Credit Default Swap by Abbydoc


									Credit Default Swap

           Nargiza Ludgate
        Phuong Anh Nguyen
What is a SWAP?

l   Swap is a derivative in which two counterparties
    agree to exchange a sequence of cash flows over a
    period in the future.

l   Swaps are usually used to hedge risks (ex. interest
    rate risk), or to speculate on changes in the
    underlying prices.

l   Swaps can be interest rate swaps, currency swaps,
    commodity swaps, equity swaps, and credit default
Credit Default Swaps
l   A Credit Default Swap (CDS) is similar to an
    insurance contract, providing the buyer with
    protection against specific risks associated
    with defaults, bankruptcy or credit rating
l   CDS is the most widely traded credit
    derivative product. Typical term of CDS
    contract is 5 years (up to 10-year CDS).

l   CDS documentation is governed by the
    International Swaps and Derivatives
    Association (ISDA), which provides
    standardized definitions of credit default
    swap terms, including definitions of what
    constitutes a credit event.
l   One party “sells” risk and the counterparty
    “buys” that risk.

l   The “seller” of credit risk - who also tends to
    own the underlying credit asset - pays a
    periodic fee to the risk “buyer”.

l   In return, the risk “buyer” agrees to pay the
    “seller” a set amount if there is a default.
Transaction Diagram

Risk Buyer or                                                                  Risk seller or

Source: Credit Derivatives and Synthetic Structures, John Wiley & Sons. 2001
Potential Benefits
l       In addition, to hedging event risk, the CDS
        provides the following benefits:
    l     A short positioning vehicle that does not require an initial
          cash outlay.
    l     Access to maturity exposures not available in the cash
    l     Access to credit risk not available in the cash market due
          to a limited supply of the underlying bonds.
    l     Investments in foreign credits without currency risk.
    l     Ability to effectively ‘exit’ credit positions in periods of low
Quoting CDS
l   5 year CDS for Ford Motor Company debt
    l   Nominal amount = $10 million
    l   160 bp on April 27, 2004
    l   5-year protection

l   How much will you pay for protection?
    l   (0.0160 / 4) x 10,000,000 = $40,000 (every
        quarter as a premium for protection against
        company default)
1-year CDS Contract

               Premium payments
    Investor    No default: Zero         Bank

                 Loss recovery

                                             ($10 mln)

                             High-risk entity for default
1-year CDS Contract

          t=0        t=1       t=2     t=3       t=4
    Effective date

l   Nominal amount = N
l   Premium = c
l   Quarterly payment = Nc/4

There are 5 possible outcomes in this CDS contract:
  l No default (4 premium payments are made by bank to investor
     until the maturity date)
  l Default occurs on t1, t2, t3, or t4
CDS Pricing
l   Assign probability to each five outcome
l   Calculate PV of payoff for each outcome
      l   Determine the price of CDS
      l   Determine premium “C” paid

l   PV of CDS = PV of five payoffs multiplied by
    their probability of occurrence
      l   Recovery Rate = R
      l   Probability = P1 [ no default at to + t1 ]
                      1 – P1 [ default at t1 ]
Bank’s Perspective

               1- P1                P1

                            1- P2                   Nc/4
          N(1-R)                             P2

  Nc/4                              1- P3                  Nc/4      Nc/4
                   N(1-R)                           P3

  Nc/4        Nc/4                          1- P4                 Nc/4      Nc/4      Nc/4
                                N(1-R)                     P4

   Nc/4       Nc/4           Nc/4                                    Nc/4      Nc/4          Nc/4   Nc/4
Calculation of PV, given
discount factor of δ1 to δ4

  Description    Premium Payment PV            Default Payment PV      Probability

Default at t1                0                    N (1 – R) * δi         (1 – P1)

Default at t2           - Nc/4 * δi              N (1 – R) * δ2        P1 (1 – P2)

Default at t3        - Nc/4 * (δi + δ2)          N (1 – R) * δ3       P1 P2 (1 – P3)

Default at t4     - Nc/4 * (δi + δ2 + δ3)        N (1 – R) * δ4      P1 P2 P3(1 – P4)

No default      - Nc/4 * (δi + δ2 + δ3 + δ4)            0           P1 x P2 x P3 x P4
 Calculation of PV of CDS

Present Value of Credit Default Swap =

  = (1 – P1) x N (1 – R) δi   + P1 (1 – P2) x [N (1 – R) δ2 -
  Nc/4 δi]   + P1 P2 (1 – P3) x [N (1 – R) δ3 - Nc/4 (δi + δ2)]
  + P1 P2 P3(1 – P4) x [N (1 – R) δ4 - Nc/4 (δi + δ2 + δ3)]
  – (P1 x P2 x P3 x P4) x [Nc/4 (δi + δ2 + δ3 + δ4)]
l   Due to its protection nature CDS market
    represents over one-half of the global credit
    derivative market.

l   CDS allows a party who buys protection to
    trade and manage credit risks in much the
    same way as market risks.

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