The popular replication formula to price variance swaps assumes continuity of traded option strikes. In practice, however, there is only a discrete set of option strikes traded on the market. We present here different discrete replication strategies and explain why the continuous replication...

This paper explores the stochastic collocation technique, applied on a monotonic spline, as an arbitrage-free and model-free interpolation of implied volatilities. We explore various spline formulations, including B-spline representations. We explain how to calibrate the different...

We present in this paper the practical aspects of pricing of variance swaps, volatility swaps, variance options and volatility options under the model of Carr and Lee. Popular related derivative products to the pure vanilla variance swaps are reviewed: the forward starting variance swaps,...

Under the local volatility model, the convergence of Monte-Carlo with Milstein discretization and Euler discretization are compared for the pricing of Vanilla, Digital, discrete Barrier options as well as a more exotic variety of option, the Accumulator. A finite difference approach is also...

The implied volatility surface is built from a discrete set of vanilla option quotes. To move from a discrete set to a continuous surface, interpolation and extrapolation are therefore needed in the expiry dimension as well as in the strike dimension. This paper will study the interpolation and...