EBA欧洲银行-EBA-CP-2016-03-28CP-on-GL-on-corrections-to-modified-duration-for-debt-instruments29_43页_908kb

Summary of EBA/CP/2016/03: Guidelines on Corrections to Modified Duration for Debt Instruments under Article 340(3) of Regulation (EU) 575/2013

Core Content

This Consultation Paper (CP) outlines proposals for guidelines on how to correct the Modified Duration (MD) of debt instruments subject to prepayment risk under Article 340(3) of the Capital Requirements Regulation (CRR). The aim is to improve the accuracy of capital requirements calculations by incorporating the effects of prepayment risk, which is not accounted for in the standard MD formula.

Main Views and Key Information

1. Mandate and Rationale

• The CRR establishes two standardised methods for computing capital requirements for interest rate risk: the Maturity-Based (Article 339) and the Duration-Based (Article 340) methods.
• The MD formula, as defined in Article 340(3), is valid only for instruments without prepayment risk.
• Prepayment risk arises from embedded options in debt instruments, such as callable or puttable bonds, and must be corrected to reflect the actual risk exposure.
• The EBA is tasked with issuing guidelines on how to perform this correction, which is crucial for accurate capital calculations.

2. Proposed Correction Methods

Two approaches are proposed to correct MD for instruments with prepayment risk:

• Method 1: Treat the debt instrument as a combination of a plain vanilla bond and an embedded option. The correction involves adjusting the MD of the vanilla bond with the delta of the embedded option, estimated from a 100 b.p. interest rate movement.
• Method 2: Directly reprice the entire instrument after a 100 b.p. interest rate movement and calculate the change in value, without using the delta approximation.

3. Convexity and Gamma Considerations

• Negative convexity from embedded options (sold by the institution) reduces the sensitivity of the bond to interest rate changes, thus lowering the MD.
• The gamma impact (second-order effect) of the embedded option should be considered in the correction to avoid overestimating potential gains or underestimating potential losses.
• For the second approach, the effect of convexity is already included in the revaluation, so no further correction is needed.
• Only negative gamma is included in the standardized capital calculation, as positive gamma is considered less relevant for loss underestimation.

4. Transaction Costs and Behavioural Factors

• These factors should be reflected in the correction to ensure a conservative estimate of prepayment risk.
• Transaction costs reduce the value of the embedded option, making it less likely to be exercised.
• Behavioural factors are relevant for certain types of clients, particularly retail clients, who may not exercise the option even if it is in the money.
• These factors should be incorporated based on historical data or external assessments.

5. Formula for Corrected Modified Duration (CMD)

The EBA proposes the following formula to calculate CMD:

$$
C M D = M D \times \Phi \times \Omega
$$

Where:

• $MD$ = Modified Duration of the plain vanilla bond
• $\Phi = \frac{B}{P}$ = Ratio of the price of the vanilla bond to the price of the bond with embedded optionality
• $\Omega = 1 + \Delta + \frac{1}{2} \Gamma dB + \Psi$ = Correction factor including delta, gamma, and additional factors

6. Impact of Prepayment Risk on Capital Requirements

• Prepayment risk typically reduces the effective maturity of the bond, leading to a lower Modified Duration.
• This results in lower capital requirements for instruments with prepayment risk, as the risk is mitigated by the early termination feature.
• For deep in the money options, the correction to MD underestimates real losses, while for deep out of the money options, the CMD approximates the MD closely.

7. Illustration of the Two Methods

A theoretical example is provided for a 20-year bond with a 6% coupon and an embedded American call option. The table compares the results of the two proposed correction methods (Method 1 and Method 2) with actual losses and gains under different interest rate scenarios. It shows that Method 1 accounts for delta and gamma, while Method 2 uses direct repricing without delta approximation.

Conclusion

The proposed guidelines aim to enhance the accuracy of capital requirements calculations for debt instruments with prepayment risk by incorporating delta and gamma adjustments, as well as transaction costs and behavioural factors. The EBA is seeking feedback on these proposals to ensure they are appropriate and effective in reflecting the real risk exposure of such instruments.