Assignment $5(10$ points$)$

Suppose a four$-$year corporate bond provides a coupon of $4\mathrm{.}5\%$ per year payable annually

at the end of the year and has a yield of $5\%.$ The yield for all maturities on risk$-$free bonds

is $3\mathrm{.}9\%$ per annum.

Assume that defaults can take place every year immediately before a coupon payment and

the recovery rate is $xx\%$ of the principal.

$5\mathrm{.}1.$ Make your estimation of $xx\%$ as the recovery rate, between $20\%$ and $90\%.$

$5\mathrm{.}2.$ Estimate the default probability of the bond assuming a$)$ the unconditional default

probabilities are the same on each possible default date and b$)$ assuming that the default

probabilities conditional on no earlier default are the same on each possible default date.

Assignment $6(5$ points$)$

Suppose that the price of Asset X at close of trading yesterday was $100$ and its volatility

was estimated as X$.$X$\%$ per day. The price of X at the close of trading today is $96.$

Suppose further that the price of Asset Y at the close of trading yesterday was $14,$ its

volatility was estimated as Y$.$Y$\%$ per day, and its correlation with X was estimated as o$\mathrm{.}8.$

The price of $Y$ at the close of trading today is unchanged at $14.$

$6\mathrm{.}1.$ Choose your own estimates for the different volatilities X$.$X$\%$ and Y$.$Y$\%$ between

$1\mathrm{.}00\%$ and $5\mathrm{.}00\%.$

$6\mathrm{.}2.$ Update the volatility of X and Y and the correlation between X and Y using

$6\mathrm{.}2\mathrm{.}1.$ The EWMA model with $1=0\mathrm{.}95$

$6\mathrm{.}2\mathrm{.}2.$ The GARCH$(1,1)$ model with $w=0\mathrm{.}000002,a=0\mathrm{.}03,$ and $b=0\mathrm{.}95$

Assignment $7(5$ points$)$

A bank rated AA estimates its losses on loans as $1\mathrm{.}30\%$ of the outstanding principal in

average. The economic capital required is $8\%$ of the outstanding principal. The spread

between the cost of funds and the interest charged is $1\mathrm{.}80\%.$ Lending administrative costs

total $0\mathrm{.}60\%$ of the amount loaned.

Suppose that the bank's sole business is to lend in two regions of the world. Lending to

Region $A$ is $3$ times as great as lending to Region $B.$ The correlation between loan losses in

the two regions is $0\mathrm{.}4.$

Estimate the total RAROC.