One way to extend the binomial pricing model is by including multiple time periods. Suppose Splittime, Inc., is currently trading for

per share. In one month, the price will either increase by

$($ to

$)$ or decrease by

$($to

$).$ The following month will be the same. The price will either increase by

or decrease by

$.$ The risk$-$free rate is $1$ percent per month. Find the value today of an option to buy one share of Splittime in two months for a strike price of

$.($Hint: To do this, first find the value of the option at each of the two possible one$-$month prices. Then use those values as the payoffs at one month and find the value today.$)$

One way to extend the binomial pricing model is by including multiple time periods. Suppose Splittime, Inc., is currently trading for

per share. In one month, the price will either increase by

$($ to

$)$ or decrease by

$($to

$).$ The following month will be the same. The price will either increase by

or decrease by

$.$ The risk$-$free rate is $1$ percent per month. Find the value today of an option to buy one share of Splittime in two months for a strike price of

$.($Hint: To do this, first find the value of the option at each of the two possible one$-$month prices. Then use those values as the payoffs at one month and find the value today.$)$