Problem $10.$ Please start by building an $n=6-$period binomial model for the short$-$rate, $r_{i,j}.$ The

lattice parameters are: $r_{0,0}=5\%,u=1\mathrm{.}1,d=0\mathrm{.}9$ and $q=1-q=\frac{1}{2}.$

Compute the price of a zero$-$coupon bond $($ZCB$)$ that matures at time $t=6$ and that has face

value $100.$ Give your answer rounded to $2$ decimal places.

Compute the price of a forward contract on the same ZCB as in $($a$)$ where the forward contract

matures at time $t=4.$ Give your answer rounded to $2$ decimal places.

Compute the initial price of a futures contract on the same ZCB as in $($a$)-($b$)$ where the futures

contract has an expiration of $t=4.$ Give your answer rounded to $2$ decimal places.

Compute the price of an American call option on the same ZCB as in $($a$)-($c$).$ The option has

expiration at $t=3$ and strike of $80.$

Answer:

Apply the calculation in Slides $15$ of Lecture Note $6$ but modify it to a version of maturity at $t=6.$

Apply the calculation in Slides $24-26$ of Lecture Note $6$ but modify it to a version of zero$-$coupon

bond for the underlying.

Apply the calculation in Slides $29-30$ of Lecture Note $6$ but modify it to a version of zero$-$coupon

bond for the underlying.

Apply the calculation in Slides $21$ of Lecture Note $6$ but modify it to a version of call option.