Pricing and Valuation of Forward Contracts at Expiration
__Forward contracts__ allow one party to purchase an underlying asset from another party, at some point in the future, and at a price that is set today.
The forward price is set when the contract is created and is represented as $$F_{0}\left ( T \right )$$.
The asset's spot price at expiration is $$S_{T}$$.
The value of the contract at expiration is $$V_{T}\left ( T \right )$$.
So the value of the forward contract at expiration is:
$$\displaystyle V_{T}\left ( T \right )= S_{T}-F_{0}\left ( T \right )$$
The value of the forward contract at expiration depends on the price of the underlying asset and whether the party bought or sold the asset.
Suppose you are at a family gathering and are stuck sitting next to your annoying cousin. He is fascinated by your grasp of finance and proceeds to spend the next hour telling you all about his experiences as a novice trader. He tells you that he recently agreed to sell all of his mother's gold jewelry, unbeknownst to his mother, to a buyer through a three-month forward contract. The agreed-upon selling price is USD 1,000 per ounce.
If the price at the end of three months is USD 950 per ounce, what do you think the value of your cousin's forward contract would be?
Incorrect.
Exactly!
Your cousin may ultimately be disowned by his mother, but at least he will have profited from his forward contract. The value of the contract is:
$$\displaystyle V_{T}\left ( T \right )= S_{T}-F_{0}\left ( T \right )$$
Substituting the USD 1,000 forward price and the USD 950 asset price at expiration yields:
$$\displaystyle V_{T}\left ( T \right )= 950- 1,000$$
$$\displaystyle V_{T}\left ( T \right )=- 50$$
This is the value to the buyer, however, since values are typically quoted from a buyer's perspective. So the value to your cousin, the seller, is simply USD 50. One party's gain is another party's loss.
Now suppose that several months have passed, and your cousin is still a member of the family. As you are sitting down for a holiday dinner, he mentions to you that his successful forward transaction has given him the confidence he needs to be a full-time trader. As you clutch your gold watch tightly, he says that he believes gold prices have bottomed and would like to buy some using another forward contract.
If your cousin can purchase gold for USD 950 per ounce using a new three-month forward contract, what do you think would need to happen to the price of gold to give him a USD 250 profit on his trade?
Incorrect.
Correct!
In order for your cousin to reap a USD 250 profit on his new trade, the price of gold would need to _increase_ by USD 250, since he would be the buyer in this particular transaction. So the price at expiration would have to be
$$950 + 250 = 1{,}200$$.
As a check, you can use the formula for calculating the value of a forward contract at expiration:
$$\displaystyle V_{T}\left ( T \right )= S_{T}-F_{0}\left ( T \right )$$
and rearrange the expression as:
$$\displaystyle S_{T}= V_{T}\left ( T \right )+F_{0}\left ( T \right )$$
which will give you:
$$\displaystyle S_{T}= 250 + 950 = 1{,}200$$
To summarize:
[[summary]]
USD –50
USD 50
The price of gold would need to decline to USD 700
The price of gold would need to increase to USD 1,200
Continue
Continue
Continue
