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# Zone of convergence

#### idcnik01

##### New Member
Hi,

Can someone help explain this term.

"As the Futures contract approaches maturity, the spot price should converge with the
Futures price"

Sorry I do not find much explanation in the the Notes. I am not clear how the Spot price of a commodity will converge as per Future Price.

idcnik01

#### ShaktiRathore

##### Well-Known Member
Subscriber
Hi,
The futures price F0 should converge to the spot price ST as the Futures contract approaches maturity T its because otherwise arbitrage is possible. If F0>ST the arbitrageur would step in and short the expensive future and buy the underlying asset at spot price ST just before the maturity and at maturity sell the asset at F0 so that a net profit of F0-ST is realized. similarly if F0<ST the arbitrageur would step in and long the expensive future and short the underlying asset at spot price ST just before the maturity and at maturity buy the asset at F0 so that a net profit of ST-F0 is realized.

thanks

#### idcnik01

##### New Member
Thanks for your response Shakti. Probably I am lacking understanding here. Once a forward price is decided in a contract, does it change on a regular basis? and if yes, then how and what are the factors drive it.

Idcnik01

#### ShaktiRathore

##### Well-Known Member
Subscriber
Hi,
The forward price remains the same in the contract until the maturity of the contract but its the value of the contract that keeps on changing. For e.g. 1 year forward on oil with price of $100 would remain the same that is the agreement to buy the oil in 1 year at$ 100 would be the same after 3 months also with time to maturity of 9 months and not change but the value of forward changes with the change in the spot price of the oil. If at time t=0 the spot price of oil is 100*exp(-.05*1),after 3 months spot price of oil changes to St so the value of the forward is St-100*exp(-.05*.75) while the price to buy oil at $100 after 9 months shall remain the same at$ 100 while value shall keep on changing with the change in the spot price St.
thanks

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#### idcnik01

##### New Member
Thanks Shakti.

Is this also called 'Mark to Market'?

idcnik01

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @idcnik01 In Hull Chapter 5 there is a helpful formula for the value, denoted by small (f), of a futures contract: f = [F(0) - K)*exp(-rT). The exp(-rT) is simply discounting the difference given by F(0) - K. When the contract is entered, its value (f), will be zero. The delivery price (aka, strike price) of K does not change, but the F(0) is the traded price that does change. A better notation for the forward price is maybe F(0,T); e.g., F(0, 0.25) is the forward price today of a contract that matures in three months. This forward price, F(0) or F(0,T) is the price that should converge toward the spot at the contract approaches maturity. "Marking to market" suggests (at least to me) an action by somebody to assign a value based on observed market prices (or market variables). The futures contract already has a traded, observed price so we don't need marking to market for the convergence to occur, which will happen simply because non-convergence creates arbitrage opportunities (it creates a profitable cash and carry or reverse cash and cary). Hull does say that "marking to market" is a synonym for "daily settlement" in the case of futures: "At the end of each trading day, the margin account is adjusted to reflect the investor’s gain or loss. This practice is referred to as daily settlement or marking to market." So daily settlement has a purpose but it is not the key to the natural convergence of the traded futures price toward to the spot price. I hope that's helpful!