Credit Default Swap (CDS)
A credit default swap is a financial derivative that allows an investor to hedge or speculate on the credit risk of a reference entity. In a CDS contract, one party pays a periodic premium (the CDS spread) in exchange for a contingent payment if a specified credit event, such as a default, occurs. The two main components of a CDS are the premium leg, which consists of regular payments, and the protection leg, which represents the contingent payoff upon default.
Risk-Free Interest Rate and Continuous Compounding
The risk?free interest rate is the theoretical rate of return of an investment with no risk of financial loss. When using continuous compounding, this rate is applied exponentially over time to discount future cash flows. A flat risk-free zero curve implies that the same interest rate (in this case, 7% per annum) is used for discounting cash flows from all maturities, simplifying the valuation of both the premium and protection legs of a CDS.
Default Probability
The default probability is the likelihood that a reference entity will default within a certain period. In the context of a CDS, the default probability is used to assess the expected losses from the protection leg. It is often assumed to be conditional on survival up to that period, and the probability influences the expected payout in the event of a default, thereby affecting the CDS spread.
Recovery Rate
The recovery rate represents the percentage of the notional amount that is expected to be recovered by creditors in the event of a default. In a CDS, the loss given default is calculated as one minus the recovery rate. This figure is crucial in determining the size of the protection leg payout, as a higher recovery rate reduces the loss in the event of default and, therefore, the value of the protection leg.
Valuation of CDS Premium and Protection Legs
Valuing a CDS involves comparing the present value of the premium leg (the series of regular payments) to that of the protection leg (the expected loss payment in the event of default). The premium leg is discounted using the risk-free rate and adjusted for survival probabilities up to each payment date, while the protection leg is determined by the probability of default, the loss given default, and the timing of the default events. The CDS spread is set so that these two present values are equal at inception.
Payment Frequency and Default Timing
CDS contracts specify the frequency of premium payments, which in this context is annual. However, defaults may occur between these payment dates (for example, halfway through the year). Timing assumptions, such as the mid-period default assumption, are used to estimate accrued premium payments up to default. This timing is important for accurately computing the expected cash flows and discounting them to present value.
Credit Spread
The credit spread, or CDS spread, is the periodic payment made by the protection buyer that compensates the protection seller for taking on the credit risk of the reference entity. It is calculated by balancing the present value of expected premium payments against the present value of expected losses from defaults. The credit spread encapsulates the market’s assessment of the credit risk, including the default probability, recovery rate, and the timing of cash flows under the risk-free interest rate assumptions.