A power call option pays off $(max(S_{TT}-x,0){)}^2$ at time $T,$ where $S_{TT}$ is the stock price at time $T$ and $x$ is the exercise price. A stock price is

currently $$54.$ It is known that at the end of one year it will be either $$60$ or $$50.$ The risk$-$free rate of interest with continuous

compounding is $6\%$ per annum. Calculate the value of a one year power call option with an exercise price of $$55.$

a$.$ What is the delta of the power call option?Blank $1($sample answer: $1\mathrm{.}55$ or $0\mathrm{.}55)$

b$.$ What is the risk neutral probability of up movement?Blank $2($sample answer: $55\mathrm{.}50\%)$

c$.$ What is the value of the power option?Blank $3($sample answer: $15\mathrm{.}50)$

E

B

BI$,$