# Level 1 CFA® Exam:

Pricing & Valuation of Futures

As in the case of forward contracts, the value of a futures contract at initiation is equal to 0.

Also, we can use the same formulas for the futures price as in the case of a forward contract (including modifications for benefits and costs related to the underlying asset):

\(F = S_{0}\times (1+r)^{T}\)

- \(F\) - forward price
- \(S_{0}\) - underlying price at contract initiation
- \(r\) - risk-free interest rate
- \(T\) - time until contract expiration

\(F=(S_{0}-i+c)\times (1+r)^{T}\)

- \(F\) - forward price
- \(S_{0}\) - underlying price at contract initiation
- \(i\) - Present Value of benefits (e.g. dividends, income, interest, convenience yield)
- \(c\) - Present Value of costs (e.g. storage cost)
- \(r\) - risk-free interest rate
- \(T\) - time until contract expiration

**NOTE:** When calculating the forward price when there's the net cost of carry given (defined as the difference between the benefits of holding the underlying and the cost related to holding the underlying), we decrease the underlying price by this net cost of carry.

Futures contracts are marked-to-market on a daily basis, so the value of a futures is equal to 0 at the end of the day. Also, at the end of the day, the balance of an investor's accounts is adjusted based on a new settlement price. As a result of marking-to-market, at the end of each day, the balance of our account alters depending on how the settlement price changes. If the balance goes below the maintenance margin requirement, we will have to make a payment to bring it back to the required level (equal to the initial margin).

Forwards and futures are characterized by different cash flow patterns, which may lead to different prices and values. In the case of a futures, we can expect small cash flows during the life of the contract (because futures are marked-to-market on a daily basis), whereas in the case of a forward – there is one bigger cash flow at the contract expiration. This different cash flow pattern may produce different prices of forwards and futures when we take the time value of money concept into account. However, the difference is generally very small.

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- As in the case of forward contracts, the value of a futures contract at initiation is equal to 0.
- Futures contracts are marked-to-market on a daily basis, so the value of a futures is equal to 0 at the end of the day.
- When interest rates are constant, there will be no differences between futures and forward prices.