Introduction

In the world of commodity forwards and futures, understanding the concept of the lease rate and its implications is essential. The lease rate plays a crucial role in determining the no-arbitrage values for commodity contracts. This chapter delves into the lease rate’s definition, its significance in the context of derivatives, and how it influences the pricing of commodity forwards and futures.

Lease Rate and Its Importance

The lease rate refers to the cost associated with leasing or borrowing a commodity for a specific period. It reflects the interest rate at which an investor can borrow a commodity while simultaneously entering into a short position on the forward contract for the same commodity. The lease rate is a critical factor in the determination of the no-arbitrage values for commodity derivatives. A higher lease rate indicates greater demand for the underlying commodity, which can impact both futures prices and market expectations.

Relationship with Commodity Forwards and Futures

The lease rate’s relationship with commodity forwards and futures lies in its influence on the arbitrage opportunities in the market. When the lease rate is higher than the risk-free rate, investors have an incentive to borrow the commodity, sell it forward, and invest the proceeds at the risk-free rate. This creates arbitrage pressure that affects the pricing of both forward and futures contracts.

Determining No-Arbitrage Values

The no-arbitrage principle dictates that identical securities or contracts should have the same price. In the context of commodities, this principle applies to commodity forwards and the corresponding cash-and-carry portfolios. The no-arbitrage value for a commodity forward contract is influenced by the spot price, the risk-free rate, and the lease rate. The relationship can be expressed as:

$$F=Se^{(r+\lambda−c)t}$$

Where:

• $F$ is the forward price of the commodity
• $S$ is the spot price of the commodity
• $r$ is the risk-free rate
• $\lambda$ is the lease rate
• $c$ is the cost of carry
• $t$ is the time to maturity of the contract

Implications in Real-World Trading

In practical trading scenarios, the lease rate can vary based on supply and demand dynamics, market sentiment, and economic conditions. Traders and investors closely monitor changes in the lease rate to gauge the market’s expectations regarding the future price of the underlying commodity. A higher lease rate can indicate scarcity and heightened demand, potentially leading to upward pressure on forward and futures prices.