Riassunto esame Risk management, Prof. Gioia Aldo, libro consigliato Risk Management, Mario Valletta

Managing Model Risk

Ccope with some weaknesses in the models and, hence, also the model risk.This multiplier is “applied to”… [m ]… “(floor m=3”… (therefore, this multiplier is at least 3C“it slide… “weaknesses”… So,for all banks), but can be increased”... we spoke about modelrisk and, in the supervisory practice, this multiplier is one of the ways for mitigating themodel risk.So, if the supervisor deems [ritiene] that our model has some weaknesses, this multiplier can beincreased to take into account those.The IRC, instead, is computed on a weekly (!) basis and its value that we have to put in theregulatory formula is the maximum between the IRC at the last day of the quarter and theaverage of the 12 observations in a quarter of the weekly IRC.This risk figure is already a capital requirement figure and there is no multiplier (!) for it.We will see why because the IRC is more a credit risk measure. Whereas the VaR

Common approach, and which will be more important with the moving to the fundamental review of the trading book.

So, the historical simulation is important because we take the volatility of each risk class from the history (!): therefore, we don’t make any assumption about the distribution of the risk factors.

Usually, we take into account 250 days of history and the daily shock of the price of each to “cut” asset in order to define the probability distribution of losses and, then, the distribution at the 99 percentile. 673

So, we compute the VaR on a daily basis, but we are now talking about the regulatory capital: therefore, in order to move from a daily VaR which is used for ? [38.55] credit monitoring in a day-by-day process of the bank to the number that we need to put in the regulatory requirement, we need to move from a daily VaR to a 10-days (!) VaR, because regulators require it.

How do we move to it? Using the square root of time: therefore, when we need to calculate the capital,

We apply the formula before, but we need to multiply the average of the daily VaR[termine 2] not only by the multiplier, but also by the square root of time. So, at the end, the final calculation is the average of the 6 observations during a quarter multiplied by the multiplier for the model risk multiplied for the square root of time in order to take into account 10-days shocks (instead of daily shocks).

How does it work the model validation test under Basel 2.5? How does the bank assure that the VaR is robust and that it is a good risk figure to compute the capital requirement?

The model validation is based on a backtesting exercise, which means that the bank has to perform the "conservativeness check of the internal model" and this is achieved by the means of a "retrospective test"... 674[paragrafo 2]... "in the portfolio's value"... The following are the P&Ls and, therefore, on the positive part, we see the profits and, on the negative,

the losses.“whether the measures”… slide… “theSo, to assess if a VaR is conservative, we need to checktrading results”… : therefore, in theory, to be perfect, we should never achieve breaches, butwe should have always a risk figure which is higher than the loss that the bank can occur in 1to put aside the capital to cope with potential losses…day. Given that the VaR is used… But we know that the VaR is computed at the 99% of the confidence interval: therefore, theregulators established also how many breaches are allowed for a VaR figure.So, the supervisors monitor the vastness of all the VaRs and they count the overshootings,which, at last, can imply an increase of the multiplier m .CSo, in order to test if our VaR is sound, the supervisors require to take into account thenumber of overshootings.This means that, if we have less than 5 overshootings, no addend is required and, therefore, themultiplier will be equal to 3 [vedi

[floor dell'm di prima] because our VaR is rightly capable to cope with the 99% of the 1-day loss; if we have 5 overshootings, the multiplier will be equal to 675...

Of course, if we have 10 or more breaches, supervisors could decide to make an inspection to check what is wrong in the risk figures.

So, this is currently the way in which supervisors assess the soundness of our internal models.

So, which are the risk figures and the PL figures that are compared?

We need to count the breaches on 2 different PLs figures: therefore, we need to take into account the VaR vis-à-vis the actual backtesting PL and the current VaR vis-à-vis the hypothetical backtesting PL. The difference between the actual and the hypothetical backtesting is that the 1 takes into account intra-days activities: therefore, it is more similar to the managerial PL that is reported to the trading floor.

The only things that are not included

Are fees and commissions, that are an extra charge and have nothing to do with the risk factor movements. The hypothetical PL, instead, does not include intra-days activities, but it has the same perimeter as of the VaR, which, indeed, is computed at the end of each day (!). 676 So, we need to take into account the maximum number of breaches between those of the VaR against the actual PL and those of the VaR against the hypothetical PL. For example, if we have 5 breaches against the hypothetical PL and 6 against the actual, we need to take into account 6 overshootings and to increase our multiplier by 0.5. Before Basel 2.5, backtesting was only required against the hypothetical PL, which, however, only takes into account the position at the end of the day. After Basel 2.5, regulators wanted to be more challenging: therefore, this actual PL was used because some traders do a lot of intra-day activities. Now, we move to the 2 component of the capital requirement which is the stressed VaR.

“applies to”…First of all, the stressed VaR is another VaR[punto 1]… “of internal models”… (therefore, if we have an internal model approved for the interest rate and we report the credit spread with the standardized approach, we need to compute the stressed VaR for the interest rate, only for (!) the risk factors that have been approved).(Before, we said that, in order to use an internal model, we need to receive the approval from the supervisors. We could receive the approval also on single (!) risk factors: that we have the approval for all).[punto 1]… “in the capital requirements”… (because the VaR is a statistical measure that assumes that the history explains the volatility in the market: therefore, if we take into account 1 year of history for our risk factors, the volatility that the VaR takes into account is the one of 1 year of history.Therefore, if we meet an unprecedent shock which

is higher than the precedent year, we may have some breaches because the VaR takes some time to incorporate the new scenarios in the volatility estimation)... So, the stressed VaR is meant to be a kind of buffer that we need to compute by calculating the VaR "by choosing the scenario"... slide.. "for the bank's portfolio"...: therefore, it means that we need to compute the VaR by taking into account an horizon of at least 10 years and to take it as the scenario of the VaR that we apply to our current portfolio... So, the purpose of the stressed VaR is to "maintains"... slide... "low volatility"... So, if we have a period of 1 year of low volatility and the VaR is lower because of it, the stressed VaR never follows this trend because it is not sensitive to the current volatility, but to the worst scenario (!) for our portfolio. Therefore, what we have to do is: we keep the today's portfolio,

Clearer and of 2 different portfolios, bank A and bank B, that have 2 different scenarios... First of all, we can see that the history that is taken into account goes back to 2008: therefore, generally speaking, we need to take into account a long history and we need to compute the VaR backward in order to find the 1-year horizon which maximizes the losses for our portfolio. Therefore, in the example, bank A has as stressed VaR scenario the Lehman Brother Crisis; bank B, the Sovereign Debt Crisis... What does it mean? We have 2 banks, one is the investment bank and the other is the Treasury, where, usually, the 1st has a lot of financial issuers in its portfolio, whereas the 2nd has a lot of sovereign bonds. Therefore, if we have a book which is mainly made of sovereign bonds, our portfolio will be more sensitive to the Sovereign Debt Crisis and, therefore, the scenario that maximizes the losses.