Forward equations for option prices in semimartingale models

Abstract

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.

Proof shortened+ reference added. Final revision before publication

References in corpus (2)

• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
• Mimicking the marginal distributions of a semimartingale

Cited by in corpus (5)

• Short-time asymptotics for marginal distributions of semimartingales
• Don't stay local - extrapolation analytics for Dupire's local volatility
• Generalized entropy minimization under full marginal constraints
• Performance of tail hedged portfolio with third moment variation swap
• Modeling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps