Ch6 Measuring & Marking Counterparty Risk

1. Definitions

Counterparty risk

A risk that a party to an OTC derivatives contract may fail to perform on its contractual obligations, causing losses to the other party

- replacement cost

- bilateral

Counterpary exposure

The larger of zero and the market value of the portfolio of derivative positions with a counterpary that would be lost if the counterpaty were to default and there were zero recovery

Current exposure (CE)

The current value of the exposure to a counterparty

Potential future exposure (PFE)

The maximum amount of exposure expected to occur on a future date with a high degree of statistical confidence

- MPFE

- PFE(t )

Expected exposure (EE)

The average exposure on a future date

** expected exposure profile (=credit equivalent or loan equivalent exposure curve)

The Expected Exposure Profile is derived using a Monte Carlo simulation and calculating the probability weighted mean(average) exposure of the distribution of exposures at any future date for the portfolio of transactions. The EE profile is commonly used by banks that use a simulation approach to calculate exposures for their credit limits

- a graph of EE(t ) across time

- credit-equivalent/loan-equivalent exposure curve -> economic capital & credit pricing

Expected positive exposure (EPE)

The average EE(t ) for t in a certian interval; the weighted average over time of the expected exposure, where the weights are the proportion that an individual expected exposure represents of the entire exposure horizon time interval.

Right-way/wrong-way exposure

Positively/negatively correlated with the credit quality of the counterparty

Credit risk mitigants

Designed to reduce credit exposures, such as netting rights. collateral agreements. & early settlement provisions

- Liquidity puts. a knock-in barrier option, where the barrier is a liquidity metric. A investor holds bond and buys a liquidity put that is knocked into existence only if the bond’s liquidity reaches some low barrier (e.g. trading volume falls below X for Y consecutive days). If barrier is reached (option knocks-in), investor has the right to sell the bond to the option seller at the market price.

- Credit triggers

2. Estimating PFE

*PFE measurement system include:

- Historical databases

- Monte Carlo simulation engines

- Trading pricing calculators

- Exposure calculators

- Reporting tools

2-1. Simulation engine

- normal diffusion process. e.g.) low interest rates

- lognormal diffusion process. e.g.) high interest rates, major foreign exchanges

- jump-diffusion process. emering market => a normal continuous price diffusion process modelled by Geometric Brownian Motion with mean-reversion and a volatilities term structure

-> an abnormal, discontinous jump process modelled by a Poisson distribution

- mean-reversion. random walk process; fluctuating around values determined by the cost of asset and the level of demand

- risk-neutral probabilities. used for the arbitrage-free pricing of assets for which replication strategies exist.

- correlations among market risk factors

2-2. Trading pricing

- all trades with the counterparty must be priced to calculate the exposure in the future market scenario

2-4. Exposure calculation

- fundamental concepts: netting & margin node

- conterparty exposure determined by (i) calculating the exposure in each netting node, (ii) adding all netting node exposures. (iii) calculating the collateral posted/received for each margin code, (iv) adding collateral posted/received. & (v) calculating the net exposrue to the counter party as (ii) — (iv)

2-5. Model validation & control

- standards comparable to front-office calculators

2-6. Applications of Exposure Modeling

PFE models are used for

- trade approvals against credit line limits

- credit risk valuation

- economic & regulatory capital

* gross-up factor = EC under market & credit uncertainty / EC under credit uncertainty

**BASEL I: Capital = EAD x Counterparty Risk Weight x 8% & EAD = CE + PFE & RW=F(PD,LGD,Maturity); EAD=exposure of default, RW=risk weight

3. Market Valuation of Credit Exposures

CVA (credit valuation adjustment) of an OTC derivatives portfolio with a given counterparty is the market value of the credit risk due to any failure to perform on agreements with that counterparty. CVA adjusts payment to reflect changes in the credit risk changes relative to the counterparties.

** mid-market price. price of a security in-between its offer and bid price, used in computing investment performance statistics

e.g.) Party A’s, pound receiver, OTC pound-dollar currency swap with Party B; mid-market value = 150, effective maket value for default risk= 3, net market value of default risk to A of 8

=> downward credit risk adjustment = 8 — 3 = 5. hence, fair m.v. to A = 150 — 5 = 145

3-1. Risk premia

— the difference between the expected return on a security or portfolio and the riskless rate of interest

Risk-neutral mean loss rate inc. an artificially high mean loss rate that reflects a risk premia for accepting the higher default risk

3-2. Mean* exposure times mean* loss rate

Computing total market vlaue, V(t), of default risk during the t-th future time period

i. Calculate EE*(t ), the risk-neutal expected exposure for period t

ii. Calculate the risk-neutral mean default loss rate L*(t ) associated with the period

iii. Obtain C(t ), the price of a default-free zero-coupon bond of maturity t

iv. Calculate V(t ) = EE*(t ) x L*(t ) x C(t )

3-2-1. Mean Loss Rate ; expected loss on a risky bond due to default risk

Mean Loss Rate = PD x (1 — Recovery Rate)

e.g.) A bond with F.V. of $1000,000, probability of default = 40%, recovery rate = 50%, actual price = $700,000

=> Mean Loss Rate = 40% x (1 -50%) = 20%

Assuming that interest rates are zero, the bond value = 100,000 x (1 — .2) = $80,000

Risk-neutral mean loss rate = 1 — 70,000 / 100,000 = 30%

** risk-neutral mean loss rate. A rate at which investors act as if they are risk-neutral because the rate includes an artificially high mean loss rate that reflects a risk premium for accepting the highter default rsik

- credit spread. the difference between the risky bond rate and the risk-free rate

=> a proxy for the annualized risk-neutral loss rate

- default swap rate. a proxy for the risk-neutral mean loss rate paid by the protection buyer in a credit default swap agreement

3-3. General Monte Carlo approach

Risk-nuetral Monte Carlo simulation used to obtain the estimate of the market value of credit risk in bilateral OTC portfolio

i. Initiate a new independently simulated scenario

ii. Simulate the next exposure of Counterparty A to default by Counterparty B

iii. Simulate whether or not B defaults at that date, and whether A defaults at that date

iv. If, at a given date, Counterparty B defaults and Counterparty A has not already defaulted, then simulate the fraction of the net exposure that is lost

v. Simulate the path of short-term interest rates

vi. Discount to present market value, using the compunded short-term interest rates for this scenario, the losses to Counterparty A

vii. Return to Step 1, unless a sufficiently large number of scenarios have been run to obtain the approximate effect of the law of large number

viii. Average the result of (vi), over all independently generated scenarios

3-4. General remarks on credit adjustments