Editing Rational pricing (section)

===Futures===<!-- This section is linked from [[Contango]] -->
In a [[futures contract]], for no arbitrage to be possible, the price paid on delivery (the [[forward price]]) must be the same as the cost (including interest) of buying and storing the asset. In other words, the rational forward price represents the expected [[future value]] of the [[underlying]] discounted at the risk free rate (the "[[Rational pricing#An asset with a known future-price|asset with a known future-price]]", as above); see [[Spot–future parity]]. Thus, for a simple, non-dividend paying asset, the value of the future/forward, <math>F(t)\,</math>, will be found by accumulating the present value <math>S(t)\,</math> at time <math>t\,</math> to maturity <math>T\,</math> by the rate of risk-free return <math>r\,</math>.

:<math>F(t) = S(t)\times (1+r)^{(T-t)}\,</math>

This relationship may be modified for storage costs, dividends, dividend yields, and convenience yields; see [[Futures contract#Pricing|futures contract pricing]].

Any deviation from this equality allows for arbitrage as follows.

* In the case where the forward price is ''higher'':
# The arbitrageur sells the futures contract and buys the underlying today (on the spot market) with borrowed money.
# On the delivery date, the arbitrageur hands over the underlying, and receives the agreed forward price.
# He then repays the lender the borrowed amount plus interest.
# The difference between the two amounts is the arbitrage profit.

* In the case where the forward price is ''lower'':
# The arbitrageur buys the futures contract and sells the underlying today (on the spot market); he invests the proceeds.
# On the delivery date, he cashes in the matured investment, which has appreciated at the risk free rate.
# He then receives the underlying and pays the agreed forward price using the matured investment. [If he was [[short selling|short]] the underlying, he returns it now.]
# The difference between the two amounts is the arbitrage profit.