$($Note that sub$-$questions $($a$)$ to $($c$)$ were asked in assignment #$2.$ You can either use the

solution from assignment #$2$ directly or re$-$do the calculation for completeness.$)$ The

current on$-$the$-$run yields for the Ramsey Corporation are as follows:

Assume that each bond is an annual$-$pay bond and trading at par. Answer the questions

below.

a$.$ Using the bootstrapping methodology, complete the following table:

b$.$ Using the spot rates, what would be the value of a three$-$year $3\mathrm{.}5\%$ coupon option$-$

free bond of this issuer?

c$.$ Using the one$-$year forward rates, what would be the value of a three$-$year $3\mathrm{.}5\%$

coupon option$-$free bond of this issuer?

d$.$ Using the same binomial interest rate model as describe in the lecture note. $($That is$,$

at date $t,$ if the interest rate at the lowest node is $r_t,$ then the interest rate one node

above is $r_t{e}^2,$ two nodes above is $r_t{e}^4,$dots, where $$ is the assumed standard

deviation of one$-$year interest rate.$)$ If $$ is assumed to be $10\%,$ what is the lower

one$-$year spot rate one year from now? What is the one$-$year spot rate two years

from now? Draw the complete binomial interest rate tree.

e$.$ Determine the value of a three$-$year $3\mathrm{.}5\%$ coupon option$-$free bond for this issuer using

the binomial interest$-$rate tree.

f$.$ Determine the value of a three$-$year $3\mathrm{.}5\%$ coupon bond that is callable at par $(100)$

after one year.

g$.$ Determine the value of a three$-$year $3\mathrm{.}5\%$ coupon bond that is puttable at par $(100)$

after one year.. $1.($Note that sub$-$questions $($a$)$ to $($c$)$ were asked in assignment #$2.$ You can either use the

solution from assignment #$2$ directly or re$-$do the calculation for completeness.$)$ The current on$-$the$-$run yields for the Ramsey Corporation are as follows:

Maturity $($years$)$Yield to Maturity $(\%)$Market Value

$12\mathrm{.}5100$

$2$

$2\mathrm{.}6100$

$3$

$2\mathrm{.}7100$

Assume that each bond is an annual$-$pay bond and trading at par. Answer the questions below.

a$.$ Using the bootstrapping methodology, complete the following table:

Year Spot Rate $(\%)$One$-$Year Forward Rate $(\%)123$

b$.$ Using the spot rates, what would be the value of a three$-$year $3\mathrm{.}5\%$ coupon option$-$

free bond of this issuer?

c$.$ Using the one$-$year forward rates, what would be the value of a three$-$year $3\mathrm{.}5\%$

coupon option$-$free bond of this issuer?

d$.$ Using the same binomial interest rate model as describe in the lecture note. $($That is$,$

at date t$,$ if the interest rate at the lowest node is rr$,$ then the interest rate one node above is rte$20,$ two nodes above is rte$4$o$,...,$ where a is the assumed standard deviation of one$-$year interest rate.$)$ lf a is assumed to be $10\%,$ what is the lower one$-$year spot rate one year from now? What is the one$-$year spot rate two years from now? Draw the complete binomial interest rate tree.

e$.$ Determine the value of a three$-$year $3\mathrm{.}5\%$ coupon option$-$free bond for this issuer using

the binomial interest$-$rate tree.

f$.$ Determine the value of a three$-$year $3\mathrm{.}5\%$ coupon bond that is callable at par $(100)$

after one year.

g$.$ Determine the value of a three$-$year $3\mathrm{.}5\%$ coupon bond that is puttable at par $(100)$

after one year..

Assignment $5$ Page $1$