the HFT: First day and Second day and the post 3rd Day in Stuttgart and Cryptography.
Have a great week. Hope you liked this post, and if you would like to see more let me know. Any feedback is appreciated so use the like and share buttons and also comment below with your favorites, too.
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