Valuing an Existing CDS Contract

The current value, or mark-to-market, of an existing CDS contract is the amount of money the contract holder would receive (if positive) or pay (if negative) to unwind this contract. The upfront of the contract is the current value expressed as a fraction of the notional amount of the contract, and it is commonly used to quote market values.

The value of existing CDS contracts is obtained with `cdsprice`. By default, `cdsprice` treats contracts as long positions. Whether a contract position is long or short is determined from a protection standpoint, that is, long means that protection was bought, and short means protection was sold. In the following example, an existing CDS contract pays a premium that is lower than current market conditions. The price is positive, as expected, since it would be more costly to buy the same type of protection today.

```Settle = '17-Jul-2009'; % valuation date for the CDS MarketDates = datenum({'20-Sep-10','20-Sep-11','20-Sep-12','20-Sep-14',... '20-Sep-16'}); MarketSpreads = [140 175 210 265 310]'; MarketData = [MarketDates MarketSpreads]; ZeroDates = datenum({'17-Jan-10','17-Jul-10','17-Jul-11','17-Jul-12',... '17-Jul-13','17-Jul-14'}); ZeroRates = [1.35 1.43 1.9 2.47 2.936 3.311]'/100; ZeroData = [ZeroDates ZeroRates]; [ProbData,HazData] = cdsbootstrap(ZeroData,MarketData,Settle); Maturity2 = '20-Sep-2012'; Spread2 = 196; [Price,AccPrem,PaymentDates,PaymentTimes,PaymentCF] = cdsprice(ZeroData,... ProbData,Settle,Maturity2,Spread2); fprintf('Dirty Price: %8.2f\n',Price+AccPrem); fprintf('Accrued Premium: %8.2f\n',AccPrem); fprintf('Clean Price: %8.2f\n',Price); fprintf('\nPayment Schedule:\n\n'); fprintf('Date \t\t Time Frac \t Amount\n'); for k = 1:length(PaymentDates) fprintf('%s \t %5.4f \t %8.2f\n',datestr(PaymentDates(k)),... PaymentTimes(k),PaymentCF(k)); end```

This resulting payment schedule is:

```Dirty Price: 56872.94 Accrued Premium: 15244.44 Clean Price: 41628.50 Payment Schedule: Date Time Frac Amount 20-Sep-2009 0.1806 35388.89 20-Dec-2009 0.2528 49544.44 20-Mar-2010 0.2500 49000.00 20-Jun-2010 0.2556 50088.89 20-Sep-2010 0.2556 50088.89 20-Dec-2010 0.2528 49544.44 20-Mar-2011 0.2500 49000.00 20-Jun-2011 0.2556 50088.89 20-Sep-2011 0.2556 50088.89 20-Dec-2011 0.2528 49544.44 20-Mar-2012 0.2528 49544.44 20-Jun-2012 0.2556 50088.89 20-Sep-2012 0.2556 50088.89 ```

Also, you can use `cdsprice` to value a portfolio of CDS contracts. In the following example, a simple hedged position with two vanilla CDS contracts, one long, one short, with slightly different spreads is priced in a single call and the value of the portfolio is the sum of the returned prices:

```[Price2,AccPrem2] = cdsprice(ZeroData,ProbData,Settle,... repmat(datenum(Maturity2),2,1),[Spread2;Spread2+3],... 'Notional',[1e7; -1e7]); fprintf('Contract \t Dirty Price \t Acc Premium \t Clean Price\n'); fprintf(' Long \t \$ %9.2f \t \$ %9.2f \t \$ %9.2f \t\n',... Price2(1)+AccPrem2(1), AccPrem2(1), Price2(1)); fprintf(' Short \t \$ %8.2f \t \$ %8.2f \t \$ %8.2f \t\n',... Price2(2)+AccPrem2(2), AccPrem2(2), Price2(2)); fprintf('Mark-to-market of hedged position: \$ %8.2f\n',sum(Price2)+sum(AccPrem2));```

This resulting value of the portfolio is:

```Contract Dirty Price Acc Premium Clean Price Long \$ 56872.94 \$ 15244.44 \$ 41628.50 Short \$ -48185.88 \$ -15477.78 \$ -32708.11 Mark-to-market of hedged position: \$ 8687.06```