An S&L has the following characteristics

Assets $($$M$)450$

Duration Assets $5\mathrm{.}5$

Liabilities $($$M$)325$

Duration Liabilities $4$

Yields on Assets & Liabilities $(\%)4\mathrm{.}50\%$

Option d Premiums $($$ per $$100$ of face amount$)$

Call $0\mathrm{.}30\mathrm{.}25$

Put $-0\mathrm{.}50\mathrm{.}35$

Underlying Instrument on Options US Treasury

Price $($$ per $$100$ of face amount$)95$

Duration $6$

Yield to maturity $4\mathrm{.}50\%$

a$.$ Which type of option should be used to immunize the S&L$?$

b$.$ How many options should be used?

c$.$ What happens to economic value of equity if rates rise $75$bps$?$

d$.$ What happens to the options hedge if rates rise $75$bps$?$

e$.$ What is the cost of the options hedge?

f$.$ How much do interest rates need to move against the hedge position

for the increase in economic value of equity to offset the hedge costs?