A certain underlying state graph is a tree where each node has three successor nodes, indexed \(a,b, c\). There are two assets defined on this tree which pay no dividends except at the terminal time \(T\). At a certain period it is known that the prices of the two assets are multiplied by factors, depending on the successor node. These factors are shown in Table 19.2.

(a) Is there a short-term riskless asset for this period?

(b) Is it possible to construct an arbitrage?

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TABLE 19.2 a b C Security 1 1.2 1.0 0.8 2 1.2 1.3 1.4