Calculating Loan Exposure at Default from Remaining Cash Flows
Summary
The document explains how to calculate the present value of a lender’s remaining contractual cash flows if a borrower defaults before payments due at that time have been exchanged. In its example, a maturing loan pays annual interest and returns the principal at maturity. The exposure is obtained by discounting each unpaid interest payment from the default time onward, then adding the discounted principal repayment at the end of the loan term.
The calculation uses the stated loan rate as the discount rate and includes the cash flow due on the default date, reflecting the assumption that default occurs before that payment is exchanged. A second explanation illustrates the process by valuing the final payment first and adding earlier unpaid interest when default occurs sooner. This is a worked present-value example under specific timing and discounting assumptions; it does not address recovery value, collateral, or alternative credit exposure conventions.
Key ideas
- Exposure is calculated as the present value of contractual payments remaining after default.
- The example includes interest payments from the default date onward and principal at maturity.
- The stated loan rate is used to discount the remaining cash flows.
- The timing convention assumes default occurs before cash flows due on that date are exchanged.
- The example does not incorporate recovery, collateral, or other exposure adjustments.
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Full text
# Exposure At Default: Calculating the present value
# Exposure At Default: Calculating the present value
In this numerical example, I can't figure out with which numbers (when using the PV formula) to calculate exposure at default (EAD) as shown in the table.
The EAD is the value of the discounted future cashflows (CF) at the time of default.
With my calculations I do not get the EAD shown there starting from t=2. How do I replicate the the EAD in the table?
The following parameters are given in the calculation:
```
nominal amount: 1000
Duration: 6 years
Interest rate: 10%.
Effective interest rate: 10%.
Date of payment of interest: Annual
Credit structure: maturing loan
```
## Answer by Pontus Hultkrantz (score 3, accepted)
https://quant.stackexchange.com/a/59655
I can see that you provided an answer on your own question, but let me provide the general procedure.
We are standing at time $t=0$, we have just issued a loan (bond) with notional $N=1000$ to our counterparty (borrower). In return we will collect $K=0.1 N=100$ every year in interest payments, where interest rate is $r=10\%$. At the end of the final term (6 years), we will collect our last interest rate payment, as well as the full notional. If the borrower defaults at time $t=\tau$, we will neither receive our payment due on this date, nor any other future payments thereafter.
That is, if the borrower defaults at time $t=\tau$, before any cashflows due on this date have been exchanged, our value exposure today ($\mathcal{F}_0$) will be
\begin{align} EAD(t)|\mathcal{F}_0 &= \sum_{k=t}^6 \frac{r N}{(1+r)^k} + \frac{N}{(1+r)^6} \\ &= \sum_{k=t}^6 \frac{10\% \cdot 1000}{(1+10\%)^k} + \frac{1000}{(1+10\%)^6}. \end{align}
## Answer by user51037 (score 1)
https://quant.stackexchange.com/a/59650
I would like to share with you the answer from saulspatz, from math.stackexchange
> They are computing the present value, at the time fo the loan of the defaulted payments, using the same rate as the rate of the loan. If the debtor defaults on the last payment, the present value is $1100*1.1^{-6}=620.92$ If he default at the end of year 5 that will add another $100*1.1^{-5}=62.09$ bringing the total to 683.01.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.