Forward Price: Definition, Calculation Formulas, and Examples

A comprehensive overview of forward prices in forward contracts, covering definitions, calculation methods, examples, and applications in financial markets.

In the realm of financial derivatives, the forward price is the predetermined delivery price agreed upon by the buyer and seller of a forward contract. This price is determined at the initiation of the contract and dictates the future transaction price of the underlying asset.

Calculation Formulas for Forward Price

The forward price is generally determined using arbitrage-free pricing principles. The key formula used to calculate the forward price \( F \) of an asset with a current spot price \( S_0 \), is given by:

Without Dividends

For a non-dividend-paying asset:

$$ F = S_0 \cdot e^{rT} $$

where:

• \( F \) - Forward price
• \( S_0 \) - Current spot price of the asset
• \( r \) - Risk-free interest rate
• \( T \) - Time to maturity (in years)
• \( e \) - Base of the natural logarithm

With Continuous Dividends

For an asset paying continuous dividends at a yield \( q \):

$$ F = S_0 \cdot e^{(r-q)T} $$

where:

• \( q \) - Continuous dividend yield

With Discrete Dividends

For an asset with discrete dividends, the formula modifies to account for the present value of the dividends \( D \):

$$ F = (S_0 - D) \cdot e^{rT} $$

Examples

Consider a non-dividend-paying stock:

Example 1: No Dividends

• Current spot price \( S_0 \): $50
• Risk-free interest rate \( r \): 5% per annum
• Time to maturity \( T \): 1 year

The forward price \( F \) can be calculated as:

$$ F = 50 \cdot e^{0.05 \cdot 1} \approx 50 \cdot 1.0513 = 52.565 $$

Thus, the forward price is approximately $52.57.

Example 2: With Continuous Dividends

• Spot price \( S_0 \): $100
• Risk-free rate \( r \): 4%
• Dividend yield \( q \): 2%
• Time to maturity \( T \): 0.5 years

$$ F = 100 \cdot e^{(0.04 - 0.02) \cdot 0.5} \approx 100 \cdot 1.01 = 101 $$

Thus, the forward price is $101.

Applications in Financial Markets

Forward prices are essential in various financial markets, including:

• Commodity Markets: Hedging against price fluctuations.
• Currency Markets: Locking in exchange rates.
• Interest Rate Markets: Managing interest rate exposure.
• Equity Markets: Speculating or hedging stock price movements.

Comparisons and Related Terms

• Spot Price: The current price of the underlying asset.
• Futures Price: Similar to the forward price, but in the context of futures contracts, which are standardized and traded on exchanges.
• Option Price: The price of an option, which includes premiums for the right but not the obligation to buy/sell the asset.

FAQs

What is the difference between a forward price and a futures price?

A forward price is agreed upon in over-the-counter (OTC) contracts, which are customizable but incur counterparty risk. A futures price pertains to standardized contracts on exchanges, which mitigate counterparty risk via clearinghouses.

How does the risk-free rate affect the forward price?

An increase in the risk-free rate typically raises the forward price, as the cost of carrying the asset to the future date is higher.

Can the forward price be lower than the spot price?

Yes, particularly if the asset pays significant dividends (negative yield) or if market conditions expect a price decline.

Summary

The forward price is a critical financial concept used to determine the future transaction price in forward contracts. It is based on current spot prices, adjusted for the cost of carry, risk-free interest rates, and potential dividends. This mechanism plays a pivotal role in various finance sectors, facilitating effective risk management and speculative strategies.

References

1. Hull, J. C. (2017). Options, Futures, and Other Derivatives. Pearson.
2. Chance, D. M., & Brooks, R. (2015). An Introduction to Derivatives and Risk Management. Cengage Learning.
3. McDonald, R. L. (2013). Derivatives Markets. Pearson.