Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some components of the solution at discrete times. Since exact...

In this paper, we introduce a new Fourier method for computing value-at-risk for a portfolio with derivatives and for return models with fat tails. The new method does not assume that the characteristic function for the return model is known explicitly. We define a class of admissible models for...

Regulators require banks to employ value‐at‐risk (VaR) to estimate the exposure of their trading portfolios to market risk, in order to establish capital requirements. However, portfolio‐level VaR analysis is a high‐dimensional problem and hence computationally intensive. This article...

The paper considers the pricing of a range of volatility derivatives, including volatility and variance swaps and swaptions. Under risk-neutral valuation closed-form formulae for volatility-average and variance swaps for a variety of diffusion and jump-diffusion models for volatility are...