# Lifetime Expected Credit Losses

From Open Risk Manual

## Definition

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

## Formula

Conceptually the definition is captured in the following mathematical expression

- 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)
- d
_{i}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
- F
_{t}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 d
_{i}

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