Under the assumption of absence of
arbitrage, European option quotes on a given
asset must satisfy well-known inequalities, which have been described in the landmark paper of Merton [Merton, R., 1973. Theory of rational option pricing. Bell Journal of Economics and Management Science 4 (1), 141–183]. If we further assume that there is no interest rate volatility and that the underlying
asset continuously pays deterministic dividends, cross-maturity inequalities must also be satisfied by the bid and ask option
prices.
In this paper, we show that there exists an arbitrage-free model, which is consistent with the option quotes, if these inequalities are satisfied. One implication is that all static arbitrage strategies are linear combinations, with positive weights, of those described here. We also characterize admissible default probabilities for models which are consistent with given option quotes.