We introduce a class of stock models that interpolates between exponential Lévy models based on Brownian subordination and certain stochastic volatility models with Lévy-driven volatility, such as the Barndorff-Nielsen–Shephard model. The driving process in our model is a Brownian motion subordinated to a business time which is obtained by convolution of a Lévy subordinator with a deterministic kernel. We motivate several choices of the kernel that lead to volatility clusters while maintaining the sudden extreme movements of the stock. Moreover, we discuss some statistical and path properties of the models, prove absence of arbitrage and incompleteness, and explain how to price vanilla options by simulation and fast Fourier transform methods.

A method is introduced for testing the distribution of yield curves that are produced by asset scenario generators. The method is based on historical relationships in the conditional distributions of yield spreads given the short-term rate. As an illustration, this method is used to test a few selected models. To provide background, stochastic modeling for interest rates and fitting methods are briefly discussed.