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stonybrooknick
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Joined: January 24th, 2011, 4:37 pm

Modified Bessel Functions

October 28th, 2011, 3:32 am

Any one care to explain there role in finance , and accurate approximations used?
 
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Alan
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Modified Bessel Functions

October 28th, 2011, 10:30 pm

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.
Last edited by Alan on October 28th, 2011, 10:00 pm, edited 1 time in total.
 
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acastaldo
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Modified Bessel Functions

October 28th, 2011, 11:06 pm

If you want to see the transition density of the CIR process expressed in term of modified Bessel functions you can find it here.
 
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ACD
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Joined: April 19th, 2004, 8:09 am

Modified Bessel Functions

October 29th, 2011, 6:22 am

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.
Last edited by ACD on October 28th, 2011, 10:00 pm, edited 1 time in total.
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