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Identifying Model Risk under Basel 2.5 and the FRTB Disclaimer: The contents of this presentation are for discussion purposes only, represent the presenter’s views only and are not intended to represent the opinions of any firm or institution. None of the methods described herein is claimed to be in actual use. Risk Week Cambridge September 2014 Péter Dobránszky

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Generic credit spread curves by a fully cross-sectional method 2

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Evolution of risk aversion premium 3 Negative risk premium may appear nowadays for HY

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Dynamics of the generic credit spread curves 4

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Autocorrelation of rating transitions It is more likely that a downgrade is followed in a year by a downgrade / default and an upgrade is followed by an upgrade. A downgrade in the past three months implies a conditional PD as high as a non-conditional PD 4-5 notches down. 6 1Yupstaydown up 15%78%7% stay 10%77%14% down 6%71%23%

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Arrival to defaults Expected vs. unexpected defaults – What is incremental? Implicit equity-credit link Differences for corporates, financials and sovereigns by fundamentals 7

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Arrival to defaults Consistency and coherency issues between capital charges Potential exposure within a year does not capture that losses in case of a future default have potentially been realised already by CVA VaR when spreads were climbing up – this CVA variation is capitalised now Similarly for IRC vs. VaR – if being long credit for Greece, daily MtM losses were capitalised by VaR, while there was no further loss at the time of default, thus IRC capital charge was questionable Sudden and expected defaults shall be separated and capitalised accordingly 8

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Black swan events on the equity market 9 StDev(C US 30/12/05-12/09/08) = 2.35% Log-return on 15/09/08 was % -7σ event assuming normality this should happen once in years

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Mixing observations from various distributions 10 Assume stochastic volatility daily log-returns are not from the same population! Normalise daily log-returns by dividing them by the concurrent short-term implied volatility (easily available in Bloomberg). Less extreme events (most extreme is IV) and closer to the Gaussian shape.

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Through-the-cycle vs. point-in-time Case: equally weighted, daily rebalanced, long-only portfolio of Eurostoxx 50. Pure 1-day 99% Historical VaR and Monte-Carlo VaR showed 9-10 excesses in 2008 suggesting “extraordinary” behaviour of the market. Black Swan events: unexpected and inexplicable by a given model. Key property of market crisis: increased market activity rate. 11

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Through-the-cycle vs. point-in-time 12 YearUnfilt. VaREWMA HVaRFilt. HVaRFilt. MC VaR

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Through-the-cycle vs. point-in-time Once in 2.3 billion year event– N ( N-1 ( 99%, 60% ), 20% ) 99% 1-day VaR 60% - average VIX in Q 20% - 25-year average of VXO/VIX One may need to consider the designed purpose of the model. Using an appropriate weighting scheme, ceteris paribus, the number of excesses may be fine. For such a small linear portfolio, no dependence on the copula choice. However, weighting scheme is incompatible with regulatory requirements. 3x increase in few weeks – potential for large pro-cyclicality. Solution of regulation for capital pro-cyclicality are the Stressed VaR and Stressed ES measures. Economic interpretation of such stressed measures may exist only for simple linear portfolios. As traders follow other risk limits as well, market pro-cyclicality may persist. The emergence of new risk types in times of stress is not addressed by the stressed measures. Divergence between risk models and capital models Even more the case with the liquidity horizons of the FRTB Back-testing issues in case of changing regimes: 1-year TTC measure vs. traffic light approach 13

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Heteroscedastic returns seen as co-jumps Often said that co-jumps are more frequent in times of stress and are a key characteristic of crises. Pearson correlation assumes that correlation was the same each day. Gaussian correlation structure underestimates the probability of large co-movements in large portfolios. Frequent co-jumps may be captured by HVaR but not by Gaussian copula based MCVaR. Case: example of Eurostoxx 50 In theory: 2-3 times a year that more than 2/3 of constituents jumped In practice: 22 times in

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Heteroscedastic returns seen as co-jumps Accounting for the stochastic behaviour of the business time: Frequency of co-jumps reduces significantly. A large part of observed correlation increase may be explained. Applying no weighting scheme is seen as smoothing: Gaussian copula is seen as even more smoothing (average correlation). Thanks to Stressed VaR and Stressed ES, HVaR and MC VaR disagree now in benign periods also. How reactive Stressed VaR should be? 15

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Risk metrics of quadratic payoffs Eurostoxx 50 – such well-behaved portfolio hardly exists in practice How the risk metrics scale as a function of risk factor volatilities? No weighting scheme – Stressed VaR is not a PIT measure at the peak of the crisis, but rather a TTC measure through the stress period Around twice as volatile risk factors – similarity to ten-day scaling 16

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Risk metrics of quadratic payoffs 17

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Risk metrics of quadratic payoffs 18

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Risk metrics of quadratic payoffs 19 1-day VaR4-day VaR1-day SVaR Mean0.00% 0.09% 1% VaR-0.03%-0.13%-0.03%

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Accounting for risk premium 20

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Accounting for risk premium Case: short protection portfolio of CDSs written on BB rated issuers as of 30 June 2009 Average 1Y CDS spread of the constituents was 600 bps. In case no default or migration event happens, expected portfolio P&L is around 6%. Not accounting for time value, expected portfolio P&L is around -1% (TTC). Numerous default events may occur before any effective loss is realised. Dislocation is hidden behind the IRC figures. 21

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Recovery rates What are the local and foreign currency recovery rates and probabilities of defaults? Sovereigns may go default on their hard currency and local currency obligations separately Various approaches to adjust the LC recovery rates to account for FX depreciation risk or to interpret the problem as what is the LC bond value in case the HC bond migrate or default. However, FX risk and, accordingly, the risk of FX depreciation in case of default is excluded from IRC and IDR! What are the recovery rates for covered bonds and government guarantees? The rating of issuing bank is taken, which implies “high” PD, but when the issuer goes to default, there is still a pool of assets or another guarantor to meet the obligation. Recovery rates may be adjusted to compensate that “wrong” PDs are used. However, if for instance the recovery rate for covered bonds is 90%, but the dirty price of a covered bond is 82% at the moment, then what is the P&L in case of default? Recovery remarking process – general problem of enforcing that RR < PV. Stochastic recovery rates: One may distinguish stochastic expected recovery rates and stochastic realised recovery rates. If the expected recovery rates are already modelled by a stochastic process and the risk is already captured in the VaR / ES, which may be required in case the institution trades fixed recovery rate exotic deals and / or distressed bonds, then the realised recovery rate is not stochastic anymore except in case of sudden defaults. If the recovery rates are assumed to be stochastic, the related risks are captured in VaR / ES, then the default risk incremental to VaR / ES includes only the rare cases of sudden defaults. 22

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Estimation of transition and default probabilities 23

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Joint defaults and correlated migrations Common practice: default correlation modelling through asset value correlation (AVC) The approach is in line with the earlier presented strong equity-credit link. However, this means also model deficiency because sovereigns can hardly be treated as companies. Often, copula approach is mixed with the structural Merton model. However, in the Merton model the default can be triggered only at maturity. Hence, it does not qualify without specific treatments to tackle multiple step simulations and various LHs. Gaussian copula approach is not a consistent continuous-time model. 24 If originally the default events and migration moves were simulated in one time step, then simulations cannot be split into two or more time steps in a way that will result in the original joint law of defaults at the end. The forward density does not exist. What asset value correlation parameter to use for the various time horizons?

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Joint defaults and correlated migrations Fix the AVC and measure the Pearson default correlation for various horizons (annual PD = 2%, 2- state Markov chain with jump-to-default) Similar term structure of default correlations by ratings: The lower the cumulative probability of defaults the lower is the default correlation. Most copula based approaches imply that the defaults of highly rated names are basically independent. 25

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Content LH in ES Results and key findings of QIS1 Equity correlations and CDS spread correlations – note on sovereigns Structural change of market, pricing and risk management Higher risk aversion rate, rescaling of ratings Multiple conservatism – what is really “incremental” – spread evolution vs. migration and default P&L - stochastic expected and realised recovery rate In case of intensity correlation the joint PD is limited, Sovereign correlation modelling challenge Scaling of 1-day returns is accepted, but back-tests move even further away from application. Amortisation of sensitivities, vega, implied correlation, etc. Long-term modelling in the CCR framework is already a challenge. Hardly possible to back-test. On top of it, CCR focuses only on traditional risk types, while MR exposure is mainly on spreads, bases, for which proper processes can be hardly designed and calibrated with confidence. Option positions cannot be assumed being unhedged, rebalanced for months. It assumes no trade at all until the first LH. There may be illiquidity for some underlyings, but not for all at the same time. 27

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