Introduction

In this chapter, we delve into the calculation of the forward price for various financial assets and explore the concept of arbitrage between spot and forward prices. Forward contracts are widely used in financial markets to manage risk and speculate on future price movements. Understanding how to calculate the forward price and identify arbitrage opportunities is crucial for participants in these markets.

Calculating Forward Price from Spot Price

The forward price is the agreed-upon price today for an asset that will be delivered at a specified future date. To calculate the forward price, we consider factors such as the current spot price of the asset, the time until delivery, and the prevailing risk-free interest rate. The formula to calculate the forward price $(F)$ is:

$$F = S \times e^{(r \times T)}$$

Where:

• $F$ is the forward price
• $S$ is the current spot price of the asset
• $r$ is the risk-free interest rate
• $T$ is the time until delivery in years

Arbitrage Argument between Spot and Forward Prices

Arbitrage refers to the practice of taking advantage of price discrepancies to make risk-free profits. In the context of forward and spot prices, arbitrage opportunities arise when the forward price differs from the calculated forward price using the formula mentioned above. If the forward price is too high or too low, traders can engage in arbitrage to generate profit without taking on any risk. For example, if the calculated forward price is lower than the actual forward price, traders could buy the asset in the spot market and enter into a short forward contract. Conversely, if the calculated forward price is higher, traders could sell the asset in the spot market and enter into a long forward contract.

Example: Suppose the current spot price of a commodity is $100, the risk-free interest rate is 5%, and the time until delivery is 6 months. Using the formula, the calculated forward price would be:

$$F = 100 \times e^{(0.05 \times 0.5)} = 100 \times e^{0.025} \approx 102.53 $$

If the actual forward price in the market is significantly different from $102.53, arbitrage opportunities may arise.