Arbitrages and Arrow-Debreu Prices

The goal of this work is to check that there are no arbitrage opportunities in the CBOE market for S&P500 options and to extract from their quotes the state-price density consistent with the Merton model. The structure of the article is as follows: in Section 1 we examine the relations between arbitrages and Arrow-Debreu prices; in Section 2 we consider two models which seem to be consistent with the market prices of index options: the CEV model and the Merton model; finally, in Section 3 we estimate the state-price density consistent with the Merton model. Some conclusions follow.