## Pricing of futures

May 26th, 2008

After having introduced futures yesterday in Introduction to futures, we will explain the basics of futures pricing. It must be noted that the pricing of futures is a theoretical concept, which is what the price shoud be. In real life, the actual price could deviate from its theoretical prices for various reasons.

The pricing of futures is very simple:

Futures price = spot price + carry cost

The spot price is the prices fetched by the underlying in the market.

Next, what is the carry cost? The carry cost is basically the cost to hold the underlying. One of the components that makes the carry cost is the opportunity cost of interest foregone when holding the underlying till expiry of the futures. For example, let’s say you want to hold 1000 stocks of a company at \$1 (which is the spot price or market price) each for 12 months. What is the carry cost for holding those 1000 stocks? At 10% interest rate, the carry cost is \$100 (or \$0.10 per stock) over 12 months. Therefore, if a futures contract expires in 12 months time, then the futures price for that stock as underlying is:

\$1 (spot price) + \$0.10 (carry cost, which is the interests foregone for holding that stock over 12 months) = \$1.10

If the stock pays dividend within the 12 months, then this dividend plus the interests associated with that dividend itself will be adjusted in the carry cost to arrive at the theoretical value of the futures.

For stocks, since it is an intangible thing, the carry cost is basically the interest foregone (and the dividends plus the interest on dividends). But for physical commodities (e.g. oil, gold, copper), the carry cost involves warehousing, insurance and other costs associated for physically holding them.

So, what if in actuality, the futures price deviates from its theoretical price? Keep in tune!

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