Jerzy Zabczyk
HJMM equation for forward rates with linear volatility.
Fri, 10/29/2010 - 15:01 — SomNambulAuthors: Jerzy Zabczyk, Michal Barski
Subjects: Probability
AbstractThe paper is concerned with the problem of existence of solutions for the
Heath-Jarrow-Morton equation with linear volatility. Necessary conditions and
sufficient conditions for the existence of semigroup solutions and strong
solutions are provided. It is shown that the key role is played by the
logarithmic growth conditions of the Laplace exponent.CDO term structure modelling with Levy processes and the relation to market models.
Tue, 07/13/2010 - 15:01 — SomNambulAuthors: Jerzy Zabczyk, Thorsten Schmidt
Subjects: Pricing of Securities
AbstractThis paper considers the modelling of collateralized debt obligations (CDOs).
We propose a top-down model via forward rates generalizing Filipovi\'c,
Overbeck and Schmidt (2009) to the case where the forward rates are driven by a
finite dimensional L\'evy process. The contribution of this work is twofold: we
provide conditions for absence of arbitrage in this generalized framework.
Furthermore, we study the relation to market models by embedding them in the
forward rate framework.Bonds with volatilities proportional to forward rates.
Fri, 11/06/2009 - 16:01 — SomNambulAuthors: Michal Baran, Jerzy Zabczyk
Subjects: Probability
AbstractThe problem of existence of solution for the Heath-Jarrow-Morton equation
with linear volatility and purely jump random factor is studied. Sufficient
conditions for existence and non-existence of the solution in the class of
bounded fields are formulated. It is shown that if the first derivative of the
Levy-Khinchin exponent grows slower then logarithmic function then the answer
is positive and if it is bounded from below by a fractional power function of
any positive order then the answer is negative. Numerous examples including
models with Levy measures of stable type are presented.
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