Summary
We derive forward partial integrodifferential equations (PIDEs) for pricing up-and-out and down-and-out call options when the underlying is a jump diffusion. We assume that the jump part of the returns process is an additive process. This framework includes the Variance-Gamma, finite moment logstable, Merton jump diffusion, Kou jump diffusion, Dupire, CEV, arcsinh normal, displaced diffusion, and Black–Scholes models as special cases.
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Carr, P., Hirsa, A. (2007). Forward Evolution Equations for Knock-Out Options. In: Fu, M.C., Jarrow, R.A., Yen, JY.J., Elliott, R.J. (eds) Advances in Mathematical Finance. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4545-8_11
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DOI: https://doi.org/10.1007/978-0-8176-4545-8_11
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