Past exam of the martingales and financial mathematics course of the University of Oxford / 2009 / B / 6 / b / Solution

For holdings $h_1,h_2$, a sure payment of 100 requiresSubtracting gives $2h_1+h_2=0$, so $h_1=-1$ and $h_2=2$. Thus sell one share of stock 1 and buy two shares of stock 2. Its initial cost is $100(-1+2)=100$.

This synthetic zero-coupon bond pays exactly its initial cost after one period, and thereforeAt later nodes the holdings can be rescaled to generate the same one-period risk-free return; a physical bond need not be listed separately.