# 6.6 Futures Prices

Futures prices are generally collected as settlement prices. Because the contracts mature, and because multiple contracts usually trade simultaneously for a given underlier, futures prices do not form a continual time series. Instead, they form multiple overlapping time series corresponding to different contracts. Each one begins when the corresponding contract starts to trade and ends when that contract matures. This is illustrated in Exhibit 6.4 with monthly futures prices for flaxseed.

Multiple overlapping time series of futures prices poses a problem for value-at-risk analyses. Techniques of time series analysis require data to be in a continual time series. There are two ways to convert discontinual futures price data into continual time series. We can construct nearbys or constant-maturity price series.

###### 6.6.1 Nearbys

The standard means of obtaining continual time series from futures prices is to use **nearby series** or simply **nearbys**. Consider futures trading on a particular exchange for a given underlier. At any point in time, there will be contracts trading for several maturities. A **first nearby** is a time series comprising the price, at each point in time, of the nearest-to-maturity contract. The **second nearby** comprises the price, at each point in time, of the second nearest-to-maturity contract, etc. The actual umber of contracts trading at any point in time for a given underlier may vary, but if there are always at least *n* contracts trading for a particular underlier, then it is posible to construct at least *n* nearbys for that underlier.

Exhibit 6.5 indicates monthly settlement price data for municipal bond index futures traded on the CBOT. Prices are in USD and reflect the last settlement price for each month. Data is provided for six contracts maturing between September 1998 and December 1999. Exhibit 6.6 presents a first and second nearby constructed from the data. To clarify how the nearbys are constructed, we have used shading in Exhibits 6.5 and 6.6 to indicate the prices used to form the second nearby.

*t*, the price of the future that was closest to expiration at that time

*.*The second nearby represents, for each time

*t*, the price of the future that was second closest to expiration at that time. To clarify the construction of nearbys, the futures prices used to construct the second nearby have been shaded in both Exhibits 6.5 and 6.6.