Futures Pricing: Models and Calculations

futures-pricing-models-and-calculations

Futures contracts are complex financial instruments, and accurately pricing them requires specific models and calculations. This article introduces some of the basic models used for pricing futures contracts and provides examples to illustrate how these calculations are made.

Introduction to Pricing Models for Futures Contracts

Pricing models for futures contracts are essential tools used by traders and investors to estimate the fair value of a futures contract. These models take into account various factors, including the current price of the underlying asset, time to expiration, interest rates, and storage costs.

Basic Models Used for Pricing Futures Contracts

Several models are employed in the pricing of futures contracts, each suited to different types of underlying assets and market conditions.

• Cost of Carry Model: This is the most fundamental model used for pricing futures, especially commodity futures. It considers the cost of carrying or holding the underlying asset until the expiration of the contract, including storage costs and financing costs, minus any benefits like dividends or interest.
• Black Model: An adaptation of the famous Black-Scholes model, the Black model is used for pricing futures options. It factors in the volatility of the underlying asset and the time value of money.
• Binomial Model: This model uses a discrete-time framework for options pricing and can be applied to futures. It models possible future movements in the price of the underlying asset.

Examples of Pricing Calculations

Cost of Carry Model for a Commodity Future

• Scenario: Consider a futures contract for crude oil. The current spot price is $50 per barrel. The annual storage cost is $2 per barrel, and the annual risk-free interest rate is 3%.

Calculation: The futures price FF can be calculated as:

F=SpotPrice×e(StorageCost+InterestRate)×TimetoExpirationF=SpotPrice×e(StorageCost+InterestRate)×TimetoExpiration

Assuming a time to expiration of 1 year, the futures price would be approximately $53.56.

Black Model for a Futures Option

• Scenario: An option on a futures contract with a strike price of $100, a volatility of 20%, a risk-free interest rate of 5%, and six months to expiration.
• Calculation: Using the Black model, the option’s price would factor in the current futures price, the strike price, the time to expiration, the volatility of the underlying future, and the risk-free interest rate.

Futures Pricing Models Wrap Up

Pricing models and calculations in futures trading are critical for traders to make informed decisions. While these models provide a framework for estimating fair value, it’s important to note that actual market prices may differ due to market sentiment and other factors not accounted for in the models. A thorough understanding of these models, combined with market analysis, is essential for successful futures trading.