SCR Calculator User Manual

Credit Default Swap Modelling

Credit Default Swaps are usually priced in a stochastic way. In the SCR Calculator, with the focus being interest rate capital calculation, a simplified deterministic cashflow model is used.

CDS contracts are modelled using two sets of cashflows: a real set of premiums and a hypothetical set of "probabilistic default payouts". There are two types of CDS contracts: "Buy Protection / Pay Premium" and "Sell Protection / Receive Premium". Both cases are then goal sought w.r.t. an implied annual default rate, so that the total present value of these two cashflows equals the market value of the contract.

• At every coupon period start, an up-to-period-start survival factor and an in-period default factor are calculated, based on the assumed implied annual default rate (constant for a scenario).
• The probabilistic default payout of that period equals [notional] x [default factor] x [Loss-Given-Default].
• The premium payment of that period equals [survival factor] x [1 - default factor] x [premium rate] x [notional].
• For the "Buy Protection / Pay Premium" type, premiums will be recorded as negative cashflows and the probabilistic default payouts will be recorded as positive cashflows. The opposite is true for the "Sell Protection / Receive Premium" type.
• Both cashflows are discounted using a risk neutral discount rate.
• The total present value of the two cashflows must equal the given market value; therefore the implied default rate is worked out.

To calculate the spread risk capital of a CDS contract, the implied default rate is shocked and the difference in market value taken as the risk capital amount.