Consider now that party A wishes to get covered from a potential loss of the face value Va of an asset in case of a credit event.

Party A decides to purchase today $($to $=0)$ some protection from party B that lasts until some specified maturity date T$.$ To pay for this protection, party A makes a regular stream of payments to party B$.$ The size of these payments is a fixed percentage of the face value of the asset being insured and it is based on the yearly contractual spread w$1$y$,$ which represents the percentage used to determine the payments' amount over one year. The payments are made every $3$ months until maturity of the contract or until a credit event occurs, whichever occurs first. Assume that the credit event occurs as the first event of a Poisson counting process$^2$ and hence default time is exponentially distributed with parameter $\backslash$lambda $.$ Denote the short rate with r$.$

The aim is to value the premium leg, i$.$e$.$ to write a mathematical expression for this stream of payments taking into account both the appropriate discounting and the probabilities of default events.

Face Value$=$Va $=35000$ pounds

Time $=$T $($months$)=30$

Wty$=0\mathrm{.}0165$

$\backslash$lambda $=0\mathrm{.}02820$

r$=\mathrm{.}0332$

Using the values provided for your chosen pack, calculate the premium leg and price the CDS$-$Credit Default swap on a spreadsheet with calculations