#####
Study note: Counterparty credit risk is harder because (i) the initial value is 0 and the future value is highly uncertain and (ii) the contract can gain or lose. Two key metrics are Expected Exposure and Potential Future Exposure (PFE, which is essentially a VaR). For more financial risk videos, visit our website!

Hello this is david a banach turtle with a quick introduction to counterparty credit risk or counterparty exposure to understand it we typically contrast it with a traditional loan or bond that’s where our investor over here on the left purchases with cash a bond and then we ask what is the exposure or the credit exposure to our investor here well in this case

It’s pretty straightforward it’s the principal that’s been invested that’s how much they can lose if the counterparty here defaults so that’s the traditional case now compare it to a derivative and the analog here could be a credit default swap so our investor instead of purchasing a bond seeks synthetic exposure by writing credit protection or going short a credit

Default swap but regardless of the particular instrument the key idea here with a derivative is instead of funding with principal they enter into a bilateral contract which references a notional amount see principle versus notional and now there are two key challenges that introduce a complexity here into counterparty risk under the derivative scenario first what is

The value or exposure on day zero or right out of the gate well this is a fair deal between the two counterparties so typically it’s priced so that the value is zero to both of them a fair deal the current exposure on day zero is pretty much zero and then going forward in time that means the value can go positive or negative to either of the counterparties so you

See the difference here where the exposure was typically the principal now we say the future exposure is not only highly uncertain but it can go in either direction so on the right now how do we treat this well i’ve modeled an interest rate swap i switched from credit default swap to interest rate swap this is easier to model so this is still a derivative contract

And then what we’ve done here is a monte carlo simulation that’s ten trials where i sort of simulated the short-term interest rate if our counterparty over here is in an interest rate swap let’s say they are receiving a fixed rate and paying in a floating rate that means if interest rates go up over time they’re going to be paying a higher floating rate and this

Counterparty here is going to be a losing and a losing position on the swaps they’re going to be down here in a negative territory and now in terms of counterparty credit risk we’re not as concerned with this here this counterparty is paying a floating rate interest rates go up this swap is losing position for them and they don’t really have counterparty credit

Risk on the other hand if interest rates go down and this counterparty is paying a floating rate now the swap is becoming valuable to them they are gaining on the swap and so we’re up here in the positive territory and this is where we say this counterparty would have counterparty credit risk or credit risk and that’s because in order to replace this contract

There would be a cost and if this counterparty were to default there would be a loss so you can see the monte carlo simulation handles the fact that we can go either direction but counterparty exposure is primarily concerned when there’s a gain on the contract because when there’s a gain on the contract it’s the default by the counterparty that will create the

Loss so what we’ve done is we simulated 10 trials so we have a future distribution and just to show you how we can sit that this can be simulated here i can rerun this montecarlo simulation 10 trials in different batches and now the last thing i wanted to show you is two terms for counterparty credit risk we have to think now about slicing a future point in time

Vertically and so if we do that if i move my chart over here and now if we think about a vertical slice or cross section here through the simulation what we have is a future time period so this could be six months in the future and we’ve simulated based on the underlying risk factors whether we could have a loss on the swap down here or a gain on the swap and

So if you think about this vertically what we have here is a future distribution on its side where perhaps we have an expect the distribution may peak where we expect the average value to be however we’re concerned with a gain on the contract because that’s where our counterparty exposure is so the two key terms we use our expected exposure and potential future

Exposure so expected exposure you’ll notice up here is going to be in the gained territory and that’s because it’s the expected exposure conditional on a mark to market game so conditional only on the value of this contract in the future being positive then conditional on it being positive what’s our expected gain on the contract and that is our expected exposure

Again because if we rent again and our counterparty defaults then that’s our loss now we have also have potential future exposure pfe notice with a significance level and the key idea here is that this is essentially the same as value at risk so it needs a confidence level and what this is is this is the future the worst expected future exposure with some level

Of confidence so this could be 95 or 99 percent so this is just like value at risk turned on its side except that it’s in the future it’s or some future point of time and again it’s associated with a gain in the underlying bilateral contract but it’s then telling us well 99 percent of the time we do not expect the exposure to be greater than this amount or conversely 1

Percent of the time we do expect the exposure to be greater than this amount so expected exposure potential future exposure both capturing a future counterparty exposure on a bilateral contract that references an underlying notional and the key to generating this future distribution again a monte carlo simulation where in this case i’ve simply simulated the change

In a short-term interest rate over time this is david harper the bionic turtle thanks for your time you

Transcribed from video

FRM: Counterparty credit exposure By Bionic Turtle