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

With the rate $r=0$, the risk-neutral probability in a binomial market must satisfyThe first stock gives $0.8+0.6q=1$, hence $q=1/3$. The second gives $0.9+0.3q=1$, confirming the same answer. ThusTake the successive up/down choices independent under this measure, so both stock prices are martingales. The martingale transition condition applies from times zero to one and one to two; the displayed $t+1$ condition in the source should be read for these two transitions.