1. Introduction
The Italian option on index MIB30 contract or AMIBO30B introduced in the Ž
. Italian Derivatives Market IDEM on November 1995 represents one of the most
important steps aimed to improve the efficiency and the liquidity of the Italian financial markets. Trading on the IDEM started on November 1994 with the
introduction of the future contract on the same index, the Mib30. The strong success of this contract, which enjoyed a rapid development and is now placed
among the five most traded future contracts in Europe, convinced the Italian Authorities to introduce an option contract on the index, the MIBO30, and later on
Ž
. in February 1996 on single stocks, the ISO a. This paper contains an empirical
analysis directed towards an investigation of whether the MIBO30 option market is efficient.
For the purposes of this study, the market is efficient if it does not present arbitrage opportunities. Since Black and Scholes published their article on option
pricing in 1972, several theoretical and empirical works have been written on option pricing. However, most of these studies have been conducted on the
Chicago Board Option Exchange and very few studies have been undertaken to test the efficiency of other option markets. In particular, the Italian Option market
is quite recent and is scarcely investigated
2
. To analyse the efficiency of the Italian Index Option Market, the Black and
Ž .
Scholes 1971,1972 model is probably the simplest valuation model, and evidence from dealers operating in the market indicates that it is widely used. However,
there are several problems in carrying out empirical research based on the Black–Scholes as on any option pricing models. The first problem is that any
statistical hypothesis about how options are priced has to be a joint hypothesis to
Ž . Ž .
the effect that i the model is valid and ii markets are efficient. To distinguish between the two hypotheses of market efficiency and model validity, one of the
two has to be taken as an assumption. A second problem concerns the choice of the best estimate of stock price volatility. A third problem is to ensure that data on
the stock price and option price are synchronous.
The current study attempts to overcome the above difficulties in three substan- tive ways. First of all, it uses a very high quality data source, which contains not
only transaction prices but also quoted bid and ask prices. Second, in the first part of the work it employs a test of market efficiency, the put–call parity test, which
do not rely for its validity on the restrictive Black–Scholes assumptions. More- over, this test can easily be manipulated and extended to take account of the
2
Ž .
Two previous studies Barone and Cuoco, 1989, 1991 investigated the premium contracts on the Italian stock exchanges. Trades on premium contracts were substituted by trades on options few months
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after the introduction of contracts. For an analysis of the MIBO30 see Cavallo 1998 and Cavallo et al. Ž
. 1999 .
frictions of the market such as transaction costs, so that new conditions are derived and subjected to empirical test. Since the put–call parity is only a weak test of
market efficiency, results obtained are further investigated in the second part of the work, where an ex-post hedging strategy is simulated to verify the possibility to
exploit the mispricing evidenced by comparing actual option prices with Black– Scholes prices. This dynamic hedging strategy, taking into account transaction
costs and relaxing some of the assumptions of the Black–Scholes model, allows verification of the hypothesis that mispricings are due to an inaccuracy of the
model rather than to the inefficiency of the market.
The paper is organised as follows. Section 2 describes the Italian option market and the data set used. In Section 3, the put call parity conditions in the presence of
transaction costs are derived and subjected to empirical test on the Italian market using infra-day synchronous option and index prices. In Section 4, different
measures of volatility are derived and used to simulate a volatility trading strategy, in order to verify the possibility to realise systematic abnormal returns on the
Italian option market. Some concluding remarks are offered in Section 5.
2. Market and data
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