Question $13$

$($a$)$ What does the acronym CVA stand for and what are its regulatory implications?

$[3$ marks$]$

$($b$)$ You have obtained the following default probabilities for a Standard and Poors

B$-$rated company, Risky Corp.:

$($i$.)$ Find the CDS spread, $s,$ per dollar of notional. To facilitate computation,

you can assume that payments are made annually in arrears and defaults

occur at year end $($no accrual calculations$),$ and the expected recovery rate

is $40\%.$

$[7$ marks$]$

$($ii$.)$ You are offered a market quote on this CDS at $400$ basis points. Is there

an arbitrage opportunity for you? How would you trade this? $[3$ marks$]$

$($iii$.)$ An investment bank is long $$10$ million of corporate bonds in Risky Corp.,

estimate the CVA assuming that the bonds reach maturity in one year.

$[3$ marks$]$

$($c$)$ A stock price is currently at $$167\mathrm{.}50$ and the quotes in the following table are

available for one month options on the stock:

$($i$)$ Construct an option portfolio to profit from a low volatility forecast for the

stock, plot the resulting payoff and report the portfolio cost. If the stock

price in one month is $$167\mathrm{.}60$ what is the profit on your trade? $[6$ marks$]$

$($ii$)$ If each option contract covers $100$ shares how many shares would you

need to purchase$/$sell to delta hedge the portfolio in $($i$)?$

$[3$ marks$]$

$[$Total Marks: $25]$