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
2.1. The A MIBO30 B market The empirical tests of this work are based on data on index options, MIBO30,
recently introduced in the IDEM. The index option contracts traded on IDEM are based on the MIB30 index, which has been proven to be a reliable indicator of the
Italian market. The MIB30 index is a capitalisation-weighted index that comprises the 30 most liquid and highly capitalised shares traded on the Italian market. The
shares in the index account for over 72 of total market capitalisation, and almost
Ž .
75 of trading volume. Its correlation with the Italian general index MIB is above 0.99. The contract size is set at 10 000 ITL for each point of the index.
MIB30 options are European style, which means they can only be exercised at expiration. The options have cash settlement.
At any given time there are options available for at least five expiration dates: Ž
the three nearest expirations dates of the quarterly cycle March, June, September .
and December , which correspond to the expiration dates of the future contract, Ž
and the two nearest monthly expirations a monthly expiration corresponds to one .
of the quarterly expirations . The expiration day is the third Friday of the expiration months. Five exercise prices are available for each contract month.
They are settled in fixed increments of 500 index points, i.e. 14 500, 15 000, 15 500. Trades are matched in real-time by the electronic trading system and
guaranteed by the Cassa di Compensazione e Garanzia, the clearing house for the Italian market.
2.2. Data and methodological issues In this section we describe and motivate some methodological issues used in
the analysis. The empirical tests were carried out only on options with a maturity of 1 month. The main reason of this choice is that the market is still very young
and the thinness of trading makes prices on other expirations not representative. Ž
. The risk-free rate was estimated by the European interbank offered rate Euribor
published daily by the Sole 24 ore.
3
This is the same interest rate used by the Ž
. CONSOB the Italian Securities and Exchange Commission to vigil the daily
behaviour of option prices and the behaviour of market makers in setting the bid and ask quotations. It is then likely that market makers refer to this interest rate in
order to verify whether their quotations are consistent with the theoretical value of the option. The value of the Euribor published in the Sole 24 ore is the ask rate;
Ž .
the bid interest rates can be obtained subtracting 1r8 0.125 from the ask rates. We eliminated options with fewer than seven calendar days to expiration. Most
dividend payments of the stocks included in the index are concentrated in the months of May and June. However, since dividend payments occur after the
expiration day of the option, they do not affect the options with 1-month maturity used for the empirical tests.
When, as in our case, the underlying security is not a single option but an index, arbitrageurs face two alternatives: replicate a portfolio representative of the
Ž .
securities included in the index, or use the futures on the index Fib30 . We decided to use the first alternative and to replicate the index. Although this choice
may appear more costly, it must be noticed that using the future the trader would incur the Abasis risk,B when the expiration of the future does not correspond to
that of the option. Moreover, the MIB30 index includes only 30 securities and is not very difficult to replicate. The high movements observed in the prices of the
securities included in the index in proximity to the maturity of the options support the assumption that replicating the index is a common practice among traders.
Another issue accounted for in the analysis is the cost of short selling the index. If the arbitrage involves a short hedge in the index, the arbitrageur should assume a
further cost represented by the cost of securities lending. The market for securities lending in Italy is an Over the Counter Market. The characteristics of the contracts
are not standardised and can be designed to best satisfy the necessities of the
4
Ž .
arbitrageur. Because data on the securities lending market interest rates repo are
3
To match the interest rate to the period of expiry of the options, we used a Relevant Interest Rate obtained by linear interpolation of interest rates for different time horizons.
4
A securities lending contract consists in a double lending: the lender give the borrower the securitiesw, and the borrower deposit the proceeds of the short selling to the leader as a gaurantee. The
lender must pay on the deposit an interest rate that is generally lower than the market risk-free rate, because of the opportunity cost for renouncing availability of the securities. The cost of securities
lending is respesented by the differrence between the market risk free rate received on the deposit.
Ž .
not available for it is an OTC market , for the empirical tests we used as a proxy the AbidB interest rate. We also account for costs due to the cash settlement
procedure, which distinguish index option from stock and commodities option. The only relevant difference in the results is that the trader has to pay the
additional commission cost to close on the market at maturity the position open on the underlying asset.
3. Put–call parity and transaction costs
