Value-at-Risk and Risk Classification

The Value-at-Risk enables to classify financial instruments according to their risk


Profit-and-Loss Distribution Example

Risk Classification

Classification of an instrument's risk-profile :

Cat. 1 Conservative -2.5% < VaR < 0%
Cat. 2 Low risk tolerance -7.5% < VaR < -2.5%
Cat. 3 Moderate risk tolerance -12.5% < VaR < -7.5%
Cat. 4 Intense risk tolerance -17.5% < VaR < -12.5%
Cat. 5 High risk tolerance -25.0% < VaR < -17.5%
Cat. 6 Extreme risk tolerance -100% < VaR < -25.0%

The risk class 1 corresponds to the least risky category and 6 to the riskiest one.
In our example, the asset belongs to the risk category 6.

The Value-at-Risk

The Value-at-Risk (VaR) measures the maximum loss not exceeded over a 10-day holding period, with probability of 99%. Statistically, the VaR value then corresponds to the 1% quantile of the Profit-and-Loss distribution, that is 1% of the returns are below the VaR value.

In our example, we have:

  • A Value-at-Risk (VaR) of -65.72% means that for a 10-day holding period, the probability of losing more than 65.72% is 1%. Conversely, there is a 99% probability of not losing more than 65.72% of this asset.
  • A Value-at-Gain (VaG) of 109.48% means that for a 10-day holding period, the probability of gaining more than 109.48% is 1%. Conversely, there is 99% probability of not gaining more than 109.48% of this asset.
  • There is a 50.50% probability to gain (Probability-of-Gain) given a holding period of 10 days.

VaR Methodology

The estimation of VaR for structured products requires a Monte Carlo simulation approach. We use a 99% probability and a 10-days holding period. A large number of simulations is performed (order of 10000) to get a statistically significant result.

We generate randomly the variations of the different risk factors considered :

  • Underlying
  • Volatility
  • Interest rate
  • Exchange rate

In our Monte Carlo sample generation, we calibrate our model with market observed data. For each scenario, the instrument fair value is computed, and added to the Profit-and-Loss distribution. Eventually, the VaR is determined as the required 1% quantile. The VaR estimates are updated daily.