Pricing and Valuation of Futures Contracts | CFA Level I Derivatives
Today, we’ll delve into the pricing and valuation of futures contracts, with a focus on interest rate futures. We’ll compare and contrast them with forwards, which we covered in our last lesson.
Forward vs. Futures Contracts: Key Differences
Before we begin, it’s crucial to understand the differences between forward and futures contracts:
- Price: Forward contracts have a constant price, while futures contracts fluctuate.
- Value: Forward contract values fluctuate according to the spot price, whereas futures contracts are reset to zero daily after the mark-to-market process.
Now, let’s explore these differences further.
Calculating Futures Prices
EXAMPLE
The spot price of gold is $1800 at the initiation of a 60-day forward contract, and the risk-free rate is 5%. Calculate the price of an equivalent 60-day futures contract.
Solution: Using the same method as in our forward contract lesson, we find that the initial price of the futures contract should be $1814.50.
f0 = S0 x (1+Rf)T = 1800 x 1.0560/365 = $1814.50
Margin Requirements and Mark-to-Market
Unlike forwards, futures contracts require traders to deposit an initial margin into their account.
EXAMPLE
Continuing our gold futures contract example, let’s say the initial margin requirement is 10%, and the trader longs 100 contracts. How much should the trader deposit into their margin account?
Solution: The total value of the position is $181,450. For a 10% margin account, the trader must make an initial deposit of $18,145 into their margin account.
As the futures price changes, the daily gain or loss is added or subtracted from the trader’s margin account through the mark-to-market process. For example, if at the end of the first trading day the spot price of gold rises to $1820, the price of the futures contract should increase to $1834.41. If this is the settlement price, the trader’s margin account should have an added $1991. The value of the contract resets to 0 after the mark-to-market process.
Price Differences Between Forwards and Futures
The initial pricing of forwards and futures is typically the same. However, due to the margin requirement for futures, certain factors can cause price differences, such as the correlation between interest rates and futures prices.
- Positive Correlation: Futures prices will be higher than forward prices when interest rates and futures prices are positively correlated.
- Negative Correlation: Futures prices will be lower than forward prices when interest rates and futures prices are negatively correlated.
Pricing and Valuation of Interest Rate Futures
Interest rate futures are exchange-traded equivalents to forward rate agreements (FRAs). Like FRAs, they reference the market reference rate (MRR) between two points in time. However, interest rate futures are quoted on a price basis using this general formula:
FP = 100 – 100xMRRA,B-A
There’s an inverse relationship between the MRR and the price of interest rate futures. Traders expecting the MRR to increase should short interest rate futures, while those expecting it to decrease should long them.
Mark-to-Market for Interest Rate Futures
To calculate the mark-to-market amount for interest rate futures, use the contract’s basis point value (BPV) formula:
BPV = notional principal x 0.01% x period
The BPV is the change in contract price for a 1 basis point move in the forward rate.
EXAMPLE
If an interest rate futures contract has a notional principal of $1M and a loan of 3 months, the BPV of the contract is $25.
BPV = notional principal x 0.01% x period = $1M x 0.01% x 3/12 = $25
This means that an increase or decrease of MRR by 1 basis point will cause the value of the contract to decrease or increase by $25.
EXAMPLE
If the futures price increases to 97.8 by the end of the next trading day, what is the mark-to-market amount on the trader’s account?
Solution:
FP = 100 – 100xMRR2m,3m -> MRR2m,3m = (100-97.8) / 100 = 2.2%
The implied MRR is now 2.2%, a reduction of 30 bp. Since BPV is $25, the value of the futures contract should increase by $750 ($25×30), resulting in a mark-to-market of +$750.
Summary
And there you have it! You should now understand the key differences between forward and futures contracts, their pricing and valuation, as well as interest rate futures and the mark-to-market process. Next, we will dive into the pricing and valuation of swaps.
✨ Visual Learning Unleashed! ✨ [Premium]
Elevate your learning with our captivating animation video—exclusive to Premium members! Watch this lesson in much more detail with vivid visuals that enhance understanding and make lessons truly come alive. 🎬
Unlock the power of visual learning—upgrade to Premium and click the link NOW! 🌟
