# Valuation of Future and Swaps

25/08/2020

#### Valuation of Future

When you trade a futures contract, you agree either to buy or to sell the asset underlying the futures contract on a specified date in the future. The price at which the contract is traded is not pre-set, but is determined by market forces.

It is possible to calculate a theoretical fair value for a futures contract.

The fair value of a futures contract should approximately equal the current value of the underlying shares or index, plus an amount referred to as the ‘cost of carry’.

The cost of carry reflects the cost of holding the underlying shares over the life of the futures contract, less the amount the shareholder would receive in dividends on those shares during that time. Because the buyer of the futures contract pays only a small percentage of the contract value at the time of the transaction, they do not directly incur this funding cost.

For example, assume that:

• The S&P/ASX 200 Index is trading at 5000 points
• There are 120 days until maturity of the June futures contract
• Interest rates are currently at 7% p.a.
• The average dividend yield on stocks in the S&P/ASX200 Index is 4% p.a.

The theoretical fair value of the June ASX Mini 200 Future can be calculated as:

Fair value = current level of S&P/ASX200 + cost of carry

= 5000 + (5000 X (7% – 4%) X 120/365)

= 5049.5 points

As maturity approaches, the prices of the futures contract and the underlying asset tend to converge. The trader’s profit or loss depends on how far the price of the futures contract at maturity is above or below the price at which the contract was initially traded.

The full value of the futures contract is not paid or received when the contract is established instead both buyer and seller pay a small initial margin. The traded price is the basis on which profit or loss is calculated at maturity or on closing out the position if this takes place before maturity.

#### Valuation of Swaps

A wide variety of swaps are utilized in the over-the-counter (OTC) market in order to hedge risks, including interest rate swaps, credit default swaps, asset swaps, and currency swaps. In general, swaps are derivative contracts through which two private parties usually businesses and financial institutions exchange the cash flows or liabilities from two different financial instruments.

A plain vanilla swap is the simplest type of swap in the market, often used to hedge floating interest rate exposure. Interest rate swaps are a type of plain vanilla swap. Interest rate swaps convert floating interest payments into fixed interest payments (and vice versa).

Two parties may decide to enter into an interest rate swap for a variety of different reasons, including the desire to change the nature of the assets or liabilities in order to protect against anticipated adverse interest rate movements. Like most derivative instruments, plain vanilla swaps have zero value at the initiation. This value changes over time, however, due to changes in factors affecting the value of the underlying rates. And like all derivatives, swaps are zero-sum instruments, so any positive value increase to one party is a loss to the other.

How Is the Fixed Rate Determined?

The value of the swap at the initiation date will be zero to both parties. For this statement to be true, the values of the cash flow streams that the swap parties are going to exchange should be equal. This concept is illustrated with a hypothetical example in which the value of the fixed leg and floating leg of the swap will be Vfix and Vfl respectively. Thus, at initiation:

V_{fix} = V_{fl}Vfix​=Vfl

Notional amounts are not exchanged in interest rate swaps because these amounts are equal; it does not make sense to exchange them. If it is assumed that parties also decide to exchange the notional amount at the end of the period, the process will be similar to an exchange of a fixed rate bond to a floating rate bond with the same notional amount. Therefore such swap contracts can be valued in terms of fixed-rate and floating-rate bonds.