Introduction to counterparty risk (QRM Chapter 17)

go to the the introduction to counterparty credit risk now you may wonder why is the 17 the reason is of course been labeled the slides according to other sections of the slides according to the chapters in the book and chapter 17 and the book is concerned with dynamic portfolio credit risk models and counterparty credit risk because turned out that counterparty credit risk if you really want to treat it in a model-based way requires you to have a dynamic portfolio credit risk model and it is under the special topics under other special topics are multivariate time series multivariate extreme value theory and other things now here we do only counterparty risk and I also will not do too much technical stuff so the introduction is probably going to be most important and I want to show you nice our script by Alex good now a substantial amount of our derivative transactions stand over the counter what does that mean that means that whenever if I do an over-the-counter swap with Paul when we to just to a deal and we promise an exchange of cash flows I'm saying interest rate swap or promises me to pay fixed interest rates maybe 2% every whatever every three quarters and I promise him to pay floating interest rates however there is nobody who guarantees these payments if I default after five years then Paul has just bad luck and his obligations towards me remain but minor sort of gone and he might make a loss and in particular swaps are still very much over the counter because the DVT alternative is exchange-traded when you have an organised exchange in between then you have a system of margin requirements and so on and your trading not with directive as Paul but we would have the exchange standing between us and this exchange would guarantee that Paul gets his money even if I default and to be able to do that they use margins and so on that is of course nice because counterparty risk is gone but if you trade over an exchange it also means that you're sort of tied to standardized contracts you cannot have an arbitrary variety in particular interest rate swaps are of course very much typically tailor-made because if Paul is whatever a bank or an insurance company in the a certain finance immediate certain day into certain nominal and so on what exactly you want and it will not exist to the exchange it's another very important product if you wanted a stun over the counter without exchange in between is of course reinsurance if you tied to a reinsurance to you there's also nobody you care and teach you that the reinsurance company will actually pay they might default and then you will have to remove may a colossal you will have to replace your reinsurance contact and this risk that in a deal one of the two parties cannot pay because cannot fulfill their contractual obligations that is known as counterparty risk of course it has always been there but it was treated a little bit in a Cavalier fashion very much in practice until the financial crisis when all of a sudden people realized due to the default of LeMans that this can really happen and it's really possible there the major derivatives dealer for instance defaults AIG was also very close to default and one of the reasons that it was saved was that it was such an active dealer on the credit default swap market before that counterparty risk was considered but sort of only as or in a One Direction banks were worried about the counterparty risk to their trading of their trading partners but sort of the trading partners had to assume that the banks were default free which was not 100 percent correct as we learned so this is very important it it is a major concern it has made its way into regulation both Basel and solvency and that's why we thought it would be good to conclude the whole thing with a few words on this risk yeah now it's also in a sense of counterparty risk that he was considered low in return of being paid back yes of course so that would be a special example also what is probably new is a the thing that it's now much more symmetric what I just meant is counterparty risk in the one thing a bank if you alone and then the bank is very that you don't pay your money back that has always been there but the other way around that sort of you are worried that the bank doesn't pay your money back it has been a little bit there we ever don't know what is it deficit insurance and these things are there of course to guarantee this but it has not been considered as something I mean you have risks and risky of some sort you believe in it others which are sort of but it's a treat it differently just being getting more action okay what is different good or what is what is come more complicated one of the things that make counterparty risk management complicated and that brings me to the next slide so that's a nice question is the fact that you do not really know your exposure is much more random I mean there's also some randomness in loans because it's not always do you have credit lines and so if your bank who keeps a credit line you do not know if the other side will take the credit in full but when you have a normal loan like a mortgage stand you know your exposure you've given this guy whatever 1 million Swiss francs so that he can buy a home and that that's your exposure and full stop and you it's and in this world of derivatives this can be different because you do not even know if you really will in the future have a counterparty exposure or not and this brings me to the example of an interest rate swap which will then also look at a little bit more in an hour script so in an interest rate swap you have two parties a and P it's a pity now that I know how this works we have to stop good so we have two parties a and the middle a and B and they exchange cash flowers and just that we understand the script sort of APA something to be in the we play something back and in the example I we are having here a repeat receives fixed payment and makes floating payments a predetermined time points every three month starting maybe by the beginning of 2017 and going twenty years into the future these things go that long it's also one of the reasons why it's so important so even if whatever Paul and I are doing these contracts we both seem to be in perfect economic shape right now fifteen years down the road this might change and that's what we consider floating is to people LIBOR rate so and this can of course cause very that's the type of contract we are considering now these swaps similar to the credit default swap they are done in such a way that the fixed rate that's also the swap rate this is fixed in such a way that at the point when the two parties agree on the deal the cash flows from A to B and the ones from B to a have the same value so that there is no money being shifted around but of course this is going to change over the lifetime of the contract and it's used a lot for for longer term horizon swear bonds are not so frequently traded and very corporate bonds also are not even government bonds subject to all types of liquidity stuff and so on yes swap can go over 20-30 years easily when they are mostly used for interest rate risk management and so that's why the heft is long ya know that's why they are over-the-counter you have to go to a band to another bank and so and then ask them to do this for you well I think that's gonna be a pretty one-sided market in this SAV vouchers it's like this carbon dioxyde certificates closed this time somebody will have to drink 100 coffee you know okay but back to to this story here I want to come back why this is different good now the value of this contract will change according to the changes in this interest rate and at any given point in time I can price it if I know the value of all future Co coupon bond prices or yields but of course when the interest rate curve changes in the future the value of the swap will change so let's assume that interest rates are which is the first one yeah but interest rates rise and now we consider the whole thing from the situation of B and look at this sort of P&L that he has with the slope so if interest rates are rising he receives floating so you will receive sort of more higher payments and the value of the fixed payments he has to make in the future will be lower because he can discount them at a higher rate so the value of this but they are I mean the floating will change the fixed is of course there this in this book in gray encoded in the swap contract so that the value of the swap will be positive for him if on the other hand interest rates fall the value will be negative firm we see a picture for that soon and then it really depends now assume that a defaults and now it depends really on the realization of the interest rate if B makes a loss on it or not so if R goes up then the value of the swap is positive and hence if a defaults if our decreases then the value of the slope is negative for B and then ye won't come handy he will still have to pay but he won't make an additional loss he will be forced to realize the loss he made on the swap deal but yet it has to account for this anyhow but he will not make an additional counterparty risk related loss he will just be forced to realize his loss and pay this into the bankruptcy pool so there is an economic loss and the underlying transaction but that has nothing to do with counterparty risk you just lost on in protection but there's no counterparty loss and the size of the explosion of course also depends on how much the interest rate so that is the one thing that is really different the size of the potential loss depends on is quite random if you have one or not and how large it is depends on the economic environment and yeah therefore there's no upset of course yeah thinking also go the other way round and that's that's one thing to take into account and if you really want to model this nicely you also have interesting questions on how the default time and the economic value of the contract are linked maybe if these are interest rates and you know that the one of these guys has a very strong exposure towards interest rates from its core business can it assume that these things are independent and we also come to that a little bit later but before I want to just show you a nice our example Alex has made to illustrate this point with numbers it is in the repository in chapter 10 so we will price an interest rate swap in this Cir model so we assume that the short rate of interest follows the coxinha Soros model exactly the same as we've just seen in credit risk and we will see how the value and the counterparty credit risk evolves for the counterparties depending on the realization of the interest rates good this use is also this ste library Alex mentioned yesterday which you can use to simulate paths we consider a Cox in your service model you can just write this down here the RT is equal to times [Music] good that's what's done here there is a small twist also we need to consider this is nicely done in this example and relates to what I mentioned before with this picture we need P and Q simultaneously we need the oh it's interesting if you want to do risk management the P dynamics of the short way to maybe evaluate a lost distribution of the swap and we need the Q dynamics of the short ride to be able to value the swap in the future today we can read today pricing a standard interest rate swap you don't need a model for that you can read the price off if you know the prices of future so your coupon bonds you can discount the fixed payments and the floating ones you just invest one unit of account and roll it over but if you want a value the thing in the future it will depend on the future yield curve and that will depend on the future interest rate good so that is I already ran all these things so there's a P in the Q dynamics of the interest rates there and then we have this pricing function for zero coupon bonds there's an a and the B these are the functions which I just showed you on the slide they appeal to an interest rate modeling and then now we can price the bond and the compute its corresponding yield the current short rate is 5% and then we can simulate the also risen yes it's a realistic examples 1x yeah whatever good then we can generate 20 parts of this interest rate in the future over half a year using this package and what we're going to see are the first few days of this various paths now am I gonna plot them for you that's the next picture here so by the way you see that our works also on the windows after our studio are under windows and these are now 20 different interest rate part they all start at half of cent and then they've really around until point 2.0 troopers 0.2% and some of these parts are also rising they are now we consider such an interest rate swap which pays tau equal to 0.25 means that we have for tele exchanges of cash flows the nominal is I think 1000 and well don't have to go through all of that here and we can price it if we know the current yield curve good that's the next thing then as I said for pricing these things they fixed rate the swap rate is determined in such a way that the value of the contract at time 0 is 0 that is just done here good and I need to print it for you so the swap rate would be almost 1 percent so there will be the fixed payments we have to put in so that the value of this contract is actually zero and then the next picture plots for you the value of the swap corresponding to each of these 20 better to this one first good okay so that is the plot of the swap as seen from B that's exactly as in this example here for each of these different interest rate realizations we now get also a trajectory of the spoke value they look very similar but the scale is of course completely different can also compute here curves that's just really that's not really necessary okay and now to illustrate the point which I made before what happens to the swap depending on the realization of the interest rate we're gonna consider two scenarios one were interest rates prices that is path number 16 here and then one where interest rates are falling okay [Music] it's slightly bigger so what we see is here the interest rate here we see the corresponding value of the swap and here we see the change in the yield curve over time so the black one is the original one and the red one is no that's a bond price not the year the bond price is because they are decreasing if interest rates rise and the years come then next now down there we have now we see the years and you see it's almost this duration model does parallel shift so it's not had bad which we looked at but here it comes really out of a fully-fledged model even a very simple one for interest rates good and you see really how the swap increases in value so that would be the scenario where if the counterparty a defaulted here at time point point four would make a loss of whatever four billion or so of the underlying currency so this and similarly when interest rates for that the seventh realization can plot the same stuff so here you see the interest rate the smoke value the change in polarizes in the change in years now yields go down the swap has a negative value for P and so he has no counterparty risk loss and the size of the loss depends of course also how large the interest rate is so this is just to illustrate that point and to show which is sort of different or particular for counterparty risk management that the size of the exposure really very good okay then now a few general words not too quantitative about the management of kata party risk what can you do to mitigate it or to deal with the issue there are a lot of techniques some of them quantitative some of them qualitative one issue that arises you need to take it into account and pricing or that is currently being done and I think it's even forced at least in the bother a regulation you have to compute so-called credit value adjustments which take into account that the derivative may not be worth as much as you think because maybe your counterparty doesn't pay you you can't control it by are more or less quantitative techniques an important issue is netting typically two banks do not have only one swap between them but many different products and if they have a netting agreement what they will do is they very first in case one of the two defaults then they will first compute the P&L on the aggregated portfolio and only if the aggregated value of all contracts between them is sort of positive for one of the counterparties he makes a loss without the netting agreement so to say I have two swaps with Paul and sort of I have one swap where I pay floating and receive fixed and then I have sort of the opposite deal as well so that they almost cancel each other and if we do not have a netting agreement in divide default then I will have unable to make sort of a again on one and the loss on the other I will suffer the law a counterparty risk related loss to the one on which I made a profit and I will have to pay the other one in full if we have a netting agreement we can net them first they will almost cancel the remaining loss will be much smaller these are netting agreements which you have which are important another important thing is of course collateralization as the organize exchange to it with margins who could also do this amongst us and have collateral cash or relatively liquid securities which we move around according to the economic value of the contract that can reduce the potential loss dramatically if it's done correctly it will probably not do it perfectly because it always takes some time to adjust the collateral written interesting simulations well I think a simulation study on this was some people find interesting but it's definitely a very important technique and collateral is many things have to be collateralized by now and large amounts of securities and cash which are being shifted around well if you're a bank you have maybe or there many reasons why if you think about examples of the credit default so market I think 80 percent of all this contracts more or less cancer sometimes because people speculated on a price evolution for instance venues and similar for interest rates when these deeds are being made for speculative purposes then what happens very often is that you do one deal and then maybe not you do not reverse it immediately that would be pointless as you say but you maybe reverse it three months later or a year later because then interest rates have risen you've made your profit and you want to cancel the whole thing and these things to exist all you have a big institution like a bank and maybe this a makes one as one view on the future bank desk here's another one and once or bond-esque speculating in the spy takes one position the other desk is just meeting consumer financing requirements and has the opposite position and they have very of no clue whatsoever what the other guy is doing I remember it's not a funny it's a sad story but still somehow funny that people at Citibank who made the structuring of all this CDOs and mortgage backed securities and Salomon they knew themselves that thought the thing was increasingly shaky but they were surprised that it was still demanded only after the crisis that on they found out that this was something that they really sold it to some entity which belonged to their own company and then okay it so it can really happen that a big institution has many people taking positions and some of these cancel I think the most important reason is really that they speculate in a direction and then offset the thing not immediately but maybe stream a year later and so on a vendetta netting agreement only the remaining things strange only the net position matters for counterparty risk good a few to sort of conclude as a final bit I will say a few words about this valuation adjustments credit value adjustments and about some simplified formula which is being used in practice so the general definition of a credit value adjustment means is of the following form the true price which really should charge is equal to the counterparty risk free price out of the price that is correct at first order - adjustments for this is for the special case of you can say of a credit default swap and you this from the point of view of the protection buyer who makes the premium payments and gets the fixed payments but this is the same thing and the same definitions would work for any interest rate swap or anything but for to be specific we consider here the case of a CD s to know who is who but if you just exchange notation it works all the rest so the true price the counterparty risk free pass - the adjustment for the default of the seller because from the point of view of the protection via the contract is worth less if the seller may default beforehand plus an adjustment for the default of the buyer of course you could do exactly the same with a reinsurance contract if you're an insurance company who buys reinsurance you deprotection fire and the reinsurance company is selling your protection and you would have exactly the same type of adjustments so that's how they are generally defined but there's a whole zoo of these things and then the math on etcetera there you have titles where you call them X V a and for the X you can put in whatever you want it depends on if the deal is collateralized or not and if you consider it symmetric so bilateral on and sometimes people are to consider funding value adjustment I'm not gonna go into that and we decided also in writing the book that we would do we have some one tip type of adjustments with discuss there is more to do but only in the future when the dust has settled and when it's clear which of the adjustments will remain and which ones not so but so we consider just to hear in this text the credit value adjustment and the debt value adjustment assuming that there is no collateralization going on but this can all be extended reaches the market value of the credit default swap of you want also the market value of a reinsurance contract from the point of view of the protection buyer and the market value under the assumption that B and s are default free so that the cash flows that are written in the description of the contract are also really taking place then we have here for this example fee potential default times the reference entity can default so the person which default is written or in the reinsurance case it would be the time when the claim really happens it's a default of the seller the default of the buyer in Tao is the minimum of these and that is sort of the interest in default the interesting time when something happens in size just yet identity of the first defaulting firm so if X is equal to s it means that protection seller defaults first and we use X plus as the maximum of X 0 and X minus as the minimum and G of 0 t is a discount factor so you can consider us and then one has the following general formulas this is just basically accounting but it's an interesting formula let's consider the credit value adjustment the credit value adjustment is the surprising adjustment so it's under Q and if you have to pay something provided that first I'll test some value how happens before t if tau is after T then sort of the contract goes its natural way the credit value adjustment also is an adjustment for the case where their protection seller defaults first so where the protection buyer potentially makes a loss the loss is proportional to the value of the contract to the positive part of the value of the of the risk-free value of the contract at the first default time the days in the example of our interest rate swap if at this first time tau but it's the default time of the Center and if the swap has a positive value they never make a loss the loss may not be the whole exposure because maybe I get 50% because the seller can pay me still something that's lost even default of the seller and that's discounting and similarly for the buyer now a few comments they're also on the next slide but it's maybe better to make them while these formulas are still here at these some of them what we see is that essentially what we have to do to compute this thing is we have to price an option we strike zero it's a positive part of the value so it's either zero or the positive part so we have to price an option on the value of a credit default swap or on the value of a reinsurance treaty or on the value of the interest rate swap and an option with a random maturity why default fee that's a little bit of a convention that one says okay the losses in principle you could say if I replace it I have an other counterparty risk but then you get counterparty risk squared and you think that this is been small so what is to avoid this recursions one typically takes the default free value there because the probability that this happens should be small and then if you take it sort of you get this probability scared good so you have to you have to look at an option on listening so this sort of means that if you really want to compute this in a formal model the model you will need is at least one level more complex than the model you need to compute the underlying thing for instance to price and interest rates for per se you don't need really if you want to price it now you don't really need a model for that you can read off its price on the term structure of interest rates to price a credit default swap you don't need much this very simple hazard rate models which we had yesterday are enough to do this you need more we need to really a model for the dynamics of of this value so you need a Dom structure model to do this as the one I showed you sort of as a very simple case for the interest rate swap or we need a dynamic credit risk model in the other case or you need some model for the Evo evolution of insurance premier and the value of a reinsurance contract if you wanted to do this for reinsurance and you need only not only that if you want to do this very properly you need sort of also model that takes into account the dependence of the default times of these guys and the value of the underlying contract so this is relatively complicated if you want to do it properly and that's why all sorts of approximation are out there I think yeah that's basically most of the comments that are here yeah great value adjustment it's a loss of P due to premature default of s and the other rounds are the Beverly adjustments the value adjustments are like an option on the market value it works for types of derivative a last point the credit value adjustment is okay the death value adjustment is a little bit perverse it means that your own liabilities have a lower value if you're less likely to repay so if your bank your credit rating goes down your spread goes up it means that you liabilities have a lower value because it's not so likely they're going to repay them and there is a little bit perverse I did there's a discussion that's why if that really adjustments is really the thing you should do this enters well warned there one comes into this weird world of accounting and well it's a word which we should leave as quick as possible but but Nana one can't and I think accounting for proper economically sound accounting for derivatives is probably one of the most challenging question in this in this area and that's in this visit before [Music] yeah I think in the in the corporate case it was it's pretty clear with all this history regulations and number of cases have been there but it was probably but for a sovereign bonds I probably these things always have to go to court once before you know what they mean and then you have different legislations there and all these things suits yes of course the data is lost if default because you may get something yeah okay so these are these comments here yeah I think we finished just in time as I said we need simplified formulas to do that and one way of simplifying this formula which is being applied a lot is to assume that the yeah as I said evaluated city CVA and DVA formula correctly you need a model the stochastic credit spreads that takes the dependence between the default of SP and the market value of the city s into account so this would mean a dynamic portfolio credit risk model and because you needed I am Nemec portfolio credit risk model to do it properly that's why you find the counterparty risk at the end of the book at the moment at least the formal treatment now this is difficult and markets often work with a simpler formula where you assume that the default of S&P and the value of the underlying independent the same thing would be true for the case of an interest rate swap and under the independence assumption the formula is simpler the CVA is now the law student fold is out there integral from zero to T that's a survivor probability of B times discount factor times the expected positive so called expected positive exposure the expected value of the swap and he integrates with density of the default of s so basically if you say integration summation you sum over all times the probability that s defaults at time T times expected positive exposure discounting but you have to sort of a loss only if we didn't default before you that's a simplified formula which you get under the assumption that the market value of the contract and the default times of P and s are independent and the similar story holds you now well we're finally back to the theme of this week even if you have to mention if I would have to mention one sort of overarching theme of both this workshop and of our book I would say it's dependents modeling in its applications for risk joint extreme events under estimation of dependencies and perfect storm scenario or that it's difficult to have one only one idea in a 600 page book and it will be said if it contained only one idea but that's probably the main idea and we're back to that now an assumption of Independence what would you think in the case of the credit default swap or in the case of a reinsurance let's consider maybe a reinsurance treaty you have a reinsurance treaty could you really assume that the default time of a reinsurance company and the value of the reinsurance contracts a market value of your reinsurance contract it has written that these things are independent but not necessarily the way I asked it this is known as wrong-way risk let's take the other example of the credit default swap and assume that all three guys as very often happens here so the reference entity the protection buyer and the protection seller are banks so say the protection center is whatever Deutsche Bank and protection buyer is UBS and the reference entities whatever so city general to place place it over three different countries and now assume that the protection seller Deutsche Bank defaults well a it is very likely that torture defaults okay they might also default because they lost it another lock lawsuit but it is quite likely that they default because it's a situation where life is very difficult for banks be if torture defaults because they made so many deals it's very likely that the reference entity which was associate a general comes into trouble so this means that the value of a protection by opposition on societal general in this scenario that torture default it is quite high probably these credit spreads would if torture really defaulted favorites would really jump upward if you think about what happened at laments default so they are definitely not independent in this case and this is known as wrong-way risk if you want to really understand it quantitatively how much that matters with it isn't one you need an again a dynamic model and you can assimilate these things and so on you find it maybe it's around underestimate the credit value adjustment or maybe 50 60 percent of course banks know that and they tried some adjustments there but it's again a nice example I think of risk management in a situation where many things can go wrong together that's what is written on these slides well maybe if you wanna mo know if you wanna know more with nice books by John Gregory they mix nicely mathematical modeling and also institutional features on these markets maybe even more the institutional ones but they of course very important for counterparty risk management well this brings me to the end of my presentation I said there's a lot of similarity between credit risk and survival analysis so you've survived it by now and being the last speaker I should say a couple of thank yous that should take a couple of verse and Petrea couple of thank yous well our first thank you and I think I can say this for Paul marios and Alex s well goes to you the participants you have been a very active audience it can sometimes be a little bit stressful to get too many questions but it is far worse to get no questions because then you're thinking you're speaking for an audience is just thinking one with lunch what do I have to do maybe I should do my email or whatever and you've definitely been a very active participating audience that motivated us in a very patient audience in Moline I found a time to listen to my colleagues and I knew the stuff so thank you for that the more important thank you of course goes to also and his team for organizing it for making the perfect week for organizing the beautiful excursions the lovely weather and all of that and I think he deserves a last round of applause [Applause] you

Channel: QRM Tutorial

Views: 2,387

Rating: 5 out of 5

Keywords:

Id: f2ng9HU6ZRo

Length: 46min 5sec (2765 seconds)

Published: Sun Jan 21 2018