Q. The current 6-month short rate sits at 3% per year. The mean growth rate of the short rate is 3%; the volatility of short rate growth is 25%. ( short rate is insurance premium rate, t=0.5=6 month, t=1=1year) a) What would be the 6-month short rate in the up state at time t=0.5 (units: % per year)? t=0.5 is 6 month. b) What would be the 6-month short rate in the down state at time t=0.5 (units: % per year)? c) Consider a 1-year floater indexed to the short rate with a face value of $100. What is the payout to this floater at time t=0.5 (units: dollars)? d) Consider a 1-year floater indexed to the short rate with a face value of $100. What is the payout to this floater at time t=1.0 if the up state is realized at time t=0.5 (units: dollars)?

e) Consider a 1-year floater indexed to the short rate with a face value of $100. What is the payout to this floater at time t=1.0 if the down state is realized at time t=0.5 (units: dollars)? f) Now consider a capped 1-year floater indexed to the short rate with a face value of $100 and a 3.4% cap rate. What is the payout to this capped floater at time t=0.5 (units: dollars)? g) Now consider a capped 1-year floater indexed to the short rate with a face value of $100 and a 3.4% cap rate. What is the payout to this capped floater at time t=1.0 if the up state is realized at time t=0.5 (units: dollars)? h) Now consider a capped 1-year floater indexed to the short rate with a face value of $100 and a 3.4% cap rate. What is the payout to this capped floater at time t=1.0 if the down state is realized at time t=0.5 (units: dollars)?