EBA欧洲银行-Final-report-on-Guidelines-on-corrections-to-modified-duration-for-debt-instruments-28EBA-GL-2016-0929_37页_798kb

Summary of EBA/GL/2016/09: Guidelines on Corrections to Modified Duration for Debt Instruments under Article 340(3) of Regulation (EU) 575/2013

Core Content

This document outlines the EBA's final guidelines on how to correct the modified duration (MD) for debt instruments subject to prepayment risk, as mandated by Article 340(3) of the Capital Requirements Regulation (CRR) (Regulation (EU) No 575/2013). The correction is necessary because the standard MD formula, which assumes fixed cash flows, does not account for prepayment risk, leading to potential inaccuracies in capital requirements.

The EBA proposes two approaches to calculate the corrected modified duration (CMD):

1. Approach 1: Treat the instrument as a combination of a plain vanilla bond and an embedded option. The CMD is calculated by adjusting the MD of the vanilla bond with the theoretical delta of the embedded option, based on a 100 basis points (b.p.) interest rate shock. Additionally, the convexity (gamma) of the embedded option should be considered, as well as transaction costs and behavioural factors.

2. Approach 2: Directly reprice the instrument after a 100 b.p. shift in the internal rate of return (IRR), and compute the CMD from the difference in price. This approach does not require a gamma correction since the revaluation captures the full effect of the rate movement.

Both approaches require the inclusion of transaction costs and behavioural factors where relevant. These are intended to reflect the real-world execution of options, especially by retail clients, who may not always act in a purely rational manner.

Main Points

• Modified Duration (MD) is used in the standardised approach for general interest rate risk, but it is only valid for instruments without prepayment risk.

• Prepayment risk introduces variability in the maturity of the instrument, making the MD formula unreliable.

• The correction to MD is necessary to reflect the impact of embedded optionality (call or put) on the sensitivity of the instrument to interest rate changes.

• The CMD is defined as:

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

  Where:

  • $MD$ = Modified Duration as per Article 340(3)
  • $\Phi = \frac{B}{P}$ (theoretical price of vanilla bond divided by price of the instrument with embedded optionality)
  • $\Omega = 1 + \Delta + \frac{1}{2} \Gamma dB + \Psi$
  • $\Delta$ = Delta of the embedded option
  • $\Gamma$ = Gamma of the embedded option
  • $dB$ = Change in value of the underlying
  • $\Psi$ = Additional factor for transaction costs and behavioural variables consistent with a 100 b.p. IRR shift

• Gamma (convexity) is important for capturing the non-linear relationship between interest rates and bond prices. However, under the standardised approach, only negative gamma is considered, as it relates to loss underestimation. Positive gamma is ignored unless it has a material impact.

• Transaction costs and behavioural factors are essential to reflect the real-world execution of options. These factors are not included in the delta approximation but are considered in the CMD calculation to ensure conservatism and accuracy.

• The CMD should never be shorter than the MD without correction, as it is designed to reflect a more realistic maturity profile of the instrument.

Key Information

• Purpose: To ensure that capital requirements for debt instruments with embedded prepayment options are calculated accurately, taking into account the impact of these options on the sensitivity of the instrument to interest rate changes.

• Approaches:

  • Option Decomposition: Treat the instrument as a combination of a vanilla bond and an embedded option.
  • Direct Repricing: Reprice the instrument after a 100 b.p. IRR shift and compute the CMD from the price difference.

• Impact on Capital Requirements:

  • For long positions (e.g., callable bonds), the CMD will generally be lower than MD, reducing capital requirements.
  • For short positions (e.g., puttable bonds), the CMD will be higher than MD, increasing capital requirements.
  • The effect is non-linear, and the CMD provides a more accurate estimate of potential losses or gains.

• Data and Examples:

  • Table 1 demonstrates that CMD underestimates real losses for long positions and overestimates real gains, which is the opposite of MD.
  • Graphs illustrate the non-linear relationship between IRR and bond prices, and the difference between real and estimated PL under MD and CMD approaches.

• Implementation:

  • The guidelines apply from 1 March 2017.
  • Financial institutions and competent authorities must comply with the guidelines, and report compliance status to the EBA by a specified deadline.

Scope and Applicability

• The guidelines apply to debt instruments with prepayment risk, including:
  • Callable bonds (issuer can redeem early)
  • Puttable bonds (holder can demand early repayment)
• They are directed at competent authorities and financial institutions within the European Union.
• The standardised approach for general interest rate risk under the CRR is the framework for these corrections.

Conclusion

The EBA's guidelines provide two methods for adjusting modified duration to reflect prepayment risk, ensuring that capital requirements more accurately capture the true interest rate sensitivity of hybrid debt instruments. The inclusion of gamma, transaction costs, and behavioural factors enhances the conservatism and accuracy of the CMD calculation, aligning it with real-world market conditions.