The internal and cross market efficiency in index option markets: an investigation of the Italian market

Abstract

The aim of the present paper is to provide evidence on the internal efficiency of the Italian index option market and to verify the consistency of the latter notion of efficiency with the cross market one. To this end a model-free approach is taken, whereby strategies involving only options are tested by means of a high frequency dataset. These strategies may provide a superior test of parity among index options since they do not involve the index replication issues and usefully complete previous studies which focused on cross-market efficiency only. The results obtained clearly support the efficiency of the Italian market and comparatively highlight a high level of consistency between internal and cross market efficiency.

Acknowledgements

The authors thank for helpful comments and suggestions an anonymous referee, participants at the 11th Conference on Computing in Economics and Finance (Washington DC, 2005) and at the XXVIII Amases Conference (Modena, 2004). We are also grateful to Borsa Italia S.p.A. for kindly providing the data and to MIUR for financial support. Usual disclaimers apply.

Notes

¹ In line with most of the literature cited in this paper, this is the notion of efficiency adopted here. However, it should be stressed that, even when the no-arbitrage restrictions hold, the market may still be inefficient in other respects: for example, market prices might still deviate from theoretical (e.g. Black and Scholes, 1973) prices.

² Earlier works include Chesney et al . (1995) on the Swiss index option market and Puttonen (1993) on the Finnish index option market.

³ Since 2 June 2003 a new index has been quoted on the Italian Market: the S&P/Mib. This index, whose components are not fixed and that at the time of writing consists of 40 assets, is the new underlying of the Italian index derivatives since September 2004. However, contract specifications have remained practically unchanged (see www.borsaitalia.it).

⁴ By contrast, some authors test the option market efficiency by means of arbitrage trading strategies based on some model-dependent (e.g. GARCH, Black and Scholes (1973) implied volatility) volatility forecast. This approach is motivated by the purpose of comparing different volatility forecast models. See for example Chong (2004) and Corredor and Santamaria (2004).

⁵ In the following, only the negotiation hour is considered as an indicator of the time of the exchange, given that the gap between the negotiation and the clearing hour is less than one second in 99.11% of the cases.

⁶ The filters applied imply that out of the 229 070 original observations the percentages of observations retained are: 12.04% (11.59%) for the call (put) spread, 2.73% (2.67%) for the call (put) butterfly spread and 0.39% for the box spreads. The sensible disparity in the number of observations retained is due to the different number of options involved in the arbitrage relationships: two in the spreads, three in the butterfly spreads and four in the box spreads.

⁷ Even though this period does not correspond with the one under investigation, it can be assumed that the average bid–ask spread of index option prices has not remarkably changed, given that it is taken constant over time.

⁸ As for the length of the execution window, in literature different choices are made: Capelle-Blancard and Chaudhury (2001) take a 15-min window, while Mittnik and Rieken (2000a) take different lengths ranging from one minute to one day.

⁹ In fact, Ackert and Tian (1998, 2001) are mainly aimed to assess whether efficiency of the index option market (Canadian and US respectively) was enhanced by the introduction of traded stock baskets, so they split the analysis on subsamples and, among the internal market pricing relationships, consider only the box spread.

¹⁰ Given the lack of a one-to-one relationship between the Scenarios set up in the French and in the present study, a comparison between Scenario C in this study and other scenarios in Capelle-Blancard and Chaudhury (2001) may in principle be interesting. Such a comparison is omitted for reasons of space and also because conclusions would remain essentially unaltered.