The problem of pricing European options based on multiple assets with transaction costs is considered. These options include, for example, quality options and options on the minimum of two or more risky assets. The value of these options is the solution of a nonlinear parabolic partial...

We introduce an explicitly solvable multiscale stochastic volatility model that generalizes the Heston model. The model describes the dynamics of an asset price and of its two stochastic variances using a system of three Ito stochastic differential equations. The two stochastic variances vary on...

We propose a numerical method to price corporate bonds based on the model of default risk developed by Madan and Unal. Using a perturbation approach, we derive two semi-explicit formulae that allow us to approximate the survival probability of the firm issuing the bond very efficiently. More...

We investigate the performance of the Heston stochastic volatility model in describing the probability distribution of returns both in the case of single assets and in the case of asset portfolios. The R. parameters of the Heston model are estimated from observed market prices using a simple...

An increasingly popular and promising approach to solve option pricing models is the use of numerical methods based on radial basis functions (RBF). These techniques yield high levels of accuracy, but have the drawback of requiring the inversion of large full system matrices. In the present...