Credit Exposure Measurement Fixed Income & FX Derivatives

Transcription

1 1 Credit Exposure Measurement Fixed Income & FX Derivatives Dr Philip Symes

2 1. Introduction 2 Fixed Income Derivatives Exposure Simulation. This methodology may be used for fixed income and FX derivatives. This is Monte-Carlo based calculation as detailed (for general approach see MC For Finance presentation). Calculates portfolio exposure and credit income deferral.

3 2. Contents 3 Generating Market Rate Scenarios. Generating Foreign Exchange Scenarios. Revaluation and Decomposition of Customer's Portfolio. Interpolation Methodology. Monte Carlo Simulations. Credit Income Deferral for Derivatives based on Expected Exposure.

4 3. Generating IR Scenarios 4 Zero curves used for: 1, 3 and 6 months; 1, 2, 3, 4, 5, 7, 10, 15 and 30 years. Three Basic Movements (BM) for interest rates: Parallel shift (PS); Steepening (ST); Curvature (CU). These can be shifted by ±1.645, ± or 0 (PS only). Mean reversion based on Vasicek model. Diverges from t behaviour.

5 4. Generating IR Scenarios (cont.) 5 zero rate with maturity i under scenario s at point m factor loadings for BM (weekly) customer specific factor, 1 (by default) or greater r =r e [l x l x l x ] 2 PS PS ST ST CU CU c s t 2 1 e 2 f 261 zero rate with maturity i today contribution of BM to S: up, down or none GROWTH FACTOR α is mean reversion speed (0.4576), κ is IR volatility scaling (1.6) and f is offset from m (weekdays)

6 5. Scaling Basic Movements 6 BM's account for 95% of variance in historical rates: BM's are scaled to account for 100%. Factor loadings are taken from 4 years of data (200 rates): Weekly: taken at COB every Wed; Correlated using eigenvalues of a covariance matrix.

7 6. Estimating Factor =[ Loadings correlation matrix 1, c m,c r ln 2 1, c r ln r 2 1 r m,c 1 R c ln r 1, c T ln r m,c T 1, c T is most recent r T 1 ] m,c r T 1 historical zero rate on date t with maturity i for currency c 7 covariance matrix = 1 T 1 Rc T R c Factor loadings l BM come from the eigenvalues of the covariance matrix Σ

8 7. Generating FX Scenarios 8 Calculate FX scenarios as IR scenarios. historical FX volatility matrix historical volatility of c w.r.t. CLC F=[ ln ln f 1 2 f 1 1 ln f 2 f c 1 f T 1 ln 1 f T 1 c f T c c ] f T 1 c hist= 52 T 1 ln f c T ln f c historical FX rate of currency c against credit line currency (CLC)

9 7. Generating FX Scenarios 9 14 major currencies can be used as CLC. Other currencies classified as non-major short term stable (NMSTS) or non-major snap (NMS). Table shows how different currencies are treated depending on appreciation factor X c: FX Scenario Major NMSTS NMS <1 year: historical volatility; Depreciation, X c <0 Historical volatility >1 year: high volatility (1) High volatility (2) Appreciation, X c >0 Historical volatility Snap factor of 30% allows instantaneous depreciation.

10 7. Generating FX Scenarios 10 Historical simulation scenarios: S=F c e x c c hist / 261 number of working days FX scenario appreciation of c w.r.t. CLC High volatility (1) NMSTS: S=F c e x c c 2 c 2 hist high High volatility (2) NMS (with 30% snap factor): S=F c min[0.7, c high exc / 261 ]

11 7. Generating FX Scenarios (cont) 11 Collateralised transactions have the FX risk of the collateral added as a perturbation This takes the same form as the historical scenario. The model requires daily (10 day) or monthly (32 day) margining with extra time for close-out. Historical FX rates are normalised and correlated in the same way as the IR The factor values are calculated for each BM based on weekly, uncorrected factor loadings. Cholesky decomposition is used to create random variables with this correlation.

12 8. Revaluation of Customer Portfolios 12 Revaluation under extreme IR scenarios. FIDES model can handle: 1+ legs from a trade; Using yield curve to discount cash flows; Margining during close-out periods (2+ weeks); Change of zero curve over close-out; Decomposition of trade legs (net and non-nettable).

13 8. Revaluation of Customer Portfolios 13 Aggregation of nettable trade legs: 8 extra MTM values required to calculate Δ; These are 95% CL shifts of BM; Instantaneous: not necessary to calculate nonperturbed scenario over close-out period. Distinctions between non-nettable transactions: IR (nettable) and FX (non-net) trades; FX trades cannot be aggregated.

14 9. Mutual Puts 14 Mutual put means that either party can unwind the transaction. Counterparties are considered either Pro (MT friendly) and non-pro. First upcoming mutual put is tenor reducing if transaction is collateralised or CP is a pro; Mutual puts are treated as mandatory puts (obligation to surrender the security) in the system; Cashflows are nettable only up to first mutual put date.

15 10. Interpolation Methodology 15 3 BM's described as 9 scenarios: 4 PS scenarios (includes half up/down); 2 for CU and ST; No change scenario. Correlated random variables of values from these scenarios held in column vector X. MTM values are interpolated for each sub-portfolio: MTM value under scenario X M X = BM M X M original MTM value change in MTM value under different BM's

16 10. Interpolation Methodology 16 Interpolation for PS (4 scenarios): scenario movement: random variable between ±½u 95 u A =-½u 95,0,½u 95,u 95 u A =u 95,½u 95,0,-½u 95 M X cmt 95% movement: =2 u A x PS u 95 c M A 2 u B x c PS M u B M 0 95 scenario MTM values: M A =,½,0,½ M B =½,0,½, no change MTM value

17 10. Interpolation Methodology 17 Interpolation for ST & CU: random variable +ve or -ve M X cmt = x c BM u M M 0 scenario movement: u=-u 95 or u 95 scenario MTM value: M= or

18 11. Interpolation Assumptions 18 Interpolation methodology assumes linearity: Method checks monotonic behaviour; Checks whether MTM values M M M or M M M for ST & CU and PS; Warns if this is not the case. Method checks accuracy of interpolated MTM values: Checks are made per BM; For ST & CU use average M value; For PS have 3 formulae to include half movements; Must be accurate to 25% threshold.

19 12. Monte Carlo Simulation 19 For one market rate scenario: FIDES needs 1 random no. set per MC iteration (X); Produces 75 non-negative MTM values; An additional set is needed for collateralised exposures (Y); Y may have fewer elements than X. Non-collateralised exposures easily calculated. exposure E cn C X = c 1 X M cmn X F cm measuring point netting agreement

20 13. Monte Carlo Simulation (cont) 20 Collateralised portfolios based on elements of x and y from now to m (measuring point); Calculate change in M y ; Interpolate as described before. Calculate change in exposure, Δ xy : xy =[ cn M x M xy ] F y Converted to CLC; Boundary conditions applied based on threshold and minimum transfer amounts; Limits on customers calling collateral. c F C M x

21 13. Monte Carlo Simulation (cont) 21 Total exposure is given by: E m x = t x [max 0,M ] cmt Customer exposure profile E xy calculated from portfolio exposures: E xy = mp n Use all nettings in same agreement; Use 5,000 MC iterations. max 0, E x mn E xy x mn E m

22 13. Monte Carlo Simulation (cont) 22 Can calculate expected exposure profile: Use customer exposure profile. customer E m p = 1 S S p E sm from customer exposure profile Can calculate peak exposure profile: Peak is at 95th percentile: used for OBSI exposure. p E peak m =P 95 {E p SM } S simulation run, s 95%-ile

23 14. CIDD Based on Expected Exposure 23 Credit Income Deferral for Derivatives (CIDD) for customer p: change in expected exposure m C p = m=2 E m m p S m p n=2 [ D c n n 1 ] n 261 E m credit spread m p S m p n=2 [ D c n n 1 ] n 261 Discount factor: based on the yield curve of zero rates; Use 13 points from 0d to 30y; Use continuous compounding; Exponential interpolation is used via the logs of yield curve parameters..

24 14. CIDD Based on Expected Exposure 24 Example has m=7 years with exposures of 3,5,7,4,6,2,1. CIDD is the product of S (S=1 here), δ<e> and m. Using the equation given, the CCID is given by: [-2*1*1]+[-2*1*2]+[3*1*1]+[-2*1*4]+[4*1*5]+[1*1*6]+[1*1*7] Therefore C = = 28 Note that positive changes in <E> reduce CCID. There is an extra movement at the last point <E> (i.e. 7). 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year CCID Example M

25 15. Summary 25 FIDES uses MC to calculate credit exposure. The main elements of this are described in this presentation: Scenario generation; Correlations; Revaluations; Interpolations. Exposure profiles are then made on portfolio and client level: The client's CIDD is calculated.