Using stock data that covers the period from 6th April 2001 to 17th June 2009, including data for the recent crisis period, we perform Value at Risk risk model validation by backtesting the performance of VaR models in predicting future losses of a portfolio of stocks, futures and options. The...

In this paper we describe methods of decomposing risk into subcomponents such as contributing instruments, subportfolios or underlying risk factors e.g., equity, foreign exchange, economy-wide systematic and interest rate risk factors. The Euler allocation principle for allocation of instrument...

Portfolio risk measures such as Value at Risk is traditionally measured using a buy and hold assumption on the portfolio. In particular the 10-day market risk capital is commonly measured as the 1-day Value at Risk scaled by the square root of 10. While this scaling is convenient to obtain n-day...

The measurement of firms funding liquidity risk is in general complex. In particular, liquidity insolvency happens the first time the firm cannot generate sufficient counterbalancing capacity from the liquidity hedging portfolio to cover the funding gap. The complexity arises from the fact that...

Risk aggregation is the roll-up of low-level risks or sub-risks to higher levels. Risk management for banks or insurance institutions involves risk measurement and risk control at the individual risk level, including market risk, credit risk, and operational risks and also the aggregated risk of...