Let T $>0,$ K $>0,$ and $\backslash$alpha in $(0,1)$ be given and let S be a stock. Consider

a $($European$-$style$)$ derivative security V that pays its holder the amount

VT $=$ max$\{\backslash$alpha ST $,$ ST $$ K$\}$

at time T $.$ Determine constants $\backslash$beta $,\backslash$gamma $,$ and $$K such that the arbitrage$-$free price V$0$ of this

security is given by

V$0=\backslash$beta S$0+\backslash$gamma $$C$0,$

where $$C is a European call option on S with expiration T and strike price $$K$.($The

constants that you find may depend on $\backslash$alpha and K$.)$