Forward equations for option prices in semimartingale models

Economy – Quantitative Finance – Pricing of Securities

Scientific paper

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Proof shortened+ reference added. Final revision before publication

Scientific paper

We derive a forward partial integro-differential equation for prices of call
options in a model where the dynamics of the underlying asset under the pricing
measure is described by a -possibly discontinuous- semimartingale. A uniqueness
theorem is given for the solutions of this equation. This result generalizes
Dupire's forward equation to a large class of non-Markovian models with jumps.

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