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Modified Bessel Functions

Posted: October 28th, 2011, 3:32 am
by stonybrooknick
Any one care to explain there role in finance , and accurate approximations used?

Modified Bessel Functions

Posted: October 28th, 2011, 10:30 pm
by Alan
Well, there is a very popular stochastic process in finance variously known asFeller sqrt process/CIR process/Heston volatility process (all these are essentially the same).The transition density is given in terms of those modified Bessel funcs. More generally, if you throw a dart at some paper in finance that uses a special function,excluding Erf function-related (cumulative normal, etc.),I will guess 90% of the time is it either Bessels or confluent hypergeometric.

Modified Bessel Functions

Posted: October 28th, 2011, 11:06 pm
by acastaldo
If you want to see the transition density of the CIR process expressed in term of modified Bessel functions you can find it here.

Modified Bessel Functions

Posted: October 29th, 2011, 6:22 am
by ACD
The Generalized Hyperbolic Distribution has one of the Modified Bessel functions in it's pdf. It's quite a flexible distribution can can be used in risk management as something that can capture a few features (fat tails, skewness) that the normal distribution will not and it contain several other families of distributions as special cases of it.