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 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...

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...

We describe a number of ideas for speeding up and improving the performance of the Cheyette (1992) yield curve model with particular attention to the pricing of Bermudan swaptions. Specifically, we present: a better skew specification, a more efficient method for pricing, closed-form...

In the context of a stochastic local volatility model, we present a numerical solution scheme that achieves full (discrete) consistency between calibration, finite difference solution and Monte-Carlo simulation. The method is based on an ADI finite difference discretisation of the model

We present an effcient algorithm for interpolation and extrapolation of a discrete set of European option prices into a an arbitrage consistent full double continuum in expiry and strike of option prices. The method is based on an application of the fully implicit finite difference method and...

In this paper we find very accurate approximation formulas for single barrier option prices in the ZABR model. The formulas are based on a combination of put-call symmetry and short maturity expansions. For the SABR model we get closed form formulas and in the more general ZABR model an ODE must...

We extend the widely used SABR model (Hagan et al (2002)) to include a general volatility function and a CEV power on the stochastic volatility process itself. Using a short time expansion we derive results for the Dupire local volatility which in turn is inserted into a single time step finite...

We consider the option value of cash when nominal interest rates are no longer constrained by the zero lower bound. We provide a general valuation principle and solve for the value of cash in semi-closed form under Vasicek (1977) dynamics for the nominal short rate. In the absence of a zero...