Question $1$

Background: please start by building an n$=$n$=10-$period binomial model for the short$-$rate, ri$,$jri,j$.$ The lattice parameters are: r$0,0=5\%$r$0,0=5\%,$ u$=1\mathrm{.}1$u$=1\mathrm{.}1,$ d$=0\mathrm{.}9$d$=0\mathrm{.}9$ and q$=1$q$=1/2$q$=1$q$=1/2.$

Compute the price of a zero$-$coupon bond $($ZCB$)$ that matures at time t$=10$t$=10$ and that has face value $100.$

Submission Guideline: Give your answer rounded to $2$ decimal places. For example, if you compute the answer to be $73\mathrm{.}2367\%,$ submit $73\mathrm{.}24.$

$2.$ Background: Please use the same binomial model as the previous question.

Compute the price of a forward contract on the same ZCB of the previous question where the forward contract matures at time t$=4$t$=4.$

Submission Guideline: Give your answer rounded to $2$ decimal places. For example, if you compute the answer to be $73\mathrm{.}2367\%,$ submit $73\mathrm{.}24.$

$3.$

Question $3$

Background: Please use the same binomial model as the previous question.

Compute the initial price of a futures contract on the same ZCB of the previous two questions. The futures contract has an expiration of t$=4$t$=4.$

Submission Guideline: Give your answer rounded to $2$ decimal places. For example, if you compute the answer to be $73\mathrm{.}2367\%,$ submit $73\mathrm{.}24.$

$4.$

Question $4$

Background: Please use the same binomial model as the previous question.

Compute the price of an American call option on the same ZCB of the previous three questions. The option has expiration t$=6$t$=6$ and strike $=80=80.$

Submission Guideline: Give your answer rounded to $2$ decimal places. For example, if you compute the answer to be $73\mathrm{.}2367\%,$ submit $73\mathrm{.}24.$