{c}

The <risk-neutral probability> obeys $R=qu+(1-q)d$. Thus
$$
R=\frac23\frac43+\frac13\frac23=\frac{10}{9},
\qquad R^{-1}=\frac9{10}.
$$
Substitution into the <risk-neutral pricing> recursion gives
$$
\boxed{V_t=\frac9{10}\left(\frac23V^u_{t+1}+\frac13V^d_{t+1}\right)
=\frac3{10}\left(2V^u_{t+1}+V^d_{t+1}\right).}
$$

Solution

Past exam of the mathematical models of financial derivatives course of the University of Oxford / 2015 / 1 / c / Solution

 Solution (source code)