This lecture is given at the University of Leonard de Vinci, in Paris, France, to students of the School of Engineer program in Finance. It is a general introduction to the understanding of building blocks of the non-gaussian world and the shortcomings of the normal paradigm when pricing and...

Standard risk management approaches fail to consider parameter uncertainty, which has led to improper risk management. Blind faith in parameter estimates has too often led to blind faith in the resulting VAR outputs, and when these estimates are too often exceeded the proposed solution is...

The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be integrated into the theoretical framework of convex...

The Basel Committee of Banking Supervision has recently set out the revised standards for minimum capital requirements for market risk. The Committee has focused, among other things, on the two key areas of moving from Value-at-Risk (VaR) to Expected Shortfall (ES) and considering a...

Market participants use leveraged derivatives to gain access to equity market exposure through broker banks. Leverage and interconnectedness via overlapping portfolios of dealer banks can amplify adverse market movements, potentially causing sizeable losses. I propose a model, based on granular...