At time 0.5, the price of $1 par of a zero maturing at time 1 will be either $0.96 or $0.98. The current price of the zero maturing at time 1 is $0.94 and the current price of the zero maturing at time 0.5 is $0.97. Consider also a claim that pays off $1 at time 0.5 if the zero maturing at time 1 is worth $0.96, and 0 otherwise. This information is summarized in the payoff diagrams below.
Determine a portfolio of the 0.5- and 1-year zeroes that has the same payoff as the claim at time 0.5.What is the value of the claim today in the absence of arbitrage? What are the risk-neutral probabilities of the two possible time 0.5 values of the zero maturing at time 1?