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It looks like the financial crisis based due to CDOs, CDS, and other exotic products did not have any effect on making the financial terms any easier.
Popular risk analysis tools were based on the 'simple' Geometric Brownian Motion, but that seems now to be based on wrong assumptions. AIG paid the cost of it I would say.
Using models is good. Models are powerful to help you understand the mechanisms behind what happens in real world. It will always be just a model and not reality, but the insights that you can get from using models is the first big step towards becoming an expert. However, the models have to be based on sound assumptions, and in finance the assumptions are wrong.
First of all, the main assumption behind todays financial models is that risk is 'normally' distributed. Risk is probabilistic aspect of price changes that is random compared to what we expect. This randomness in finance is assumed to be normally distributed, a well-known distribution that is too simplistic compared to what really happens in the markets. For example, a normal distribution can be expected if the market incorporated all the information and priced that information correctly.
Definitely, we know that this is not the case, because we would not have booms and busts like we have seen in the recent years. If all information is correctly priced, stock markets would move slowly, up and down. Downtrends would still be present, but no radical crashes would be expected.
Other assumptions are taken into account in todays model, such as constant volatility over time (just check the VIX index to see that this is absolutely not the case), independent price variations from one day to another, etc.
The outcome of it is that new models are coming up, one of them is the Fractional Brownian Motion in Multifractal Time. A big name, a complex model, and the way to generate a computer output is to use Monte Carlo simulations. Not very nice, this is a just brute force way of computing a set of possible outcomes...
A more analytical way would be nice, but before that, it is of uttermost importance to clearly understand the way markets behave to be able to put it in simulation models for us to understand!
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