A forward contract is a contract that gives the buyer the obligation to purchase a specific amount of the underlying asset at a specific time (T), and at a specific price (F). F is set at time t=0, when the forward contract is drawn up.
We then defined the asset price and forward price/value. The spot price of the asset is S(0), S(t), or S(T), depending on the time. The forward price or value is f(0), f(t), or f(T), depending on the time. The value of the forward contract at time T is the spot price minus the specific price of the forward contract:
An important thing to note is that the forward price F is set so that at time t=0, the value or price of the forward contract is = 0.
As I discussed above, we then learned about short selling. Short selling is when an investor borrows shares of a stock from his or her broker, then sells them on the market. The investor must then buy back the same number of shares at a later date and return them to their broker to "cover" the short.
This can be dangerous because if the price of the stock increases, then the investor could potentially lose an unlimited amount of money.
We then used no-arbitrage to set F so that it was deterministic, and not dependent upon the market. To do this, we bought a future contract, shorted the underlying asset, and lent the proceeds from the short to collect interest.
In this case, we can negotiate for a minimum forward price F, so as to break even. We simply set the net cash flow at time t=T equal to 0 and solve for F:
For example: if the forward contract matures in 6 months, the current spot price is $50, and the interest rate for a 6-month bond is 4% per year, then:
Which gives us the F we should agree on.
We then used a similar method to create a new portfolio of deterministic cash flows using only forward contracts. In this case, we went long a forward contract from time t=0 to t=T and shorted a forward contract from time t=t to t=T.
so the value of the contract bought at time t=t should be equal to:
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