Question $4$

The US$-$based XYZ Bank has a foreign asset which is worth $20$ million. The current spot

exchange rate is $$\frac{1\mathrm{.}10}{}.$ XYZ bank wants to hedge the Foreign Exchange risk of this

asset over the next month using option. It buys a $1-$month vanilla European put option

whose underlying is the spot exchange rate $\frac{\text{\$}}{},$ with the strike price $$\frac{1\mathrm{.}10}{}$ and the size

of the option $20$ million. The premium of this put option is $$10,000.$

$($a$)(10$ marks$)$ What is the gain or loss of XYZ bank from this hedged position

$($foreign asset and option$)$ if the exchange rate becomes $$\frac{1\mathrm{.}11}{}$ after one month?

What is the gain or loss if the exchange rate becomes $$\frac{1\mathrm{.}09}{}$ after one month?

$($b$)(10$ marks$)$ If the exchange rate after one month is a random variable $$\frac{e^x}{},$

where $x$ follows a normal distribution with mean $0\mathrm{.}08$ and variance ${0\mathrm{.}02}^2,$ what is

the $95-$th percentile of the profit from this hedged position? Question $1$Question $2$

A Financial Institution considers a $1-$year loan with the following attributes

The Financial Institution estimates that the borrower of the loan has a $1-$year default

probability of $0\mathrm{.}20\%$; however, if default happens, no value can be recovered from this loan.

$($a$)(5$ marks$)$ What is the gross return per dollar lent of this loan?

$($b$)(5$ marks$)$ What is the expected loss of this loan due to default risk?

Consider a bank whose asset and liability both consist of bonds only. The asset consists of

a $20-$year coupon bond with face value $$120$ million, coupon rate $7\mathrm{.}5\%,$ and its coupons

are paid once per year. The liability consists of a $6-$year zero coupon bond with face value

$$190$ million. The current yield for all these bonds are $6\mathrm{.}5\%.$

$($a$)(5$ marks$)$ What is the bank's current market value of equity $($expressed in million

dollars$)?$

$($b$)(5$ marks$)$ What is the bank's current leverage$-$adjusted modified duration gap?

$($c$)(5$ marks$)$ Assume parallel yield shift. Based on the prediction from the duration

model, how much would the market value of equity change $($expressed in million

dollars$),$ for a $10$ basis points increase in the yield?

$($d$)(5$ marks$)$ Assume parallel yield shift. Based on the prediction from the duration

model, what is the range of the yield change $($expressed in basis points$)$ for which

the market value of equity would become negative?