F being 100 and the term rate of 1 + 1 year corresponds to 1.10. As a result, the futures price is 90.91 USD. The buyer of a futures contract bets that the price will increase between today and the deadline on the futures price. The seller expects the contrary. Similarly, if considered at the beginning of period 1 in order to avoid the creation of an arbitrage opportunity, the present value of the futures price must be equal to the price of the underlying zero-coupon bond. To continue the example below, we assume that the initial price of Andy`s house is $US 100,000, and Bob takes a futures contract from today to buy the house for a year. But since Andy knows that he can sell for $100,000 and put the product in the bank, he wants to be compensated for the late sale. Assuming the risk-free return R (the bank interest rate) for a year is 4%. The money in the bank would increase to $104,000, without risk. So Andy would like at least $104,000 in a year to make the contract worth it for him – the opportunity costs will be covered. Case 2: Assuming that F t, T < S t e r ( T – t) {displaystyle F_ {t,T}<S_ {t} e^ {r (T-t)}}. An investor can then do the opposite of what he did at the top in Case 1.

This means selling a unit of the asset, putting that money in a bank account, and entering into a long-term contract that will cost 0. The relationship between the spot price and the futures price of an asset reflects the net costs of taking (or carrying) that asset relative to maintaining the futures value. Thus, all the costs and benefits mentioned above can be summarized as shipping costs c {displaystyle c}. Therefore, {displaystyle r} is the continuous risk-free return and T is the time to maturity. The intuition behind this result is that if you want to own the asset at time T, there should be no difference between buying the asset today and maintaining and buying the futures contract and delivery in a perfect capital market. Therefore, both approaches must cost the same value in present value. You can find proof of arbitration as to why this is the case in Rational Pricing below. If S t {displaystyle S_{t} the spot price of an asset at time t {displaystyle t} and r {displaystyle r} is the continuous composite rate, then the futures price must be at some point T {displaystyle T} F t , T = S t e r ( T − t ) {displaystyle F_{t,T}= S_{t}e^ {r (T-t)}} Conversely, in markets where spot prices or base rates are easily accessible, especially the foreign exchange market and the OIS market, dates are usually quoted with bonus points or term points. That is, the use of the spot price or base interest rate, since reference advances are reported as a difference in pips between the Outright price and the spot price for FX or the difference in basis points between the forward rate and the base rate for interest rate swaps and futures. [13] Where I = {displaystyle I=} is the present value of discrete income at time t 0 < T {displaystyle t_{0}<T} and q % p. a. {displaystyle q%p.a.} the yield on continuous composite dividends over the term of the contract.

The intuition is that when an asset pays income, it has an advantage in keeping the asset rather than the advance, because you get that income. It is therefore necessary to subtract the income (Idisplaystyle I} or q {displaystyle q} to reflect this advantage. . . .