CDS Flashcards
Ways of settlement
Cash AND Physical (protection buyer gives loan, gets cash in credit event)
Cash settlement -> what gets paid?
face value minus RR, calculated based on dealers quotes or market price after event
Elements affecting CDS price
1) PD
2) exp. RR
3) maturity of CDS
4) PD of protection seller (counterparty risk)
5) correlation between default of reference entity and protection seller
6) presence of CTD options for protection buyer
How to replicate CDS
Use ASP: long fixed rate bond, financed by shorting bond on repo market at LIBOR + S1, enter into IRS (pay C, receive Libor+S2). This replicates payoff of CDS
No arbitrage spread of CDS according to ASP approach
should be S2-S1 (S2 spread from asset swap, S1 spread from repo market)
Definition basis
CDS_spread - (IRS_S2 - Repo_S1) -> should be zero
Why is CDS basis not zero?
1) technical differences in payoff structure
2) liquidity in CDS and bond market
3) market participants in the 2 amrkets
4) frictions in repo market
Technical:
1) CTD
2) counterparty risk differentials
3) transactionc costs of ASP
3 ways of unwinding CDS
1) agreeing an unwind payment to original CDS counterparty
2) assignemtn to another counterparty that replaces the investor in the CDS
3) offsetting tarnsaction with another counterparty
MtM of CDS position
CF you can get from current market conditions - CF that you are paying
Components of MtM a CDS
We need model for 1) survival prob 2) RR
1) intensity-based (reduced-form) models or structural models -> first time a jump occurs in a jump process in intensity model
2) from rating
Intensity-based models, pros and cons
Pros: elegant, use default-free term structure modeling, easy to estimate
Cons: no economic clues what drives default, no signal on how far a company is from default
Jarrow Turnbull with various intensities
credit event = first event of a Poisson counting process.
i1) ntensity lambda is constant. survival probabilities have sae structure as discount factors
2) Cox process -> lambda varies randomly (like bond pricing formula with short rate = intensity)
3) time-varying determinisitc intensities: lambda(t) is piecewise function of time (e.g. steps each year) -> lambda(t) independent of interest rates and RR
Hazard rate
1 - surv. prob.
h(t) = prob. given survival until t
Structural models: key idea
value of firms assets follow stochastic process. if below certain threshold (normally function of firms debt) -> default.
-> relationship between firms assets and det provide info on PD and RR
Structual models: pros and cons
Pros: intuitive/true, provides link amongst values of different asset classes
Cons: accounting data needed
Merton model: assumptions
firm as equity and debt
debt is pure discount bond with payment at T
value of firm is tradable asset and follow lognormal diffusion with constant vola and interest rate
definition equity in merton model
call on firm asset value with strike=book value of debt
PD in merton
N(-d_2) from BS
Merton: EV, DV, implied credit spread, PD depend on what?
Leverage L, T, asset volatility
Merton: drawbacks
1) company can only default at T -> PD=0 for any t credit spread behaves accordingly
2) all debt mapped into a single ZCB
3) interst rates assumed to be constant, no term structure
4) value of firm tradable - however, parameters not even observable
KMV: default point
point at which firm defaults. somewhere between total liabilities and short-term liabilities
KMV: disance to default (DD)
number of standard deviations the asset value is away fom default: (A_t - DP) / A_t*sigma_A
KMV expected default frequency
Prob. of AV falling below DP
KMV: where get the data?
take from database -> historical default and bankruptcy frequencies etc. (resulting distribution has wider tails than normal)
