Counterparty Risk CVA

Counterparty Risk

CVA

Eduardo Canabarro

Global Head of Risk Analytics

Disclaimer

This presentation contains

statements and views of

the author only.

It is not intended to

represent the views of

Morgan Stanley.

Introduction

 OTC derivatives are efficient and effective tools to transfer financial

risks between market participants

 As a byproduct of such transfer, they create credit risk between the

counterparties

 They also increase the connectedness of the financial system

 Banks have built sophisticated frameworks to manage their

counterparty credit risks

 Typically, a large bank has many thousands of counterparties,

trillions of dollars of derivatives’ notional and billions of dollars of credit exposures to their counterparties

Counterparty exposures: bilateral and market-driven

 Typically, both counterparties face credit risks with respect to each

other

 Counterparty exposures are driven by market risk factors

 It is necessary to measure potential future exposures (PFEs)

Simulation of PFEs

 Banks use Monte Carlo methods to simulate the future values of the

Thousands of simulated market paths …

 The paths start at the current value of the portfolio and they end at

zero, when all trades in the portfolio of trades with the counterparty have terminated

EPE and ENE

 For each point in time on a

simulated market path, we calculate the exposure as the

max(value of the portfolio, 0)

 Expected Positive Exposure

(EPE) is our average

exposure to the counterparty, across all paths, at each point in time

EPE and ENE

 The EPE and ENE profiles are central to the calculation of CVAs

 In sophisticated CVA models those profiles are calculated

Credit Valuation Adjustment (

CVA

)

Counterparty B

 CVA is the adjustment to the risk-free value of the

portfolio of OTC derivatives between A and B to reflect the market value of the bilateral counterparty credit risks faced them

 Eduardo Canabarro and Darrell Duffie, Counterparty Risk: Measurement and

Economic intuition

 If Bank A faces more credit risk than its Counterparty B, the CVA is negative, i.e. it reduces the value of the OTC derivatives from the perspective of Bank A

 If Bank A faces less credit risk than Counterparty B, the

CVA is positive, i.e. it increases the value of the derivatives from the perspective of Bank A

CVA is part of the valuation of derivatives

 CVA is an integral component of the value of derivatives

 Ideally, CVA should be part of each trade’s valuation model

 The reason it is calculated separately is that there are portfolio effects that transcend the valuation of each trade (e.g. netting and margin agreements)

 CVA can be attributed to each trade on a marginal contribution basis

CVA volatility

 Banks that calculate CVA are subject to the volatility of market prices

 They need to hedge their CVA’s risks

 The 2008 financial crisis showed that CVA-related losses can be much larger than default losses

 CVA risks include changes in the credit spreads of the counterparties as well as changes in the market prices that drive the underlying derivative exposures

CVA risk management

 The technology to mark to market and hedge CVA has evolved over the last 20+ years

 Investment banks started pricing and hedging CVA around 1990

 Litzenberger, R., Swaps: Plain and Fanciful, Journal of Finance, vol.47, pages 831-850, 1992.

 Sorensen, E., and T. Bollier, Pricing Swap Default Risk, Financial Analysts Journal, 50, pp. 23-33, May-June 1994.

 Duffie, D. and M. Huang, Swap Rates and Credit Quality, Journal of Finance, v. 51, pp. 921-949, 1996

 More recently, many more banks are pricing and actively hedging their CVAs

CVA calculation

s

E

s

E

CVA





 E_A is the present-valued expected exposure faced by counterparty B

with respect to Bank A;

 s_A is the market loss rate (i.e. the product of risk-neutral PD and risk

neutral LGD) of A

 E_B is the present-valued expected exposure faced by A with respect

to B;

Example 1

E_A = $200 s_A = 2% E_B = $100 s_B = 5%

CVA = 200 x 0.02 – 100 x 0.05 = 4 – 5 = -$1

 The CVA is a negative adjustment to the risk-free value of the portfolio of trades as seen by Bank A because Bank A faces more credit risk than Counterparty B

 If the risk-free value of the portfolio were -$50, the

portfolio would be worth -$51 for Bank A and +$51 for Counterparty B.

Example 2

 Now, suppose that Bank A exits the portfolio of trades with Counterparty B by transferring it to Bank C

 C has s_C = 5% and from C’s perspective:

CVA = 200 x 0.05 – 100 x 0.05 = 10 – 5 = +$5

 To effect the transfer, A pays +$51 to C

 C is a worse counterparty than A and it has to pay $6 to B in order to compensate B for the drop in the value of the portfolio of trades from $51 to $45

CVA risk sensitivities

a) Sensitivities of the CVA with respect to the credit spreads:

b) Sensitivities of the CVA with respect to the underlying exposures:

c) Cross-convexities: A A E s CVA    B B E s CVA _{ }   A A s E CVA _   B B s E CVA _{ }    CVA CVA _{ } B B A A

s

E

s

E

CVA





Should banks hedge their CVA?

 If the bank marks to market its CVA and the bank does not hedge it, it will experience P&L (and earnings)

variability

 Importantly, in a trending and deteriorating credit market environment, the bank could suffer substantial

cumulative CVA losses

 In the 2008 crisis, some banks lost many billions of

dollars in CVAs. This was particularly the case of banks that did not actively hedge their CVAs

CVA hedging: challenges

 The hedges of the CVA include hedges of the market risk factors that drive the underlying exposures and hedges of the credit spreads of the counterparties

 There are important cross-gammas which can be of substantial size when the changes in spreads and exposures are large

 During the 2008 crisis, due to the large size of the CVAs and the high volatility of markets (i.e. large ΔE and Δs), the cross-gammas created difficulties for CVA desks that were dynamically hedging the CVAs

Should banks hedge their own spread?

ΔCVA / ΔE_A = s_A ΔCVA / Δs_A = E_A

Δ2CVA / (ΔE_A Δs_A ) = 1

 Changes in the exposure E_A can be hedged by taking positions on the market risk factors that drive the

exposure

 Changes in Bank A’s own loss rate s_A are more

challenging to hedge. The systematic risk component can be hedged. The bank-specific, idiosyncratic risk component is more difficult to hedge

Bank 1: mainly systematic spread risk

Bank 2: some idiosyncratic spread risk

Bank 3: more idiosyncratic spread risk

CVA desks

 Some banks have opted for a central CVA desk

 Others have opted for various CVA desks deployed within their main derivatives units

 CVA desks provide counterparty credit risk protection to the derivatives trading desks

 They manage the risks of the CVA on an ongoing basis

 They are subject to market and credit risk limits and usually do not have a revenue budget

CVA risks

There are important risks that often fall outside of the scope of the risk measurement

frameworks:

 wrong way

 out of the money

 replacement costs

 dynamic hedging

“It is not what we know, but

Wrong-way risks

 There are wrong-risks that are specific to CVA hedging. Example: crowded counterparty risks

 When a counterparty has entered into similar and large OTC derivatives trades with many banks, the dynamic hedging programs of the banks will create wrong-way risk

 Usually, those wrong way risks do not show up until credit spreads and/or exposure have grown to some large levels

 During the 2008 crisis this occurred with respect to monoline insurers as well as other concentrated

Wrong-way risks

 The CVA wrong way risks are dynamic

 That is, they are a feature of dynamic hedging strategies

 They are different from the wrong way risks as usually defined in the Banking Book context

 They can be large, i.e. non-local, if there is illiquidity in exposure or credit spread hedges

Out-of-the-money risks

 Potential exposure models used for CVA calculation are not good predictors of massive market dislocations

 CVA traders need to be cautious in the pricing and hedging of out-the-money counterparty exposures

 The ability to hedge those exposures in the future, as they grow, needs to be assessed prudently considering the overall liquidity of the market

 The profitability of such trades needs to be evaluated considering the potential CVA risks and dynamic

Replacement costs

 Potential future exposure and CVA models account for the benefits of collateral in the calculation of counterparty exposures

 The models measure the residual exposures after the consideration of collateral

 Banks should not underestimate the all-in costs of replacing trades with a defaulted counterparty

 Especially when that counterparty is a large market participant and its default can impair the liquidity and increase the volatility of the markets where the

Dynamic hedging costs

 The risk management of CVAs requires dynamic re-balancing of the hedges

 When the counterparty exposures and the credit spreads of the counterparties are large and volatile, the

rebalancing requirements can be intense and costly

 The high cost is due to illiquidity, wide bid-ask spreads and overall market impact of the hedging program,

especially when in crowded risk situations

 Dynamic hedging costs are usually not explicitly

captured in the CVA pricing models but they can be the most relevant cost component of large, concentrated

Simulation of dynamic hedging costs

 We can use Monte Carlo simulation models to assess the size of the costs of replication over the life of the CVA hedging program

 The models incorporate the market frictions and provide a realistic description of the probability distribution of

potential CVA hedging costs

 During the 2008 crisis, the costs of CVA hedging proved to be quite material in some cases

CVA Stress tests

 Stress testing is a fundamental component of a sound CVA risk management program

 The fundamental goals of the stress test framework should be:

- Identification of concentrations of market and credit risks

- Identification of out-of-the-money exposures

- Identification of wrong-way risks

- Identification of potentially large dynamic hedging costs of CVA

 Basel 3 defines CVA using the Basel 2 IMM EE profiles. The market risk of CVA is then measured by the bank’s VaR model

Capital on CVA

: advanced approach

 IMM exposures for risk sensitivities

 VaR for credit spread risk

 Only spread risk; no exposure risk

 Single name and index hedges

Capital on CVA

: standardized approach

 h = 1 year

 w_i based on rating of counterparty

 M maturity factor

 B notional of hedges

 See Michael Pykhtin, Model foundations of the Basel 3 standardized CVA

Computational effort

Data Sourcing

Typically 10M trades, 2-10k netting sets and margin

agreements, market data

Trade Pricing

Typically 2-10M trades, over 1-2k paths at each of

100 dates

Simulation of Markets

Typically 1-2k paths of 2-5k risk factors over 100 future

dates per path

Exposure and CVA calculations

Typically 10k netting nodes

Back of envelope numbers:

 2M trades x 2k paths x 100 dates/path = 400B pricings

 400B pricings x 0.00001 sec/pricing = 400k secs = 111 CPU hours

CVA systems

 CVA systems are complex and computationally demanding

 Banks with large OTC derivatives franchises have

invested large resources to build up these systems over the last 10-15 years

CVA systems

 It is important to engineer the CVA system and models for computational efficiency and speed

 Various techniques have evolved to enable fast calculations

 Data storage strategies for trade and netting set data and parallel processing are key elements

 The banks that implemented the most successful CVA systems were the ones that pursued:

– Modularization

– Parallel processing capability

– Scalability

– Pragmatic analytics

“… as simple as possible; but not simpler.” - Einstein

Central Counterparties (CCPs)

 Clearing Members (CMs)

face a CPP instead of facing each other directly

 Multilateral netting, margin requirements, capital

buffers, and high

operational standards

reduce the connectedness of the financial system

 There will be trades left outside of the CCPs

 CCPs are critical components of the global financial and payments systems

 They are vital to financial stability

 They enable multilateral netting and collateralization

 They promote transparence and standardization of trades

 They provide capital buffers to absorb counterparty default losses

 They reduce connectedness and systemic risk

 Since 2009, inter-dealer clearing of OTC derivatives has accelerated

 It is expected to continue increasing

 The largest counterparty risks faced banks are rapidly shifting from peer banks to CCPs

 A typical large bank is a clearing member of tens of CCPs and it is likely that its top 5-10 counterparty exposures are already to CCPs today

 Basel 2 did not charge regulatory capital on CCPs

 Basel 3 charges capital on exposures to CCPs: about 20% EAD, IMM based

 Initial margin for OTC is typically at 95-99% confidence level, 5-day market move

 Margin may also consider liquidity characteristics, risk concentration and product-specific features

 Defaulting CM margin

 Defaulting CM’s guarantee fund

 CCP’s equity capital (small)

 Guarantee funds of non-defaulting CMs

 Additional calls for capital on non-defaulting CMs (unlimited liability)

CCPs - concerns

 Specialization

 Fragmentation

 Competition

This book describes the methods and practices used to manage OTC derivative counterparty risk and the performance of those methods during the 2008 financial crisis. It covers topics in counterparty risk measurement, CVA, CVA hedging, credit derivatives, collateralization, stress testing, back testing and integration of counterparty credit risk into economic capital frameworks. Experiences and new ideas on models are discussed by a group of world-class experts. The content of the book is particularly relevant in light of the Basel 3 rules on the regulatory capital on counterparty risks. The book contains a wealth of insights that can be useful for practitioners, regulators, consultants, accountants, lawmakers, auditors and researchers to understand the substantive, and often technical, issues related to counterparty risk management.

Chapters by: Aaron Brown • Eduardo Canabarro • Guanghua Cao • Patrick Chen • Eduardo Epperlein • Jon Gregory • Andrew Hollings • Gregory Hopper • Sean Hrabak • Phillip Koop • Darren Measures •

Counterparty Credit Risk

Measurement, Pricing and Hedging