Fever Palm

Poetry by Carol A. Alexander

Bayesian Methods for Measuring Operational Risk

The likely imposition by regulators of minimum standards for capital to cover 'other risks' has been a driving force behind the recent interest in operational risk management. Much discussion has been centered on the form of capital charges for other risks. At the same time major banks are developing models to improve internal management of operational processes, new insurance products for operational risks are being designed and there is growing interest in alternative risk transfer, through OR-linked products.

Orthogonal Methods for Generating Large Positive Semi-Definite Covariance Matrices

It is a common problem in risk management today that risk measures and pricing models are being applied to a very large set of scenarios based on movements in all possible risk factors. The dimensions are so large that the computations become extremely slow and cumbersome, so it is quite common that over-simplistic assumptions will be made. In particular, in order to generate the large covariance matrices that are used in Value-at-Risk models, some very strong constraints are imposed on the movements in volatility and correlations in all the standard models. The constant volatility assumption is also imposed, because it has not been possible to generate large GARCH covariance matrices with mean-reverting term structures.

Principal Component Analysis of Volatility Smiles and Skews

Several principal component models of volatility smiles and skews have been based on daily changes in implied volatilities, by strike and/or by moneyness. Derman and Kamal (1997) analyze S&P500 and Nikkei 225 index options where the daily change in the volatility surface is specified by delta and maturity. Skiadopoulos, Hodges and Clewlow (1998) apply PCA to first differences of implied volatilities for fixed maturity buckets, across both strike and moneyness metrics. And Fengler et. al. (2000) employ a common PCA that allows options on equities in the DAX of different maturities to be analyzed simultaneously.

Understanding the Internal Measurement Approach to Assessing Operational Risk Capital

The recent publication by the Basel Committee of CP2.5, the working paper on Operational Risk Capital Charges, has shed new light on the methods that will be proposed for the measurement of operational risks in the Basel II Accord. This paper examines the foundations of the Internal Measurement Approach (IMA), demonstrating both its tractability and its flexibility to deal with different types of operational risks

Short and Long Term Smile Effects: The Binomial Normal Mixture Diffusion Model

This paper extends the normal mixture diffusion (NMD) local volatility model of Brigo and Mercurio (2000, 2001a,b, 2002) so that it explains both short-term and long-term smile effects. Short-term smile effects are captured by a local volatility model where excess kurtosis in the price density decreases with maturity. This follows from the central limit theorem and concords with the ‘stylised facts’ of econometric analysis of ex-post returns of different frequencies. We introduce a term structure for option prices in the NMD model by assuming there is a fixed probability of each volatility state occurring in every time interval Dt, and we show that with this assumption the mixing law for the price density is the multinomial density. This very parsimonious model can easily be calibrated to observed option prices. However, smile effects in currency options often persist into fairly long maturities, and to capture at least some part of this it is necessary to introduce stochastic volatility. The last part of this paper considers only two possible volatility states in each Dt with probabilities l and (1 - l). If l were fixed, the binomial mixing law model would only apply to short-term smile effects. But by making l stochastic, longer-term smile effects that arise from uncertainty in volatility are also captured by the model. The results are illustrated by calibrating the model with and without stochastic l, to a currency option smile surfaceLocal volatility, stochastic volatility, smile consistent models, term structure of option prices, normal variance mixtures