= Solution
{c}
The <exchange option> has terminal payoffs determined by the two successive up/down moves:
$$
\begin{array}{c|c|c|c}
\text{path}&S_1(2)&S_2(2)&(S_1(2)-S_2(2))^+\\ \hline
uu&196&144&52\\
ud,\ du&112&108&4\\
dd&64&81&0
\end{array}
$$
The two stocks span both one-step states, so this finite market is complete. The <risk-neutral pricing> uses the independent transition probabilities $q=1/3$ and $1-q=2/3$. Since the synthetic risk-free rate is zero,
$$
V_0=\frac19\,52+2\left(\frac13\frac23\right)4+\frac49\,0
=\boxed{\frac{68}{9}}.
$$
The price is approximately 7.56 in the currency units of the stock prices.
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