###### Risk-Neutrality in Derivative Pricing

Remember that the value of an option is not affected by the real-world... **Read More**

Since a swap involves a series of payments over a fixed period of time, it can be viewed as a series of forward contracts expiring at various times over the life of the swap contract.

The forward price is determined by the spot price and the net cost-of-carry, where the net cost-of-carry is dependent on the length of time of the contract. The cost of carrying an asset over different time periods will vary with the length of the period. Therefore, the prices of the series of forward contracts that “make up” the swap contract will not be equal. However, for a swap, all of the fixed payments are equal.

To equate a swap with a series of forward contracts, we must assume that the forward transaction starts with a nonzero value (known as an off-market forward). Each forward contract will be created at a price that corresponds to the fixed price of the swap. Some of our forward contracts would have negative initial values and some positive, but they would have a zero value in aggregate.

We can determine the nonzero price by using the principles of arbitrage and replication, the details of which are not covered at this point.

Consider a 3-year swap that settles every year. The notional principal is 25 million, and the fixed interest rate of the swap is 7%. For simplicity, let’s say that you are the fixed rate payer and need to pay 1.75 million at the end of every year. If interest rates go up, you benefit because you are paying 1.75 million even though the market rates are higher. Conversely, if interest rates go down, that is bad because you pay a 7% rate even though the market rate is lower.

The swap above is similar to the following series of forward agreements:

- Paying 7% on a 25 million 1-year loan;
- Forward rate agreement to pay 7% on a 25 million 1-year loan which will start
**one**year from today; - Forward rate agreement to pay 7% on a 25 million 1-year loan which will start
**two**years from today; - Etc.

QuestionWhy can a swap be viewed as a combination of forward contracts?

A. Because each forward contract is created at the swap price

B. Because forward contracts are created at different forward prices, which will equal the fixed price of the swap at the end of the contract

C. Because swaps and forward contracts are exactly the same as long as the value at the initiation of both contracts are the same

SolutionThe correct answer is A.

A swap is equivalent to a series of forward contracts because each individual forward contract is said to be off-market since it is created at the swap price.