There is a market for bets on the outcome of a coin toss. The possible outcomes are
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There is a market for bets on the outcome of a coin toss. The possible outcomes are heads, tails, and edge. There are three assets traded in that market:
Asset A pays \(\$ 1\) independent of the outcome.
Asset B pays \(\$ 1.50\) for a head and \(\$ 0\) for tails and \(\$ 1\) if the coin lands on its edge.
Asset \(C\) pays \(\$ 10\) if and only if the coin lands on its edge (and \(\$ 0\) otherwise).
The prices of those assets are always constant and are fixed at \$1. We assume that the payments to the winning bidders take place immediately after the outcome is determined.
(a) What is the implied risk-free interest rate in this market?
(b) What are the risk-neutral probabilities of each of the possible coin toss outcomes (heads, tails, edge)?
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