Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 39 / 1 / iv

The European call option pays one in the state $S_1=5$ and zero in the other two states. Short one call, buy one third of a stock, and borrow one half unit of cash. Writing the option quote as $c=1/2$, the holdings and initial value areThe terminal value is $-1/2+S_1/3-(S_1-4{)}^{+}$. At stock prices $5,3,2$ it is respectivelyIt is strictly positive in every state, so this portfolio is an arbitrage.