The carry arbitrage framework enables to price forward contracts.
First let’s give a definition of a forward contract:
A forward contract is the obligation to buy or sell a specified quantity of a an underlying (stock, commodity, currency, interest rate) in the future at a prespevifued price.
For example a 3 month forward on a stock could be bought at $102 when the spot (delivery in T+2 days) price could be $101.5.
Inevitably there is relation between the spot price of the underlying, here a stock, and the forward contract price that obliges the party to either buy or sell it in 3 months at the pre agreed
pricebut without spending money at initiation of the contract.
The difference in price between the spot price and the forward is precisely because by buying or selling a forward contract you don’t need to spend money but if you want to buy the underlying
(thestock in our example) now at spot price you need money for it.
In a no arbitrage approach where you cannot make money without risk and without spending your own money, the forward price needs to be such as carrying the underlying until the maturity of
thecontract and selling it at maturity should earn the sale return then selling the forward at initiation, borrowing money at the risk free rate, burn the underlying and making delivery
atmaturity.
From those statements the price of a forward contract is the future value (FV) of the spot price + the carrying costs of holding the underlying (CC) -the carry benefits of holding the
underlying(CB).
Fo (price of the forward contract now) = FV (So+CC-CB)
Why is this so? Because if an investor carries the underlying, he must bear the costs (like delivery costs, insurance costs for a commodity forward contract) of holding it unlike the investor who
bought the forward. This advantage must be reflected in a higher price of the forward.
In the same way if buying the forward contract deprives the investor of the benefits he can get from holding the underlying. this disadvantage must be reflected in a lower price for the
investor who bought the contract.
And we consider the future value because any investment is supposed to earn at least the risk free rate.
The carry arbitrage framework enables to price forward contracts.
First let’s give a definition of a forward contract:
A forward contract is the obligation to buy or sell a specified quantity of a an underlying (stock, commodity, currency, interest rate) in the future at a prespevifued price.
For example a 3 month forward on a stock could be bought at $102 when the spot (delivery in T+2 days) price could be $101.5.
Inevitably there is relation between the spot price of the underlying, here a stock, and the forward contract price that obliges the party to either buy or sell it in 3 months at the pre agreed
price but without spending money at initiation of the contract.
The difference in price between the spot price and the forward is precisely because by buying or selling a forward contract you don’t need to spend money but if you want to buy the underlying
(the stock in our example) now at spot price you need money for it.
In a no arbitrage approach where you cannot make money without risk and without spending your own money, the forward price needs to be such as carrying the underlying until the maturity of the
contract and selling the latter at maturity should earn the same return as selling the forward at initiation, borrowing money at the risk free rate, buy the underlying and making delivery at
maturity.
From those statements the price of a forward contract is the future value (FV) of the spot price + the carrying costs of holding the underlying (CC) -the carry benefits of holding the
underlying(CB).
Fo (price of the forward contract now) = FV (So + CC-CB)
Why is this so? Because if an investor carries the underlying, he must bear the costs of holding it such as delivery costs, storage costs, insurance costs for a commodity forward contract unlike the investor who bought the forward.
This advantage must be reflected in a higher price of the forward.
In the same way, if buying the forward contract deprives the investor of the benefits he can get from holding the underlying, those disadvantages must be reflected in a lower price for the investor who bought the contract.
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