Lifetime Expected Credit Losses

From Open Risk Manual


Lifetime Expected Credit Losses are the expected credit losses that result from all possible default events over the expected life of a financial instrument.


Conceptually the definition is captured in the following mathematical expression

\mbox{LECL}_t = \sum_{i=t}^{T}  D(t,i) \mathbb{E}_{\mathbb{P}} (\mbox{LGD}_{i} \mbox{EAD}_{i} 1_{ \{ d_{i} = 1 \} } | F_t )
  • Where t is the reporting date
  • T is the Expected Life of the instrument
  • i denotes possible times of default / loss (normally associated with instrument cashflows)
  • di is the random (unknown) event of default at time i
  • LGD denotes Loss Given Default
  • EAD denotes Exposure at Default
  • D(t,i) denotes the discount rate at time t (based on the Effective Interest Rate, for the different cashflow maturities i
  • Ft denotes the subjective but Forward-Looking Information set used formulate the estimate at time t
  • P denotes the subjective assignment of default probabilities to the events di

This formula captures the essence of the definition. In practice evaluation of LECL may utilize a variety of simplified / approximate forms. A common simplification is the use of the concept of Lifetime PD

See Also