An algorithm to generate samples with approximate first-, second-, and third-order moments is presented extending the Cholesky matrix decomposition to a Cholesky tensor decomposition of an arbitrary order. The tensor decomposition of the first-, second-, and third-order objective moments...

This paper investigates the frequency of extreme events for three LIFFE futures contracts for the calculation of minimum capital risk requirements (MCRRs). We propose a semi-parametric approach where the tails are modelled by the Generalised Pareto Distribution and smaller risks are captured by...

This paper examines the ability of several different continuous-time one and two-factor jump-diffusion models to capture the dynamics of the VIX volatility index for the period between 1990 and 2010. For the one-factor models we study affine and non-affine specifications, possibly augmented with...

Most banks employ historical simulation for Value-at-Risk (VaR) calculations, where VaR is computed from a lower quantile of a forecast distribution for the portfolio’s profit and loss (P&L) that is constructed from a single, multivariate historical sample on the portfolio’s risk factors....

This paper examines the ability of twelve different continuous-time two-factor models with mean-reverting stochastic volatility to capture the dynamics of the S&P 500 and three European equity indices. The stochastic volatility models are the square root variance, GARCH, and log volatility...

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...

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. A new class of rectangular orthogonal matrices is fundamental to the methodology, and these ``L-matrices'' can be deterministic, parametric or data specific in nature....

Many popular techniques for determining a securities firm’s value at risk are based upon the calculation of the historical volatility of returns to the assets that comprise the portfolio, and of the correlations between them. One such approach is the J.P. Morgan RiskMetrics methodology using...

We present a two-factor stochastic default intensity and interest rate model for pricing single-name default swaptions. The specific positive square root processes considered fall in the relatively tractable class of affine jump diffusions while allowing for inclusion of stochastic volatility...

The article examines whether commodity risk is priced in the cross-section of equity returns. Alongside a long-only equally-weighted portfolio of commodity futures, we employ as an alternative commodity risk factor a term structure portfolio that captures the propensity of commodity futures...