Past exam of the mathematics course of the University of Cambridge / 2006 / ii / Paper 1 / 28I / Solution

The diagram has common multipliers $u=5/3,d=2/3$ on every branch, with gross riskless return $R=4/3$. The martingale condition $pu+(1-p)d=R$ givesSince $d<R<u$, these probabilities lie strictly between zero and one at each node, and the market is arbitrage-free. All valuations below use discounted conditional expectations under this measure.