Counterparty Credit Risk in Derivatives Chapter 17 Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Clearing Arrangements for OTC Derivatives (Figure 17.2, page 381) Bilateral clearing: usually governed by an ISDA Master agreement Central clearing: a central clearing party (CCP) stands between the two sides Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Regulations Standard OTC transactions must be cleared through a CCP (some exceptions) Nonstandard OTC transactions continue to be cleared bilaterally, but with much higher capital charges Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Central Clearing: Role of CCP (Figure 17.1, page 380) Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Key Questions How many CCPs Will there be interoperability? Will benefits of netting increase or decrease? Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Simple Example: 3 market participants; 2 product types (Figure 17 Simple Example: 3 market participants; 2 product types (Figure 17.3, page 382) Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Bilateral Clearing:The ISDA Master Agreement One important feature is netting This states that all transactions with the counterparty are considered to be a single transaction in the case of early termination and for the purposes of posting collateral Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Events of Default and Early Termination Declaration of bankruptcy Failure to make payments on derivatives as they are due Failure to provide collateral when it is due The non-defaulting party has the right to declare an early termination event a few days after an event of default if there has been no resolution of outstanding issues Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Collateral Arrangements The credit support annex (CSA) of the ISDA Master Agreement specifies Threshold Independent Amount Minimum Transfer Amount Eligible Securities and Currencies Haircuts Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Possible ISDA Clause: Downgrade Triggers Specify that in the event of a downgrade the counterparty has certain rights. It might specify that the counterparty can terminate outstanding transactions or that the counterparty can require collateral In AIG’s case counterparties could require collateral in the event of a downgrade below AA. This necessitated a huge government bailout. Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

CVA Credit value adjustment (CVA) is the amount by which a dealer must reduce the value of transactions because of counterparty default risk Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

The CVA Calculation ……………… ……………… ……………… Time t1 t2 t3 t4 tn=T q1 q2 t1 t2 t3 t4 tn=T ……………… Default probability q1 q2 q3 q4 qn ……………… v1 v2 v3 v4 PV of net exposure vn where R is the recovery rate Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

CVA continued The default probabilities (i.e., the qi’s) are calculated from credit spreads The PV of the net exposure is calculated using Monte Carlo simulation. Random paths are chosen for all the market variables underlying the derivatives and the net exposure is calculated at the mid point of each time interval. (These are the “default times” The vi is the present value of the average net exposure at the ith default time Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

Calculation of Net Exposure If no collateralization the net exposure is the maximum of the value of the derivatives and zero If collateral is posted we assume that there is a “cure period” (= c days) immediately before a default during which collateral is not posted. On each Monte Carlo trial we must calculate the value of the portfolio c days before each default time This determines the collateral available at the default time Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

Incremental CVA Results from Monte Carlo are stored so that the incremental impact of a new trade can be calculated without simulating all the other trades. Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

CVA Risk The CVA for a counterparty can be regarded as a complex derivative Increasingly dealers are managing it like any other derivative Two sources of risk: Changes in counterparty spreads Changes in market variables underlying the portfolio Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

Basel III (2010) Basel III requires CVA risk arising from a parallel shift in the term structure of counterparty credit spreads to be included in the calculation of capital for market risk It does not require banks to include CVA risk arising from the underlying market variables Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

Wrong Way/Right Way Risk Simplest assumption is that probability of default qi is independent of net exposure vi. Wrong-way risk occurs when qi is positively dependent on vi Right-way risk occurs when qi is negatively dependent on vi Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Examples Wrong-way risk typically occurs when Counterparty is selling credit protection Counterparty is a hedge fund taking a big speculative positions Right-way risk typically occurs when Counterparty is buying credit protection Counterparty is partially hedging a major exposure Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

Problems in Estimating Wrong Way/Right Way Risk Knowing trades counterparty is doing with other dealers Knowing how different market variables influence the fortunes of the counterparty Do counterparties become more likely to default when interest rates are high or low? The evidence is mixed and so we do not know whether receiving or paying fixed generates wrong way risk Even when there appears to be right-way risk liquidity problems can lead to a company being unable to post collateral (e.g Ashanti) Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

Allowing for Wrong-Way risk One common approach is to use the “alpha” multiplier to increase the v’s Estimates of 1.07 to 1.1 for alpha obtained from banks Basel II sets alpha equal to 1.4 or allows banks to use their own models, with a floor of 1.2 Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

DVA (more recent and more controversial) Debit (or debt) value adjustment (DVA) is an estimate of the cost to the counterparty of a default by the dealer Same formulas apply except that v is counterparty’s exposure to dealer and q is dealer’s probability of default Accounting value of transactions with counterparty = No default value – CVA + DVA Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

DVA continued What happens to the reported value of transactions as dealer’s credit spread increases? Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Expected Exposure on Pair of Offsetting Interest Rate Swaps and a Pair of Offsetting Currency Swaps (No collateral) (Figure 17.2, page 317-318) Exposure Currency swaps Interest Rate Swaps Maturity Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Interest Rate vs Currency Swaps The qi’s are the same for both The vi’s for an interest rate swap are on average much less than the vi’s for a currency swap The expected cost of defaults on a currency swap is therefore greater. Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Simple Example: Single transaction always has positive value to dealer CVA has the effect of multiplying value of transaction by e-sT where s is spread between T-year bond issued by counterparty and risk-free T-year bond Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Example 17.1 (page 391) A 2-year option sold by a counterparty to the dealer has a Black-Scholes value of $3 Assume a 2 year zero coupon bond issued by the counterparty has a yield of 1.5% greater than the risk free rate If there is no collateral and there are no other transactions between the parties, value of option is 3e-0.015×2=2.91 Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

Dealer Has Single Long Forward with Counterparty (page 392) For a long forward contract that matures at time T the present value of the exposure at time ti is F0 is the forward price today, K is the delivery price, s is the volatility of the forward price, T is the time to maturity of the forward contract, and r is the risk-free rate Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012