Introduction

In the realm of commodity trading, the consideration of storage costs is pivotal in determining the pricing of forward contracts. Commodity markets often involve physical goods that require storage, and the expenses associated with storing these goods significantly impact their forward prices. This chapter delves into the intricacies of computing forward prices while factoring in storage costs. By understanding the relationship between storage costs, spot prices, and future prices, traders and investors can make informed decisions in the volatile world of commodities.

Computation of Forward Price with Storage Costs

When calculating the forward price of a commodity, storage costs play a crucial role. Storage costs encompass expenses such as warehousing, insurance, and handling charges. These costs accrue over the contract’s duration and need to be incorporated into the forward price to accurately reflect the commodity’s future value.

The formula for computing the forward price with storage costs is:

$$F_t = S_t \times e^{(r-y) \times T} - C_t$$

Where:

• $F_t$ is the forward price at time
• $S_t$ is the spot price of the commodity at time
• $r$ is the risk-free interest rate
• $y$ is the convenience yield
• $T$ is the time to maturity of the contract
• $C_t$ represents the cumulative storage costs incurred until time $t$

Example 1: Let’sconsider a scenario where the current spot price of crude oil is USD 70 per barrel. The risk-free interest rate is 5%, the convenience yield is 2%, and the storage costs accumulated over a six-month contract are USD 3 per barrel. Using the formula, the forward price can be calculated as:

$$F_t = USD 70 \times e^{(0.05 - 0.02) \times (6/12)} - USD 3 = USD 71.39$$

Example 2: Let’s consider another example involving agricultural commodities. Suppose a wheat farmer anticipates a bumper harvest and decides to enter into a forward contract to sell wheat six months later. The current spot price of wheat is USD 400 per ton. Storage costs, including warehousing and insurance, amount to USD 10 per ton over the contract’s duration. With a risk-free interest rate of 4% and a convenience yield of 1.5%, the forward price can be computed as follows:

$$F_t = \text{USD 400} \times e^{(0.04 - 0.015) \times (6/12)} - \text{USD 10} = \text{USD 404.25}$$