This paper surveys the literatures on numerical methods from its origins to present to evaluate American-style claims. An extensive review of numerical meth- ods is provided. In particular, emphases is placed on recent trends and developments in the multi-grid and Galerkin method with the...

A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by...

In this notice we are comment popular approaches to the credit risk modeling.

We present a stochastic default intensity model where the intensity follows a tractable jump-diffusion process obtained by applying a deterministic change of time to a non mean-reverting square root jump-diffusion process. The model generates higher implied volatilities for default swaptions...

In this paper a simulation approach for defaultable yield curves is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process where the stochastic intensity represents the credit spread. The forward credit spread volatility function is affected by...

In this paper a simulation approach for defaultable yield curve is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process when the stochastic intensity repre sents the credit spread. The forward credit spread volatility function is affected by the...

The Finite Element Method is a well-studied and well-understood method of solving partial differential equations. It's applicability to financial models formulated as PDEs is demonstrated. It's advantage concerning the computation of accurate `Greeks' is delineated. This is demonstrated with...

Options on two underlyings are a common exotic product in the equity and FX derivatives market. The value of these kinds of options depends on the correlation of the two underlyings. We will present a model to compute a lower bound for the price of this option. The model, represented by a...

This paper is concerned with the pricing of European continuous-installment options where the aim is to determine the initial premium given the installment payments schedule. The particular feature of this pricing problem is the determination, along with the initial premium, of an optimal...