This issue is reports on the workshop “Models and Numerics in Financial Mathematics”, which took place at the Lorentz Center in Leiden in the Netherlands on May 26–29, 2015.
Serguei Mechkov initialises Heston model’s parameters using probability distributions
This paper applies a variety of second-order finite difference schemes to the SABR arbitrage-free density problem and explores alternative formulations.
A mixed Monte Carlo and partial differential equation variance reduction method for foreign exchange options under the Heston–Cox–Ingersoll–Ross model
The paper concerns a hybrid pricing method build upon a combination of Monte Carlo and PDE approach for FX options under the four-factor Heston-CIR model.
The Authors introduce a closed-form approximation for the forward implied volatilities.
Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous-time mean-variance asset allocation under stochastic volatility
The paper deals with robust and accurate numerical solution methods for the nonlinear Hamilton–Jacobi–Bellman partial differential equation (PDE), which describes the dynamic optimal portfolio selection problem.
In this paper the authors provide a comprehensive treatment of the discretization effect under general stochastic volatility dynamics.
This issue of The Journal of Computational Finance contains four papers that are quite different in terms of their financial applications, and they stand out because of their remarkable mathematical techniques.
Accelerated trinomial trees applied to American basket options and American options under the Bates model
This paper introduces accelerated trinomial trees, a novel efficient lattice method for the numerical pricing of derivative securities.
In this paper the use of B-splines is advocated for volatility modeling within the calibration of stochastic local volatility (SLV) models and for the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data.
Lorenzo Ravagli shows how to exploit a risk premium embedded in the vol of vol in out-of-the-money options
In this issue of The Journal of Computational Finance, we encounter different contemporary approximations and techniques for financial problems.
By means of B-spline interpolation, this paper provides an accurate closed-form representation of the option price under an inverse Fourier transform.
Marzio Sala and Vincent Thiery show the derivation of the continuous adjoint problem for PDEs