HighTop, a bakery chain which bakes and distributes bread to the Sydney market, is concerned about the impact of the war in the Ukraine on its manufacturing costs. HighTop is worried that the price of wheat could rise sharply. As a result of its concerns, HighTop is considering entering into a European call option contract with a strike price of $$420$ per metric tonne.

HighTop$$s financial modelling team have studied wheat prices and have come to the conclusion that over the next three months the price of wheat could rise by a third if the war in the Ukraine continues $($occurring with probability p $=0\mathrm{.}95)$ or fall by $25\%(=11/1\mathrm{.}333,$ occuring with probability $1$ p $=0\mathrm{.}05)$ if the war ends. The current price per metric tonne of wheat is $$400.$ HighTop can borrow money today for any period under six months atarateofj$12=4\%$p$.$a$.$ a$)$ Consider the replicating portfolio $($that is$,$ the investment strategy which will give identical payoffs, at the end of three months, to the call option contract$)$ that involves buying h metric tonnes of wheat today, and borrowing $B for three months. Find the value of B $($round your answer to five decimal places$).$

a$.140\mathrm{.}10989$ b$.143\mathrm{.}78751$ c$.144\mathrm{.}26680$ d$.144\mathrm{.}27157$

e$.$ None of the above b$)$ What is the initial cost $($net outlay$)$ today of investing in the replicating

portfolio? a$.$ $$50\mathrm{.}01891$

b$.$ $$50\mathrm{.}01414$

c$.$ $$50\mathrm{.}49820$

d$.$ $$54\mathrm{.}17582$

e$.$ None of the above