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SUMMARY:Continuously-generated jump processes - Ben Derrett (Statslab)
DTSTART:20140528T143000Z
DTEND:20140528T150000Z
UID:TALK52539@talks.cam.ac.uk
CONTACT:Vittoria Silvestri
DESCRIPTION:We construct a flexible and numerically tractable class of ass
 et models by firstly choosing a bivariate diffusion process $(U\,Y)$\, and
  then defining the price of the asset at time $t$ to be the value of $Y$ w
 hen $U$ first exceeds $t$. Such price processes will typically have jumps\
 ; conventional pricing methodologies would try to solve a PIDE\, which can
  be numerically problematic\, but using the fact that the pricing problem 
 is embedded in a two-dimensional diffusion\, we are able to exploit effici
 ent methods for two-dimensional diffusion equations to find prices. Models
  with time dependence (that is\, where the bivariate diffusion is $U$-depe
 ndent) are no more difficult in this approach.\n\nPricing a European optio
 n for a model in this class consists of solving a linear second order elli
 ptic PDE. Models in this class range from the most parsimonious\, with few
  parameters\, to those which can match the observed term structure of impl
 ied volatility. This allows flexibility. We construct an example model whi
 ch accounts for so-called volatility events\, caused by the scheduled rele
 ase of pertinent information\, such as unemployment figures\, inflation ra
 tes and economic growth rates.
LOCATION:MR14\, Centre for Mathematical Sciences
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