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...

There is no exact closed form formula for pricing of European options with discrete cash dividends under the model where the underlying asset price follows a piecewise lognormal process with jumps at dividend ex-dates. This paper presents alternative expansions based on the technique of Etore...

This paper describes a fast analytic formula to obtain the basis point volatility 'b.p. vol' for a given option price under the Bachelier normal model with near machine accuracy. The b.p. vol is simply the implied volatility of an option under the Bachelier (or normal) model. In the...

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,...

It is well known that a Quanto Process based on Lognormal Equity and Lognormal exchange rate processes can be easily simulated through a Lognormal process with modified drift. We study here what happens when both processes follow a local volatility model. In addition, we analyze the impact of...

We find lower and upper bounds for the price of Bermudan basket options by Monte-Carlo simulation through regression and look at the impact of the choice of random number generator, as well as whether including in-the-money paths or not in the regression

The SABR stochastic volatility model is a very popular interpolator of implied volatilities, with a given dynamic. This paper presents a simple and very fast method to calibrate the SABR model to given market volatilities, that is to imply the SABR parameters from a given market smile

We look at how to reproduce nearly exact bond and forward contract prices with the TR-BDF2 finite difference method applied to the Black-Scholes partial differential equation, with a term structure of interest rates or a term structure of dividends yields. We also show that a careful discretion...