Time left $0$:$13$:$17$Question $1$Not yet savedMarked out of $1\mathrm{.}00$ Flag questionQuestion textA bank estimates that its profit next year is normally distributed with a mean of $0\mathrm{.}9\%$ of assets and the standard deviation of $3\%$ of assets. How much equity $($as a percentage of assets$)$ does the company need to be $99\mathrm{.}9\%$ sure that it will have positive equity at the end of the year? Ignore taxes.Question $1$ Answera$\mathrm{.}3\mathrm{.}09$b$\mathrm{.}9\mathrm{.}27$c$\mathrm{.}8\mathrm{.}37$d$\mathrm{.}2\mathrm{.}19$Question $2$Not yet savedMarked out of $1\mathrm{.}00$ Flag questionQuestion textUsing risk$-$neutral valuation, the price of an option is $$20.$ If investors are risk$-$averse, the market price of the option will beQuestion $2$ Answera.Greater than $20$b$\mathrm{.}20$c$.$Less than $20$Question $3$Not yet savedMarked out of $1\mathrm{.}00$ Flag questionQuestion textSuppose that GARCH $(1,1)$ parameters have been estimated as $=0\mathrm{.}000002,=0\mathrm{.}04,$ and $=0\mathrm{.}94.$ The current daily volatility is estimated to be $3\mathrm{.}5\%.$ Estimate the volatility per annum that should be used to price a $60-$day option.Question $3$ Answera$\mathrm{.}18\mathrm{.}9\%$b$\mathrm{.}33\mathrm{.}1\%$c$\mathrm{.}50\mathrm{.}8\%$d$\mathrm{.}43\mathrm{.}5\%$Question $4$Not yet savedMarked out of $1\mathrm{.}00$ Flag questionQuestion textA six$-$year bond with a continuously compounded yield of $6\%$ provides a $5\%$ coupon at the end of each year. Use duration and convexity to estimate the effect of a $1\%$ increase in the yield on the price of the bond.Question $4$ Answera.Price will increase by $5\mathrm{.}16\%$b$.$Price will decrease by $5\mathrm{.}16\%$c$.$Price will decrease by $5\mathrm{.}3\%$d$.$Price will increase by $5\mathrm{.}3\%$Question $5$Not yet savedMarked out of $1\mathrm{.}00$ Flag questionQuestion textThe parameters of a GARCH $(1,1)$ model are estimated as $=0\mathrm{.}000004,=0\mathrm{.}05,$ and $=0\mathrm{.}92.$ If the current volatility is $20\%$ per year, what is the expected volatility per year in $20$ days?Question $5$ Answera$\mathrm{.}14\mathrm{.}7\%$b$\mathrm{.}1\mathrm{.}2\%$c$\mathrm{.}19\mathrm{.}3\%$d$\mathrm{.}3\mathrm{.}7\%$Question $6$Not yet savedMarked out of $1\mathrm{.}00$ Flag questionQuestion textA stock price has an expected return of $9\%$ and a volatility of $25\%.$ It is currently $$40.$ What is the price of a binary option that pays $$100$ if the stock price in $6$ month is higher than $$50?$ Assume the risk$-$free rate is zero.Question $6$ Answera$\mathrm{.}86\mathrm{.}35$b$\mathrm{.}8\mathrm{.}84$c$\mathrm{.}15\mathrm{.}44$d$\mathrm{.}13\mathrm{.}65$