This paper presents a number of new theoretical results for replication of barrier options through a static portfolio of European put and call options. Our results are valid for options with completely general knock-out/knock-in sets, and allow for time- and state-dependent volatility as well as...

The standard approach (e.g. Dupire (1994) and Rubinstein (1994)) to fitting stock processes to observed option prices models the underlying stock price as a one-factor diffusion process with state- and time-dependent volatility. While this approach is attractive in the sense that market...

This paper considers extensions of the Libor market model (Brace et al (1997), Jamshidian (1997), Miltersen et al (1997)) to markets with volatility skews in observable option prices. We expand the family of forward rate processes to include diffusions with non-linear forward rate dependence and...