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  • PROFESSOR: Our last class Yi is running from his home

  • in New Jersey due to snow.

  • So he couldn't fly in.

  • But actually, now I'm learning a lot.

  • It's a good way to run the classes going forward.

  • I think.

  • We may employ it next year.

  • So Yi will present CV modeling for about an hour.

  • And then Jake, Peter and myself, we will do concluding remarks.

  • We will be happy to answer any questions on the projects

  • or any questions whatsoever.

  • All Right?

  • So Yi, please.

  • Thank you.

  • YI TANG: OK.

  • I'm here.

  • Hi everyone.

  • Sorry I couldn't make it in person because of the snow.

  • And I'm happy to have this opportunity

  • to discuss with you guys counterparty credit

  • risks as a part of our enterprise-level derivatives

  • modeling.

  • I run a Cross Asset Modeling Group at Morgan Stanley.

  • And hopefully you will see why it's

  • called Cross Asset Modeling.

  • OK, counterparty credit risk exists mainly

  • in OTC derivatives.

  • We have an OTC derivative trade.

  • Sometimes you owe your counterparty money.

  • Sometimes your counterparty owes you money.

  • If your counterparty owes you money, on the payment date,

  • your counterparty may actually default,

  • and therefore, either will not pay you

  • the full amount it owes you.

  • The default event includes bankruptcy, failure to pay

  • and a few other events.

  • So obviously, we have a default risk.

  • If our counterparty defaults, we would

  • lose part of our receivable.

  • However, the question is before the counterparty defaults,

  • do have any other risks?

  • Imagine you have a case where your counterparty will pay you

  • in 10 years.

  • So he doesn't need to pay you anything.

  • Then the question is are you concerned

  • about counterparty risks or not?

  • Well, the question is yes, as many of you probably know,

  • it's the mark-to-market risk due to the likelihood

  • of a counterparty future default.

  • It is like the counterparty spike widens,

  • even though you do not need a payment from you counterparty.

  • If you were to sell, a derivative trade

  • to someone, then someone may actually worry about that.

  • So therefore the mark-to-market will

  • become lower if the counterparty is spread wider.

  • This is similar to a corporate bond in terms of economics.

  • You own a bond on the coupon payments date,

  • or on the principal date, the counterparty can default.

  • Of course, they can default in between also.

  • But in terms of terminology, this

  • is not called counterparty risk.

  • This is called issue risk.

  • So here comes the important concept credit valuation

  • adjustment.

  • As we know the counterparty is a risk.

  • Whenever there's a risk, we could put a price on that risk.

  • Credit valuation adjustment, CVA,

  • essentially is the price of a counterparty credit risk.

  • Mainly mark-to-market risks, of course,

  • include default risk too.

  • It is an adjustment to the price of mark-to-market

  • from a counterparty-default-free model, the broker quote.

  • So people know, there's a broker quote.

  • The broker doesn't know the counterparty risk.

  • A lot of our trade models do not know the counterparty risk

  • either, mainly because of we're holding it back,

  • which I will talk about in a minute.

  • Therefore, there is a need to actually

  • have a separate price of CVA to be

  • added to the price for mark-to-market

  • from counterparty default free model

  • to get a true economic price.

  • In contrast, in terms of a bond, typically there's

  • no need for CVA because it is priced in the market already.

  • And CVA not only has important mark-to-market implications,

  • it is also a part of our Basel III capital.

  • Not only change your valuation, but could impact your return

  • on capital.

  • Because of a CVA risk, the capital requirements

  • typically is higher.

  • So you may have a bigger denominator in this return RE,

  • return on capital or return on equity.

  • CVA risk, as you may know, has been a very important risk,

  • especially since the crisis in 2008.

  • During the crisis, a significant financial loss actually

  • is coming from CVA loss, meaning mark-to-market loss

  • due to counterparties' future default.

  • And this loss turned out to be actually

  • higher than the actual default loss

  • than the actual counterparty default.

  • Again, coming back to our question,

  • how do we think in terms of pricing a derivatives

  • and price the CVA together with the derivatives.

  • First of all, it adds some portfolio effect

  • the counterparty can trade multiple trades.

  • And the default loss or default risk

  • can be different depending on the portfolio.

  • And when people use a trade-level derivatives model,

  • which is by default what people would call a derivatives model,

  • typically you price each trade, price one trade at time.

  • And then you aggregate the mark-to-market together

  • to get a portfolio valuation.

  • So when you price one trade, you do not

  • need to know there may be another trade facing

  • the same counterparty.

  • But for CVA or counterparty risk, this is not true.

  • We'll go over some examples soon.

  • This is the one application of what

  • I call enterprise-level derivatives,

  • essentially focusing on modeling the non-linear effects,

  • non-linear risks in a derivatives portfolio.

  • Here's a couple of examples.

  • Hopefully, it will help you guys to gain some intuition

  • on the counterparty risks and CVA.

  • Suppose you have an OTC derivatives trade, for instance

  • like an IR swap.

  • It could be a portfolio of trades.

  • Let's make it simple.

  • Let's assume the trade PV was 0 on day one.

  • Of course, we assume we don't know anything

  • about the counterparty credit risk.

  • We don't know anything about CVA.

  • This is just to show how CVA is recognized by people.

  • So to start with again, the trade PV

  • was 0 on day one, which is true for a lot of co-op trades.

  • And then the trade PV became $100 million dollars later on.

  • And then your counterparty defaults with 50% recovery.

  • And you'll get paid $50 million of cash.

  • OK, so $100 million times 50% recovery.

  • If the counterparty doesn't default,

  • you eventually would get $100 million.

  • Now he defaults, you get half of it, $50 million.

  • The question is have you made $50 million dollars

  • or have you lost $50 million over the life of the trade.

  • Anyone have any ideas?

  • Can people raise your hand if you think

  • you have made $50 million?

  • Can I see the people in the class?

  • I couldn't see anyone.

  • PROFESSOR: How do I raise this?

  • YI TANG: OK, no one thinks you made the $50 million.

  • So I guess then, did you all think

  • you have lost $50 million?

  • Can people raise their hand if you think

  • you have lost $50 million?

  • OK, I see people.

  • Some people did not raise your hand.

  • That means you are thinking you are flat?

  • Or maybe you want to save your opinion later?

  • OK, so this is a common question I normally

  • ask in my presentation.

  • And I typically get two answers.

  • Some people think they've made $50 million.

  • Some people think they've lost $50 million.

  • And there was one case, someone said OK, you know they're flat.

  • Now, this would look like a new interesting situation

  • where no one thinks you made $50 million.

  • I mean, come on, you have $50 million of cash in the door.

  • And they don't think you have made $50 million.

  • You have a $0 from day one.

  • Now, you have $50 million.

  • OK?

  • All right, anyway so for those of you

  • who think you have lost money-- I don't know if it's

  • a good idea [? Ronny-- ?] can someone tell us why do

  • you think you lost $50 million?

  • You went from 0 to positive $50 million.

  • Why do you think you lost $50 million?

  • Are we equipped to allow people to answer questions?

  • PROFESSOR: Yeah, I think if someone presses a button

  • in front of them.

  • YI TANG: OK, so people choose not to voice your opinion?

  • AUDIENCE: It is because you have to pay to swap

  • and you have to pay $100 million to someone

  • on the other side of trade?

  • YI TANG: OK, very good.

  • So essentially, you are saying hedging.

  • That was what you are trying to get to?

  • So you have a swap as 0 and you have

  • an offsetting swap as a hedge.

  • Is that what you are trying to say?

  • AUDIENCE: No.

  • I'm saying that if you're the intermediary for a swap,

  • then you have to pay $100 million on the other end.

  • So if you're receiving 50 and paying 100, you have a loss.

  • YI TANG: That's good.

  • Right, so intermediary is right.

  • And that's similar to a hedge situation also.

  • So that's correct.

  • That's the basically the reason for a dealer.

  • Essentially, we are required to hedge.

  • We're very tight on the limit.

  • We actually would lose $50 million

  • maybe on the hedge fund.

  • When our trade went from 0 to a positive $100 million,

  • our hedge would have gone from to 0 to negative $100 million.

  • In fact, we receive only half of what we need to receive.

  • And yet, we have to pay the full amount that we

  • need to pay on the hedge side.

  • Essentially, we lost $50 million.

  • But that's where the CVA and CV trading, CV risk

  • management would come in.

  • Again, CVA is the price of a counterparty credit risk.

  • And you know, if you hedge, the underlying trader

  • or whoever trades swap, if you hedge with the CV desk.

  • Theoretically, you will be made whole

  • on a counterparty default. So you would receive $50 million

  • from counterparty, and theoretically you

  • receive $50 million from the CV's desk

  • if you hedge with CV desk.

  • Now, the second part is how do we quantify CVA.

  • How much is the CVA?

  • CV on the receivable, which we typically

  • charge to the counterparty, essentially

  • is given by this formula.

  • MPE means mean positive exposure,

  • meaning only our receivable sides when the counterparty

  • owes us money, and times the counterparty CDS par

  • spread, times duration.

  • The wider the spread the more likely

  • the counterparty will default, the more we

  • need to charge on the CVA.

  • And the same thing is true for the duration.

  • The longer the duration of trade is,

  • there's more time for the counterparty

  • to default so we charge more.

  • Very importantly, there's a negative sign.

  • Because CVA on the receivable side, is our liability.

  • It's what we charge our counterparty.

  • And there are some theoretical articles,

  • they don't include the sign, that's

  • OK for theoretical purposes.

  • But practically, if you miss the sign

  • things will get very confusing.

  • Now, here is more accurate formula for CVA.

  • You know how the MPE side, on the asset side.

  • So we can see to start with, there's an indicator

  • function where this capital T is the final maturity of the trade

  • or counterparty portfolio.

  • This tau is the counterparty's default time, first default