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SUMMARY:Financial Modelling with 2-EPT Levy Processes - Professor Bernard 
 Hanzon\, Edgeworth Centre for Financial Mathematics\, Edgeworth Centre for
  Financial Mathematics\, Department of Mathematics\, University College Co
 rk
DTSTART:20120619T130000Z
DTEND:20120619T140000Z
UID:TALK38610@talks.cam.ac.uk
CONTACT:Dr Jason Z JIANG
DESCRIPTION:The class of probability density functions on *R* with strictl
 y proper rational characteristic functions are considered. On the positive
  half-line as well as on the negative half-line these probability density 
 functions are Exponential-Polynomial-Trigonometric (EPT) functions which w
 e abbreviate as 2-EPT densities. EPT density functions can be represented 
 as f(x)=c.exp(Ax).b\, where ``A" is a square matrix\, ``b" a column vector
  and ``c" a row vector. The triple (A\,b\,c) is called a realization of th
 e EPT density function. The more general class of probability measures on 
 *R* with (proper) rational characteristic functions is also considered who
 se densities correspond to mixtures of the pointmass at zero (``delta dist
 ribution") and 2-EPT densities.  The well-known Variance Gamma density is 
 shown to be a 2-EPT density under a parameter restriction and we implement
  the Variance Gamma asset price process to demonstrate the benefits of ado
 pting such an approach for financial modelling purposes. Variance Gamma pr
 ocesses are Levy processes. We give conditions under which a 2-EPT distrib
 ution is infinitely divisible and gives rise to a Levy process. Here we ma
 ke use of recent results on sufficient conditions for an EPT function to b
 e non-negative (cf [1]\,[2]). In this way we arrive at a rich class of Lev
 y processes for which there are closed form formulae for many option price
 s and their corresponding Greeks. Value-at-Risk computations are also stra
 ightforward in this framework.\n\n[1]  B. Hanzon\, F. Holland\, "Non-negat
 ivity Analysis for Exponential-Polynomial-Trigonometric Functions on [0\,i
 nfinity)\," to appear in: Proceedings of IWOTA 2010\, Operator Theory: Adv
 ances and Applications (OT)\,Birkhaeuser Verlag\, Basel\, Boston\, Berlin\
 ; an earlier version of the paper can be downloaded from www.edgeworth.biz
 \n\n[2]      B. Hanzon\,   F. Holland\,  "Non-negativity of Exponential Po
 lynomial Trigonomet-\nric Functions-a Budan Fourier  sequence approach"\, 
 Poster 429 presented at the\nBachelier Finance Society Congress\, Toronto\
 , 2010\; available on-line at web-address\nhttp://euclid.ucc.ie/sta_/hanzo
 n/BFSTorontoPosterHanzonHollandFinal.pdf\n\nPapers and software also avail
 able at   %{color:red}www.2-ept.com%\n\n*Key Words*: Variance Gamma\; Rati
 onal Characteristic Functions\; Non-Negativity of EPT Functions\; Option P
 ricing\; Levy Processes
LOCATION:Cambridge University Engineering Department\, LR3A
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