Ch6 Credit Risks & Credit Derivatives (3)

4-4. CreditMetrics
* video clips: http://www.youtube.com/watch?v=CMn3q9gO3tM
http://www.youtube.com/watch?v=gyy0lXlXpCU&feature=related

Step 1: Figure out a rating class for the debt claim
Step 2: One-year rating transition matrix
Step 3: Specify Horizon
Step 4: Compute possible one-year forward values using one-year forward zero curves
*possible one-year forward values =Sum(CFi x i-1Ri)
Step 5: Compute the expected bond value
Step 6: Compute the credit VaR for a given confidence level
Step 7: Transition Probabilities -> Cumulative Probability -> Compute Threshold Values
Step 9: Compute joint probability bivariate distribution
=BIVAR(BT1i, BT2i, rho)

**first step = gathering of inputs: calculating many measures such as PD, recovery rate statistics, factor correlations and their relationship to the obligator, yield curve data, and individual exposures that are distinct from the other inputs

**The company surplus variable Sj obeys the linear factor model as follows:

The index model enales a straightforward calculation of pairwise asset correlations.
Cov(Si;Sj)




4-5. Moody's KMV Portfolio Manager
The KMV model calculates the expected default frequencies(EDFs) for each obligor. With KMV's model, the capital structure includes equity, short-term debt, long-term debt, & convertible debt. KMV solves for the firm value and volatility.
Advantage:
- probabilities of default are obtained using the current equity value
- any event that affects firm value translates directly into a change in the probabilities of default change continually rather than only when ratings change.
-> accurate and timely information from the equity market provides a continuous credit monitoring process that is difficult and expensive to duplicate using traditional credit analysis

Features:
- Distance to default threshold(ratio) determines the level of default risk, E(VT) - d*
d* = short-term debt + 0.5 long-term debt
VT = V0 exp((u-.5 sigma ^ 2) T + sigmaV ZT)
- Ability to adjust to the credit cycle and ability to quickly reflect any deterioration in credit quality
- Work best in highly efficient liquid market conditions

Weaknesses:
- it requires some subjective estimation of the input parameters
- it is difficult to construct theoretical EDFs without the assumption of normality of asset returns
- private firms EDFs can be calculated only by using some compatability analysis based on accounting data
- it does not distingquish among different types of long-term bonds according to their seniority collateral, covenants or convertiblity

e.g.) VT = $80, sigma = $10
=> 98% (confidence level) of observations lie between +2.33 and -2.33 standard deviations from the mean. Hence, there is a 1% chance that it will fall to a value of $80 - 2.33 * $10 = $56.70 or below; alternatively, there is a 99% provability that the equity holder will lose less than $80 - $56.70 = $23.30 in value; that is, $23.00 can be viewed as the VaR on the equity at the 99% confidence level.



Limitations of the Credit Portfolio Models
Models do not take into account changes in interest rates, credit spreads or current economic conditions.

5. Credit Derivatives
Credit derivatives are financial instruments whose payoffs are contingent on credit risk realizations.
Credit Events:
- fialure to make a required payment
- restructuring that makes any creditor worse off; debatable
- invocation of cross-default clause
- bankruptcy
* obligation acceleration, obligation default
**a credit agency downgrade is not a default event (if it's not under thereshold)

5-1. Credit Default Put
A put on the firm value with the same maturity as the debt and with an exercise price equal to the face value of the debt

5-2. Credit Default Swap (CDS)
With CDS, party A makes a fixed annual payment to party B, while party B pays the amount lost if a credit event occurs.
** video clips: http://www.youtube.com/watch?v=P2cUh-e_Qkc

*cash delivery: Z = midpoint between bid and ask price
cash payment = (100 - Z)% of the notional principal

5-3. Total rate of return swaps(TROR)
*video clips: http://www.youtube.com/watch?v=cmUXTFggIa0
- Protection Buyer: TROR Payer (owns preference asset, synthetically short the reference asset)
- Protection Seller: TROR Seller (synthetically long the reference asset)
-TROR Payer pays Total Return (Income + delta Value) e.g.) market value + coupon
- TROR Seller pays LIBOR + Spread (based on receiver's credit rating)
**buyer trasfer default risk, credit deterioration, market risk to seller
**seller: virtually eliminate funding costs
**spread depends on the credit risk of the reference asset, the creditworthiness of the receiver, and the correlation of credit quality between the reference asset issuer and the total-return swap receiver


6. Credit Risks of Derivatives
Vulnerable Option: an option with default risk
Without the default risk, the holder of the option at expiration receives:
Max(S - K,0)

*The payoff of the vulnerable option is:
Max[Min(V, S - K), 0]
where:
V = a firm's Value
S = underlying asset's price at expiration
K = exercise price

The correlation between firm's value & underlying asset value is important in the valuations of the vulnerable option.
- strongly negative correlation -> vulnerable option has little value
- strongly positive correlation -> no credit risk

If the option has credit risk, then a derivative can be written to eliminate the credit risk. If the price of the vulnerable option can be estimated then the price of the credit derivative to insure the vulnerable option can be determined.
The appropriate credit derivative is one that pays the difference between a call without default risk and the vulnerable caull:
Max(S - K,0) - Max[Min(V, S - K), 0]

Alternative approach:
Vulnerable Option = [(1 -PD) x c] + (PD x RR x c)
where:
c = value of the option without default
PD = probability of default
RR = recovery rate

e.g.) PD = 5%, RR = 50%
=> (1 - 0.05) x c + 0.05 x 0.5 x c = 0.9725c => the vulnerable option is worth 97.5% of the value of the option that is free of default risk

The credit risk in a swap can be reduced by requiring a margin or by netting the payments.
Netting means that the payments between the two counterparties are netted out, so that only a net payment has to be made (full two-way payment covenant).

Market Maker's payoff:
If S <> F then S - F

Swap's payoff to Market Maker:
-Max[F - S, 0] + Max[Min(S, V) - F,0]