Financial examples of distribution
- Thread starter higaurav
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higaurav,
I'd love to hear about other examples, but for starters...
The Poisson arises often in operational risk, specifically for the frequency of operational losses (i.e., frequency = discrete). We have an operational reading called "LDA at work," there you will see Deutsche Bank consider, among discrete alternatives, the Poisson as a way to model operational losses (the number of losses in a period of time, this is the classic Poisson question)
The binomial arises often in credit portfolios because default is binary (1=default, 0 = no default, or vice versa). The IRB approach in Basel, for example, does not really factor credit risk concentration (lots of obligors is same sector). So lots of research going on about how to handle that. One approach is Moody's binomial expansion technique (BET): translates a correlated portfolio of credits into its "equivalent" portfolio of uncorrelated credits. The whole point of doing that is to end up with something you can analyze with the binomial.
Also, for binomial, maybe you will like this editgrid application of an example given by Jorion: using binomial to develop a risk metric for event-driven funds.
I think the advantage of these two are: they are pretty much the *simplest* discrete distributions you can find. That, combined the empirical reality that often times simpler is "good enough" (and complex distributions, strangely enough, seem too often be "precisely wrong" instead "accurate enough") explains their popularity. But, i am sure there are plenty more and better examples than these...
David
I'd love to hear about other examples, but for starters...
The Poisson arises often in operational risk, specifically for the frequency of operational losses (i.e., frequency = discrete). We have an operational reading called "LDA at work," there you will see Deutsche Bank consider, among discrete alternatives, the Poisson as a way to model operational losses (the number of losses in a period of time, this is the classic Poisson question)
The binomial arises often in credit portfolios because default is binary (1=default, 0 = no default, or vice versa). The IRB approach in Basel, for example, does not really factor credit risk concentration (lots of obligors is same sector). So lots of research going on about how to handle that. One approach is Moody's binomial expansion technique (BET): translates a correlated portfolio of credits into its "equivalent" portfolio of uncorrelated credits. The whole point of doing that is to end up with something you can analyze with the binomial.
Also, for binomial, maybe you will like this editgrid application of an example given by Jorion: using binomial to develop a risk metric for event-driven funds.
I think the advantage of these two are: they are pretty much the *simplest* discrete distributions you can find. That, combined the empirical reality that often times simpler is "good enough" (and complex distributions, strangely enough, seem too often be "precisely wrong" instead "accurate enough") explains their popularity. But, i am sure there are plenty more and better examples than these...
David
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