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SUMMARY: Generalized sub-Riemannian cut loci and implied/local volatility 
 smiles - Peter Friz (TU Berlin)
DTSTART:20120424T153000Z
DTEND:20120424T163000Z
UID:TALK37417@talks.cam.ac.uk
CONTACT:24873
DESCRIPTION:Density expansions for hypoelliptic diffusions $(X^1\,...\,X^d
 )$ are\nrevisited. In particular\, we are interested in density expansions
  of the\nprojection $(X_T^1\,...\,X_T^l)$\, at fixed time $T>0$\, with $l 
 \\leq d$.\nGlobal conditions are found which replace the well-known "not-i
 n-cutlocus"\ncondition known from heat-kernel asymptotics (Molchanov\, Bis
 mut\, Ben Arous\,\n...). Our small noise expansion allows for a "second or
 der" exponential\nfactor\, not present in small time expansions.\n\nApplic
 ations include tail and implied/local volatility asymptotics in some\ncorr
 elated stochastic volatility models. In particular\, we are able to\nanaly
 ze the Stein--Stein model in case of negative correlation (the typical\nca
 se in equity markets)\, thereby solving a problem left open by A.\nGulisas
 hvili and E.M. Stein.\n\nJoint work with Deuschel\, Jacquier and Violante.
 \n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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