Past exam of the mathematics course of the University of Cambridge / 2005 / ii / Paper 3 / 27J / d

If the first move is bad but the buyer misses exercise, the remaining European claim is worth $2/3$, whereas the existing hedge is worth three. At that node rehedge the continuation claim: its stock holding is $(0-5)/(16-10)=-5/6$ and its bank holding is $2/3+(5/6)12=32/3$.

Starting from the original short $1/6$ and bank balance five, short another $2/3$ share for eight, giving bank cash thirteen. Retain $32/3$ for the new hedge and withdraw $\boxed{7/3}$ as guaranteed time-one profit. At time two the retained bank grows to $40/3$. If price is sixteen, covering the short costs $40/3$ and the put expires worthless. If price is ten, covering costs $25/3$ and the remaining five pays the put. Thus the profit does not depend on the second move. Investing the withdrawn profit at the riskless rate makes it $35/12$ at time two.