University of Colorado at Boulder Leeds School of Business FNCE4830 R.Caccia FNCE4830. Risk Management: Counterparty Risk

Transcription

1 FNCE4830 Risk Management: Counterparty Risk

2 What does it take to trade a derivative? (it actually takes more than two to tango) Before trading you need to have documents in place, typically negotiated with the counterparts by lawyers, but with involvement of the credit team, treasury and front office At trade time you need: Sales people to understand clients needs and sell trade ideas Strategist write models used to price derivatives + compute risk Traders to commit capital and make prices on behalf of the firm After the trade (and throughout its life) you need: Middle office to confirm the trade and exchange cash flows Valuation & Collateral to send MTM and exchange collateral Credit team to continuously monitor the counterpart s credit Risk managers and traders to actively manage the risk Controllers to measure P/L and maintain proper books&records Treasury to fund the firm, plus Technology, Strats and more

3 Counterparty Risk (a few more TLA s) MAC Master Agreement Contract (ISDA, etc.) Contains terms under which all trades will fall It spells out Termination Events (e.g. rating based ones) it establishes overall netting between the two counterparts and sets the party owed in case of default as a Senior Unsecured creditor (same as bond holders) CSA Credit Support Annex Appendix to Master Agreement Contract Contains credit/collateral terms underlying all OTC trades: Mechanics to exchange Initial and Variation Margin, e.g. thresholds Eligible collateral and interest paid on collateral Other provisions, such as rights to re-hypothecate collateral

4 Counterparty Risk Management Determine Risk Appetite (way) Before the first trade Analyzes counterparty Signs MAC and CSA Determines collateral arrangements Sets limits as to allowable exposure Before the first or subsequent trades Analyze trade Understand how trade fits into existing portfolio Approves or disapproves trade After any trades Monitor and review

5 How to Hedge Counterparty Risk? Collateral terms reduce the counterparty risk You may still be exposed to counterparty risk You need to measure that risk and adjust down the value of your trades with each counterpart This is CVA Credit Valuation Adjustment Banks need to report their CVA How do you hedge CVA? Are there any market instruments to do that?

6 Credit Default Swaps (CDS) CDS is a form of insurance against a firm defaulting on the bonds they issued CDS are used also as a way to express a bearish view on a company Before the 2008 crisis, CDS were traded more liquidly (5-8 times) than bonds Simplified Mechanics: You pay me a running fee (each quarter) If the reference entity defaults, you deliver the bond to me and I will pay you $100. Fees stop. Typical maturity is 5 years

7 CDS Structure Example Default Protection Buyer, A 120 bps per year Payoff if there is a default by reference entity=100(1-r) Default Protection Seller, B Recovery rate, R, is the ratio of the value of the bond issued by reference entity immediately after default to the face value of the bond

8 Other Details Payments are usually made quarterly in arrears In the event of default there is a final accrual payment by the buyer Settlement can be specified as delivery of the bonds or (more usually) in cash An auction process usually determines the payoff Suppose payments are made quarterly in the example just considered. What are the cash flows if there is a default after 3 years and 1 month and recovery rate is 40%?

9 Attractions of the CDS Market Allows credit risks to be traded in the same way as other market risks Can be used to transfer credit risks to a third party Can be used to diversify credit risks Can be used to protect against counterparty risk (remember, an ISDA gives you the same rights as bond holders in bankruptcy court, if you are owed money by the bankrupt party)

10 CDS Valuation Consider a simplified CDS: Pay up-front X. If the reference name defaults in the next year then receive $100 in 1 years time. The probability of default is 10% Risk-free interest rates are 5% What is the fair value X of this CDS? Approximately: $100 10% e 5% = $9.51

11 CDS Some formulas Given a CDS market, where the credit is quoted with a credit spread s and a recovery rate R we can compute: Default intensity λ = s/(1 R) Survival probability to time t Q t = e λ t Probability[dft in period j] d j = (Q j 1 Q j )

12 Survival Curve Cpty's Survival curve s = 500bp R=60% Maturity=20 years λ = s/(1 R) Q t = e λ t

13 Jan-07 Feb-07 Mar-07 Apr-07 May-07 Jun-07 Jul-07 Aug-07 Sep-07 Oct-07 Nov-07 Dec-07 Jan-08 Feb-08 Mar-08 Apr-08 May-08 Jun-08 Jul-08 Aug-08 Sep-08 Oct-08 Nov-08 Dec-08 Jan-09 Feb-09 Mar-09 Apr-09 May-09 Jun-09 Jul-09 Aug-09 Sep-09 Oct-09 Nov-09 Dec-09 Jan-10 Feb-10 Mar-10 Apr-10 University of Colorado at Boulder Leeds School of Business FNCE4830 R.Caccia Your own credit spread widens during distressed credit markets. That makes borrowing more expensive Goldman 5y Credit Spread What happened here?

14 Counterparty Risk WTI Swap Bank buys a WTI swap from an oil producer The oil producer agrees to sell a fixed number of barrels of WTI per month at a known fixed price As the price of WTI moves the value of (the remaining part of) the trade changes Bank in the Money (Asset) t Counterpart in the Money (Liability)

15 Counterparty Risk WTI Swap Assume the oil producer defaults If the trade has a positive value for the producer, the Bank has no exposure If the trade has a positive value for the Bank, the Bank has a loss Bank in the Money (Asset) Default Event: in this case the Bank owes to the producer. So no loss for the Bank. t Counterpart in the Money (Liability) Default Event: in this case, the producer owes the Bank. The Bank has a claim in bankruptcy court.

16 Margin Thresholds As part of the MAC and CSA the Bank and its counterparty will determine the levels at which margin is called. For example: The producer may have to start posting collateral only if the exposure exceeds $5mm (there are more details) The producer may start demanding collateral from the Bank if it is owed more than $3mm MAC/CSA will also determine who decides the value of the trade, frequency of collateral, type of collateral, rounding, etc. Bank in the Money (Asset) Counterpart s Margin Threshold t Counterpart in the Money (Liability) Bank s Margin Threshold Default Event: in this case, the producer owes the Bank only up to the Margin Threshold

17 Counterparty Risk Hedge CVA You can hedge your CVA by buying a CDS on your counterpart Difficulty is that you need to adjust the dollar Notional of the CDS every day Bank in the Money (Asset) t Counterpart in the Money (Liability)

18 Method 1 Monte Carlo For each path i, along each time step j: PV of the swap: M i,j exposure (asset): A i,j = [M i,j ] + liability: L i,j = [ M i,j ] + default intensity: λ = s/(1 R) Survival probability: Q j = e λ t = e λ j Δt Prob[dft in period j]: d j = (Q j 1 Q j )

19 Method 1 Monte Carlo path i Bank in the Money (Asset) CVA i,j = A i,j d c,j (1 R c ) t Counterpart in the Money (Bank Liability) A i,j is a PV

20 Method 1 Monte Carlo (cont.) Thanks to zero correlation: A i,j is a PV CVA for each MC path i is CVA i = σ j A i,j d c,j (1 R c ) Then average over N Monte Carlo paths

21 Method 2 Using Swaptions Consider the following: Exposure to your counterpart occurs only when the swap is positive for you So at each time step j, build a call option on the remainder of the swap (a swaption) The swaption price is the expected PV of the exposure to the counterpart Multiply each swaption by the prob of default in that period and account for recovery

22 Method 2 Using Swaptions At each time step j, build a call and a put swaption on the remaining periods PV of the call swaption: C j (exposure) Same as before: default intensity: λ = CDS/(1 R) Survival probability: Q j = e λt = e λ j Δt Prob[dft in period j]: d j = (Q j 1 Q j ) Bank s Funding cost: f b,j CDS b

23 Exposure Curve (using swaptions) 70,000,000 60,000,000 50,000,000 40,000,000 30,000,000 20,000,000 10,000, Months

24 Using Swaptions CVA 70,000,000 C j is a PV 60,000,000 50,000,000 40,000,000 30,000,000 20,000,000 CVA j = C j d c,j (1 R c ) 10,000, Months

25 Method 2 Using Swaptions Thanks to zero correlation: CVA calculation using swaptions is obtained by summing over all time steps j CVA = σ j C j d c,j (1 R c ) Q. Should this agree with Monte Carlo? C j, is a PV

26 How do you risk-manage CVA Trade the counterpart s name: Buy CDS on the actual entity (same seniority) Proxy-hedging: capital structure (different seniority debt or even equity!) related entity index Trade the underlying markets Trade volatility and correlation (when possible) Negotiate (more conservative) collateral terms: Lower or zero thresholds for Variation Margin Initial Margin Reserves for gap risk and against disputes Hedge my own credit (?!?)

27 Credit Indices (like S&P500?) CDX.NA.IG is a portfolio of 125 North American Investment Grade companies CDX.NA.HY is a portfolio of 100 North american High Yield companies itraxx Europe: 125 European IG names The portfolios are updated twice a year (on March 20 and Sept 20 each year) The index can be thought of as the cost per name of buying protection against all N names. If one defaults, you get 1/N payout.

28 Counterparty Risk A classic example It is September 2008 Your credit derivatives desk actively trades credit index (CDX) and CDS on the corresponding underlying names They have net sold credit protection You, their risk manager, anticipate market turmoil and ask them to flatten their position They do: they buy enough CDS&CDX protection to be flat Are you satisfied? Any other questions you would like to ask? Your turn to talk (hint: paranoia)

29 You need funding when: You buy assets (bonds, equities, ) Markets move and you need to send collateral to counterparts or exchanges Counterparts do not post collateral because of their contract or because they dispute your calculations or because they are in trouble In all these cases, you need funding Murphy s law: funding is most expensive when you need it most Other Risks Funding