Buffelhead's stock price is $$156$ and could halve or double in each six$-$month period $($equivalent to a standard deviation of $98\%).$ A oneyear call option on Buffelhead has an exercise price of $$133.$ The interest rate is $21\%$ a year.

a$.$ What is the value of the Buffelhead call?

Note: Round your answer to $2$ decimal places.

b$-1.$ Now calculate the option delta for the second six months if the stock price rises to $$312.$

b$-2.$ Now calculate the option delta for the second six months if the stock price falls to $$78.$

Note: Round your answer to $2$ decimal places.

$c-1.$ What is the option delta when a call is certain to be exercised?

c$-2.$ What is the option delta when a call is certain not to be exercised?

d$.$ Suppose that in month $6,$ the Buffelhead stock price is $$78.$ To replicate an investment in the stock by a combination of call options and risk$-$free lending, how many calls would you purchase and how much would you lend? For this problem, assume you can purchase partial calls.

Note: Do not round intermediate calculations. Round your answers to $2$ decimal places.

$\backslash$table$[[$a$.$ Value of call,$],[$b$-1.$ Delta,$],[$b$-2.$ Delta,$],[$c$-1.$ Delta,$],[$c$-2.$ Delta,$],[$d$.$ Number of calls,$],[$d$.$ Amount to lend,$]]$