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30 th August 2011, Eindhoven Lvy processes and the financial crisis: can we design a more effective deposit protection? Maccaferri S., Cariboni J., Schoutens W. European Commission JRC, Ispra (VA), Italy Department of Mathematics, K.U.

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30th August 2011, Eindhoven

Lévy processes and the financial crisis: can we design a more effective deposit protection?

Maccaferri S., Cariboni J., Schoutens W.

European Commission JRC, Ispra (VA), Italy Department of Mathematics, K.U. Leuven, Belgium

The views expressed are exclusively those of the authors and do not in any way represent those of the European Commission.

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Deposit Guarantee Schemes (DGSs) are financial institutions whose main aim is to provide a safety net for depositors so that, if a credit institution fails, they will be able to recover their bank deposits up to a certain limit.

Background and objective of the work

The choice of the appropriate size of funds DGSs should set aside is a core topic. OBJECTIVE: develop a procedure to define a target level for the fund. The approach is applied to a sample of Italian banks.

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Outline

  • Description of Deposit Guarantee Schemes.
  • Methodology to build the loss distribution:
  • a. Estimate banks’ default probabilities using CDS spreads;
  • b. Draw realizations of the asset value process and compute the

corresponding default times;

  • c. Evaluate the corresponding losses.
  • Results.
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Outline

  • Description of Deposit Guarantee Schemes.
  • Methodology to build the loss distribution:
  • a. Estimate banks’ default probabilities using CDS spreads;
  • b. Draw realizations of the asset value process and compute the

corresponding default times;

  • c. Evaluate the corresponding losses.
  • Results.
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Deposit Guarantee Schemes

KEY CONCEPTS

  • Level of coverage: level of protection granted to deposits in case of failure
  • Eligible deposits: deposits entitled to be reimbursed by DGS
  • Covered deposits: amount of deposits obtained from eligible when applying the

level of coverage HOW DOES A DGS WORK? Banks pay contributions to DGS to fill up the

  • fund. The DGS employs the fund in case of

payout to reimburse depositors. Important to choose an optimal fund size. DGS Banks Depositors

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Outline

  • Description of Deposit Guarantee Schemes.
  • Methodology to build the loss distribution:
  • a. Estimate banks’ default probabilities using CDS spreads;
  • b. Draw realizations of the asset value process and compute the

corresponding default times;

  • c. Evaluate the corresponding losses.
  • Results.
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How to build the loss distribution

The procedure to choose the target level relies upon the loss distribution. MAIN STEPS:

  • 1. Estimate banks’ default probabilities from CDS spreads market data and

from financial indicators and calibrate the default intensities of the default time distributions;

  • 2. Draw realizations of the asset value process (firm-value approach);
  • 3. From asset values’ draws compute the corresponding default times;
  • 4. Evaluate the corresponding losses.
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Outline

  • Description of Deposit Guarantee Schemes.
  • Methodology to build the loss distribution:
  • a. Estimate banks’ default probabilities using CDS spreads;
  • b. Draw

realizations

  • f

the asset value process and compute the corresponding default times;

  • c. Evaluate the corresponding losses.
  • Results.
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Default intensity parameters li

  • f

the default time ti distributions.

Loss distribution: estimate default probabilities (1)

PROBLEM: there is a small sample of banks underlying a CDS contract. SOLUTION: study a relation between risk indicators and default probability and use this relation to enlarge the sample. Attention to the difference between risk-neutral and historical default probabilities! Derived from default probabilities, which are estimated from CDS spreads.

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DPQ: risk-neutral default probability DPP: historical default probability

DPP by Moody’s historical reports Build the map DPP=f(DPQ) Build the relation

DPP=h(indicators)

Estimate DPP from the map h Estimate DPQ from the map f Financial indicators Estimate DPQ from CDS spreads Estimate intensity parameters li

Loss distribution: estimate default probabilities (2)

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Loss distribution: estimate default probabilities.

Step 1 – Credit Default Swaps

We assume the default time of the i-th bank ti to be exponentially distributed with intensity parameter li. The term structure of the cumulative risk- neutral default probability: CDS spread: At this stage we make use of the 2006 daily 5Y CDS spreads of 40 EU banks. Recovery rate Ri=40%

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Loss distribution: estimate default probabilities.

Step 2 (a) – Map between PB measures DPP=f(DPQ)

GOAL: build a one-to-one relation between 1-year DPQ and DPP. Associate every rating class with a DPQ and a DPP. DPQ (risk-neutral DP): consider all banks belonging to a common rating class, the DPQ is the average of all banks’ DPQ

i.

DPP (historical DP): from statistics on average cumulative default rates.

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30th August 2011, Eindhoven 13/31 B4 A1 Bn-1 A3

Loss distribution: estimate default probabilities.

Step 2 (b) – Map between PB measures DPP=f(DPQ)

B1 Aaa B2 Aaa B3 Aaa B5 A1

…

Sample of n banks with CDS

DPQ

Aaa

DPQ

A3

DPQ

A1

Bn-1 A3 Bn A3

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Loss distribution: estimate default probabilities.

Step 2 (c) – Map between PB measures DPP=f(DPQ)

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Loss distribution: estimate default probabilities.

Step 3 – Linear model DPP=h(financial indicators)

ROAA Excess capital/RWA Liquid assets/customer & short term funding Excess capital/total assets Net Loans/customer & short term funding Loan loss provisions/net interest revenue Cost to income Loan loss provisions/

  • perating income

GOAL: estimate a relationship between historical default probabilities and the financial indicators.

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Loss distribution: estimate default probabilities.

Steps 4 and 5 – Estimate DPP and DPQ for the banks’ sample

Using the relationship h(financial indicators), we estimate the DPP; From the DPP we estimate DPQ by inverting the map f. At this stage we turn to the banks’ sample. We assume the default time of the i-th bank ti to be exponentially distributed with intensity parameter li. The term structure of the cumulative risk- neutral default probability:

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Outline

  • Description of Deposit Guarantee Schemes.
  • Methodology to build the loss distribution:
  • a. Estimate banks’ default probabilities using CDS spreads;
  • b. Draw realizations of the asset value process and compute the

corresponding default times;

  • c. Evaluate the corresponding losses.
  • Results.
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Loss distribution: asset-value processes realizations (1)

DEFAULT’S DEFINITION: a bank goes into default when its asset value falls below a certain threshold. Asset value: generic one-factor Lévy model (r=70%)

  • One-factor Gaussian model
  • One-factor Shifted Gamma

Lévy model and thus the default times ti are A default occurs if:

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Loss distribution: asset-value processes realizations (2)

The default times ti are Asset value One-factor Gaussian model

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Loss distribution: asset-value processes realizations (3)

Asset value One-factor Shifted Gamma Lévy model is a unit-variance Gamma process such that and

  • are independent Shifted Gamma random variables;
  • and

The default times ti are

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Outline

  • Description of Deposit Guarantee Schemes.
  • Methodology to build the loss distribution:
  • a. Estimate banks’ default probabilities using CDS spreads;
  • b. Draw

realizations

  • f

the asset value process and compute the corresponding default times;

  • c. Evaluate the corresponding losses.
  • Results.
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Loss distribution: generating the loss distribution

For every bank, check if the default time ti is smaller than 1Y. If this is the case, there will be a loss attributable to bank i equal to: where EADi is the amount of covered deposits by bank i. The total loss hitting the Fund is estimated by aggregating individual bank losses.

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Outline

  • Description of Deposit Guarantee Schemes.
  • Methodology to build the loss distribution:
  • a. Estimate banks’ default probabilities using CDS spreads;
  • b. Draw

realizations

  • f

the asset value process and compute the corresponding default times;

  • c. Evaluate the corresponding losses.
  • Results.
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Probability that at least one bank defaults:4.15%

Sample: 51 IT banks, accounting for 60% of IT eligible deposits and for 43% of total assets as of 2006. Monte Carlo iterations: 100 000 runs.

Results: banks’ loss distributions

One-factor Gaussian model

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Probability that at least one bank defaults:4.91%

Sample: 51 IT banks, accounting for 60% of IT eligible deposits and for 43% of total assets as of 2006. Monte Carlo iterations: 100 000 runs.

Results: banks’ loss distributions

One-factor Shifted Gamma Lévy model

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Results: banks’ loss distributions

Comparisons

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DGS Proposal: target fund 2%

  • f eligible deposits = € 7.7

billion. Default probability = 1.2% IT DGS virtual fund: 0.8% of covered deposits = € 2.22 billion Default probability = 2.4%

Results: DGS loss distribution

One-factor Gaussian model

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DGS Proposal: target fund 2%

  • f eligible deposits = € 7.7

billion. Default probability = 0.83% IT DGS virtual fund: 0.8% of covered deposits = € 2.22 billion Default probability = 2.07%

Results: DGS loss distribution

One-factor Shifted Gamma Lévy model

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Optimum target size

The simulation procedure can be used to choose the optimal target level such that it can cover up to a desired percentage of losses.

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Sensitivity to results

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Thank you for your attention.