A new method to retrieve the risk-neutral probability measure from observed option prices is developed and a closed form pricing formula for European options is obtained by employing a modified Gram-Charlier series expansion, known as the Gauss-Hermite expansion. This expansion converges for...

Many economic and econometric applications require the integration of functions lacking a closed form antiderivative, which is therefore a task that can only be solved by numerical methods. We propose a new family of probability densities that can be used as substitutes and have the property of...

The well-known binomial and trinomial tree models for option pricing are examined from the point of view of numerical efficiency. Common lattices use a large part of time resources for calculations which are almost irrelevant for the solution. To avoid this waste of resources, the tree is...

This work develops an external habit model of the equity premium subject to long run risk in continuous time. The solution to this model is an analytic price-dividend function of the surplus consumption ratio and the long run risk variable. As a result, the equity premium can be accurately...

The Heston model is one of the most popular stochastic volatility models for Equity and FX modelling. Although it was developed more than fifteen years ago, its understanding is still not complete and many recent publications have addressed deep theoretical and implementation issues. We review...

We present an algebraic version of an iterative multigrid method for obstacle problems, called projected algebraic multigrid (PAMG) here. We show that classical AMG algorithms can easily be extended to deal with this kind of problem. This paves the way for efficient multigrid solution of...

The pricing of the European cash-settled swaptions is analysed. The standard market formula results are compared to results obtained from different models. Significant discrepancies are observed, justifying the title

We develop highly-efficient parallel Partial Differential Equation (PDE) based pricing methods on Graphics Processing Units (GPUs) for multi-asset American options. Our pricing approach is built upon a combination of a discrete penalty approach for the linear complementarity problem arising due...

We study a parallel implementation on a Graphics Processing Unit (GPU) of Alternating Direction Implicit (ADI) time-discretization methods for solving time-dependent parabolic Partial Differential Equations (PDEs) in three spatial dimensions with mixed spatial derivatives in a variety of...

In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus confirming a conjecture from Gatheral as well as providing a...