Question $2$

A JPM investment bank is valuing a $1-$year credit default swap $($CDS$)$ contract that will pay

the buyer $80\%$ of the face value of a bond issued by a corporation immediately after a

default by the corporation. To purchase this CDS$,$ the buyer will pay the CDS spread, which is

a percentage of the face value, once at the end of the year. The analyst estimates that the

risk$-$neutral default probability for the corporation is $7\%$ per year. The risk$-$free rate is $2\mathrm{.}5\%$

per year. Assuming defaults can only occur halfway through the year and that the accrued

premium is paid immediately after a default, answer the following $($Assume $1$$ notional$)$

d$0\mathrm{.}5=$discount factor for half$-$year $=$

$($SIX decimal places$)$

d$1\mathrm{.}0=$discount factor for $1-$year $=$

$($SIX decimal places$)$

PV of payments $($premium leg, which includes the spread payment and accrual$)$ is:

$S($s$=$ spread, SIX decimal places$)$

PV of payoff leg $($in the event of default$)$ is:

$($SIX decimal places$)$

$s,$ the spread $=$

basis points $($nearest whole integer$)$What is the ex$-$coupon price of a $$100$ par of a $1$ year $6\%$ semi annual coupon non callable

bond

at the up node at time $=0\mathrm{.}5($answer to four decimal places$)$

$

What is the ex$-$coupon price of a $$100$ par of a $1$ year $6\%$ semi annual coupon non callable

bond

at the down node at time $=0\mathrm{.}5($answer to four decimal places$)$

$

What is the ex$-$coupon price of a $$100$ par of a $1$ year $6\%$ semi annual coupon non callable

bond

at time $=0($answer to four decimal places$)$

S

What is the time $0$ value of long position in a $1$ year $6\%,$ plain vanilla semi annual pay fixed

receive floating interest rate swap with $100$$ notional par amount. $($answer to four decimal

places$)$

Swap value $=$

$s$