Futures Contracts: Pricing and Valuation
This module delves into the core principles of how futures contracts are priced and valued. Understanding these concepts is crucial for both hedging and speculative strategies in financial markets. We will explore the relationship between spot prices, futures prices, and the factors that influence them.
The Cost of Carry Model
The fundamental model for pricing futures contracts is the cost of carry model. This model posits that the futures price should reflect the spot price of the underlying asset plus the costs associated with holding that asset until the futures contract expires. These costs, collectively known as the 'cost of carry,' can include storage costs, insurance, and financing costs (interest), minus any income generated by the asset (like dividends for stocks or convenience yield for commodities).
Arbitrage and Futures Pricing
The cost of carry model relies heavily on the principle of arbitrage. Arbitrage is the simultaneous purchase and sale of an asset in different markets to profit from tiny differences in the asset's listed price. In the context of futures, if the futures price deviates significantly from the theoretical price dictated by the cost of carry, arbitrageurs can exploit this mispricing, which in turn pushes the futures price back towards its theoretical value.
Arbitrageurs are the market makers who ensure that futures prices remain aligned with their theoretical values based on the cost of carry. Their actions are critical for market efficiency.
Valuation of Futures Contracts
While pricing refers to determining the theoretical fair value of a futures contract at its inception, valuation refers to determining the current market value of an existing futures contract. Since futures contracts are marked-to-market daily, their value changes as the underlying asset's price fluctuates. The value of a long position in a futures contract is the difference between the current futures price and the price at which the contract was entered, adjusted for any gains or losses from previous mark-to-market adjustments. Conversely, the value of a short position is the opposite.
Arbitrage.
Factors Affecting Futures Prices
Several factors can influence the relationship between spot and futures prices, leading to deviations from the simple cost of carry model. These include:
- Convenience Yield: For commodities, holding the physical asset can provide a benefit (e.g., avoiding production disruptions). This 'convenience yield' can reduce the futures price below what the cost of carry alone would suggest.
- Market Expectations: Anticipation of future supply and demand changes, economic events, or geopolitical developments can significantly impact futures prices.
- Interest Rate Changes: Fluctuations in interest rates directly affect the financing cost component of the cost of carry.
- Storage and Insurance Costs: For physical commodities, changes in these costs will alter the cost of carry.
- Dividends or Coupon Payments: For financial futures, the expected income from the underlying asset plays a crucial role.
| Concept | Description | Impact on Futures Price |
|---|---|---|
| Cost of Carry | Expenses of holding an asset until expiration (interest, storage, insurance) minus income (dividends, convenience yield). | Higher cost of carry generally leads to a higher futures price relative to the spot price. |
| Convenience Yield | Benefit of holding the physical commodity, especially for producers or consumers needing to ensure supply. | Increases convenience yield generally leads to a lower futures price relative to the spot price. |
| Interest Rates | The risk-free rate of return on an investment. | Higher interest rates increase the financing cost, leading to a higher futures price. |
Contango and Backwardation
The relationship between spot prices and futures prices over different maturities is often described by two terms:
- Contango: When the futures price is higher than the spot price, and futures prices for longer maturities are progressively higher than those for shorter maturities. This typically occurs when the cost of carry is positive and significant.
- Backwardation: When the futures price is lower than the spot price, and futures prices for longer maturities are progressively lower than those for shorter maturities. This often happens when there is a high convenience yield or an immediate shortage of the underlying asset.
The relationship between spot and futures prices can be visualized as a yield curve. In contango, the curve slopes upward, indicating that longer-dated futures are more expensive. In backwardation, the curve slopes downward, meaning longer-dated futures are cheaper. This visual representation helps understand market expectations and the influence of cost of carry versus convenience yield.
Text-based content
Library pages focus on text content
Backwardation.
Learning Resources
Official curriculum material from the CFA Institute, providing a foundational understanding of futures pricing and valuation as per the CFA program.
A comprehensive overview of futures contracts, including their definition, how they work, and key terminology like cost of carry and arbitrage.
An introductory video series explaining futures and forwards, including their pricing mechanisms and how they are used in financial markets.
Explains the cost of carry concept in detail, including its components and how it influences the pricing of futures and other derivatives.
A practical guide to understanding futures pricing, focusing on the cost of carry model and its implications for traders.
Educational resources from a major futures exchange, explaining the principles behind futures pricing and market dynamics.
A chapter from a seminal textbook on derivatives, offering in-depth theoretical explanations of futures pricing and valuation.
Explains the concepts of contango and backwardation in the context of commodity futures, providing examples of when these conditions occur.
Defines arbitrage and explains how it works in financial markets, highlighting its role in ensuring price efficiency for futures contracts.
A university-level course that covers derivatives, including detailed modules on futures pricing, valuation, and hedging strategies.