$(15\%$; $3\%$ for each subquestion$)$ Bank SF has non$-$dividend$-$paying equity $($Et: equity value at time $t)$ and

deposit Bt $($i$.$e$.,$ SF$\text{'}$s debt value at time t; promised payment at time T is $$400$ million including all interest

payments paid at time T$).A_t$ is the asset value of the bank at time $t.$ The bank has $11$ million shares

outstanding in the stock market, and the stock price is $$\frac{7}{?}$ share. $A_0=$$$460$ million, the risk$-$free rate $r_c=$

$2\%($continuous time$),$ and $T=2$ years.

$($a$)$ Find the $($implied$)$ asset volatility $(\%).$

$($b$)$ What is the current value of risk$-$free debt $($deposit$)?$

$($c$)$ Calculate the current deposit$-$to$-$asset ratio $d=(B\frac{e^{-TT}}{A_0}).$

$($d$)$ FDIC provides deposit insurance $($a put option$)$ for bank SF$.$ Calculate the current value of deposit

insurance.

$($e$)$ Find the implied probability of default, which is calculated as $N(-D{D}_0).$ Also, $=$ the expected

continuously compounded return on asset value $=4\%.$

$D{D}_0=\frac{ln(\frac{A_0}{B})+(-\frac{{}_A^2}{2})T}{{}_A\sqrt[\phantom{2}]{T}}$