On the future contract quality option: a new look

Abstract

This article provides a new method for replicating and pricing the quality options usually embedded in many future contracts. The replicating strategies may draw on both the future contract as well as its related calls and puts. They also yield the quality option theoretical price in perfect markets, as well as upper and lower bounds for its bid or ask prices if frictions are incorporated. With respect to previous literature, this new approach seems to reflect five contributions: First, the analysis does not depend on any dynamic assumption concerning the Term Structure of Interest Rates (TSIR) behaviour; second, it incorporates the information contained in calls and puts on the future contract; third, it allows us to use real market perfectly synchronized prices; fourth, transaction costs can be considered and, finally, this article shows that the quality option may be a useful security in the portfolio of many traders. These traders will make the future contract more effective as a hedging instrument. This article also presents an empirical test involving the German market.

Acknowledgements

This research was partially supported by the Comunidad Autónoma de Madrid (Spain), grant no. S 2009/ESP-1494, and MEyC (Spain), grant no. ECO2009-14457-C04.

Notes

¹ Note that if the quality option value were really negligible, then it would be difficult to understand some speculative behaviours pointed out by several authors (e.g. Merrick et al., 2005).

² Let us remark that we do not trade the quality option itself. We just trade the replicating portfolio of the quality option, which is composed of real securities available in the market. Consequently, the returns provided by this strategy do not depend at all on the model we use to price the quality option. On the contrary, these returns are computed by using real bid/ask prices quoted in the market. They would remain the same if we drew on alternative pricing models for the quality option.

³ See Lieu (1990) for further details on this kind of option.

⁴ We follow the ideas and precision of the empirical study of Balbás et al. (2000), where the level of integration between the Spanish spot and derivative markets is verified by using a similar database.

⁵ We had the bond prices and the future price minute by minute, but we did not get the interest rates. Thus, several minutes have been removed and our analysis involved 1250 minutes.

⁶ We used strike 119 to price the quality option in 86 minutes, 119.5 was used in 182 minutes, 120 in 161 minutes and 120.5 in 92 minutes. The remaining strikes were not used due to the scarce number of minutes that we could have studied.

⁷ Profits and annual returns have been calculated for the strike 119.

⁸ Once again, it is worthwhile to recall that we do not trade the quality option, but its replica. Thus, these prices and annual returns have been computed by using available securities and their real perfectly synchronized quotes, as provided by Bloomberg. They would remain the same if the pricing model of the quality option were modified. Furthermore, the bid/ask spread has been considered