什么是远期价格

What is forward price

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A forward price is a price agreed upon by a buyer and seller in a forward contract for a predetermined delivery price of an underlying commodity, currency, or financial asset that will be paid at a determined date in the future. At the beginning of a forward contract, the forward price makes the value of the contract zero, but changes in the price of the underlying asset will make the forward price appear positive or negative.

The formula for calculating the forward price is as follows:

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Basic concepts of forward prices

The forward price is based on the current spot price of the underlying asset, plus any carrying costs such as interest, storage costs, unearned interest and other charges including opportunity costs.

Although a contract has no intrinsic value at its inception, it may gain or lose value over time. Hedging positions in forward contracts amounts to a zero-sum game. For example, if one investor holds a long position in a pork futures contract and another investor holds a short position, any gain on the long position will be equal to the second investor's loss on the short position. By setting the initial value of the contract to zero, both parties are equal at the outset of the contract.

Key Points

• A forward price is the price at which the seller delivers the underlying asset, financial derivative or currency to the buyer on a predetermined date.
• The forward price is roughly equal to the spot price plus related holding costs, such as storage costs, interest rates, etc.
• Investors may wish to lock in forward prices to hedge against future market fluctuations.
• The disadvantage of locking in a forward price is that the value of the asset may adversely affect the investor.

Forward price calculation example

When the underlying asset in the forward contract does not pay any dividends, the forward price can be calculated using the following formula:

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For example, assume a security is currently trading at $100 per unit. An investor wishes to enter into a forward contract that expires in one year. The current risk-free annual interest rate is 6%. Using the above formula, the calculated forward price is:

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106.18 \ \end{aligned} $$

If there are carrying costs, this will be added to the formula:

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Here, q is the holding cost.

If the underlying asset pays dividends during the life of the contract, the formula for the forward price is:

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Here, D is equal to the sum of the present values of each dividend, calculated as:

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Continuing with this example, assume that the security pays a 50-cent dividend every three months. First, calculate the present value of each dividend:

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0.493 \ \end{aligned} $$

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0.485 \ \end{aligned} $$

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0.478 \ \end{aligned} $$

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0.471 \ \end{aligned} $$

The sum of these present values is $1.927. That amount is then plugged into the dividend-adjusted forward price formula:

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1.927 ) \times e ^ { ( 0.06 \times 1 ) } = $104.14 \ \end{aligned} $$

What is the difference between forward price and spot price?

Investors may want to lock in forward prices to hedge against future market fluctuations. For example, a farmer may want to enter into a forward wheat contract before harvest to protect against future price drops due to a bumper harvest or other factors.

What are the disadvantages of locking in forward prices?

The main disadvantage of locking in a forward price is that the value of the asset may adversely affect the investor, resulting in losses compared to selling at the spot price when the asset is delivered. In addition, forward contracts with longer maturities increase the risk of nonpayment or default.

What are the main factors affecting the forward price of assets?

Investors determine the forward price of an asset based on the asset's current spot price plus holding costs such as storage, transportation, opportunity costs, and unearned interest. Typically, carrying costs are higher in forward contracts with longer expiration dates.

Conclusion

The forward price is the future delivery price of the asset agreed between the buyer and seller in the forward contract. Such contracts have zero value when established because market conditions have not yet changed. Investors determine the forward price by adding the spot price of the underlying asset to the cost of holding it. Using forward prices in futures contracts provides a hedge against market fluctuations, but it can also be a double-edged sword if the value of the asset moves adversely to the investor.

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远期价格的基本概念

远期价格建立在基础资产当前现货价格的基础上，加上任何持有成本，例如利息、存储成本、未收利息以及包括机会成本在内的其他费用。

虽然合约在成立之初没有内在价值，但随着时间推移，合约可能会获得或失去价值。远期合约中的对冲头寸等同于零和游戏。例如，如果一位投资者在猪肉期货合约中持有多头头寸，而另一位投资者持有空头头寸，多头头寸的任何收益将等于第二位投资者因空头头寸产生的损失。通过将合约的初始价值设为零，双方在合约成立之初是平等的。

关键要点

• 远期价格是卖方在预定日期向买方交付基础资产、金融衍生品或货币的价格。
• 远期价格大致等于现货价格加上相关的持有成本，如存储成本、利率等。
• 投资者可能希望锁定远期价格，以对冲未来市场波动的风险。
• 锁定远期价格的缺点是资产的价值可能会对投资者产生不利影响。

远期价格计算示例

当远期合约中的基础资产不支付任何股息时，远期价格可以使用以下公式计算：

$\begin{aligned} &F = S \times e ^ { (r \times t) } \\ &\textbf{其中:} \\ &F = \text{合约的远期价格} \\ &S = \text{基础资产的当前现货价格} \\ &e = \text{近似为2.7183的数学无理常数} \\ &r = \text{适用于远期合约存续期的无风险利率} \\ &t = \text{以年份计的交付日期} \\ \end{aligned}$

远期价格是买卖双方在远期合约中商定的，针对基础商品、货币或金融资产的预定交付价格，该价格将在未来某个确定的日期支付。在远期合约成立之初，远期价格使合约的价值为零，但基础资产价格的变动将使远期价格呈现正或负值。

远期价格的计算公式如下：

\begin{aligned} &F = \$100 \times e ^ { (0.06 \times 1) } = \$106.18 \\ \end{aligned} $$$100 \times e ^ { (0.06 \times 1) } = \$106.18 \\ \end{aligned}

如果有持有成本，这将被加入公式中：

$\begin{aligned} &F = S \times e ^ { (r + q) \times t } \\ \end{aligned}$

远期价格的基本概念

远期价格建立在基础资产当前现货价格的基础上，加上任何持有成本，例如利息、存储成本、未收利息以及包括机会成本在内的其他费用。

虽然合约在成立之初没有内在价值，但随着时间推移，合约可能会获得或失去价值。远期合约中的对冲头寸等同于零和游戏。例如，如果一位投资者在猪肉期货合约中持有多头头寸，而另一位投资者持有空头头寸，多头头寸的任何收益将等于第二位投资者因空头头寸产生的损失。通过将合约的初始价值设为零，双方在合约成立之初是平等的。

关键要点

• 远期价格是卖方在预定日期向买方交付基础资产、金融衍生品或货币的价格。
• 远期价格大致等于现货价格加上相关的持有成本，如存储成本、利率等。
• 投资者可能希望锁定远期价格，以对冲未来市场波动的风险。
• 锁定远期价格的缺点是资产的价值可能会对投资者产生不利影响。

远期价格计算示例

当远期合约中的基础资产不支付任何股息时，远期价格可以使用以下公式计算：

$\begin{aligned} &F = ( S - D ) \times e ^ { ( r \times t ) } \\ \end{aligned}$

这里，D等于每个股息现值的总和，计算方法为：

$\begin{aligned} D =& \ \text{PV}(d(1)) + \text{PV}(d(2)) + \cdots + \text{PV}(d(x)) \\ =& \ d(1) \times e ^ {- ( r \times t(1) ) } + d(2) \times e ^ { - ( r \times t(2) ) } + \cdots + \\ \phantom{=}& \ d(x) \times e ^ { - ( r \times t(x) ) } \\ \end{aligned}$

例如，假设某证券当前交易价格为每单位100美元。一位投资者希望签订一份于一年后到期的远期合约。当前的无风险年利率为6%。使用上述公式，计算的远期价格为：

\begin{aligned} &\text{PV}(d(1)) = \$0.5 \times e ^ { - ( 0.06 \times \frac { 3 }{ 12 } ) } = \$0.493 \\ \end{aligned} $$$0.5 \times e ^ { - ( 0.06 \times \frac { 3 }{ 12 } ) } = \$0.493 \\ \end{aligned}

\begin{aligned} &\text{PV}(d(2)) = \$0.5 \times e ^ { - ( 0.06 \times \frac { 6 }{ 12 } ) } = \$0.485 \\ \end{aligned} $$$0.5 \times e ^ { - ( 0.06 \times \frac { 6 }{ 12 } ) } = \$0.485 \\ \end{aligned}

\begin{aligned} &\text{PV}(d(3)) = \$0.5 \times e ^ { - ( 0.06 \times \frac { 9 }{ 12 } ) } = \$0.478 \\ \end{aligned} $$$0.5 \times e ^ { - ( 0.06 \times \frac { 9 }{ 12 } ) } = \$106.18 \\ \end{aligned}

如果有持有成本，这将被加入公式中：

\begin{aligned} &\text{PV}(d(4)) = \$0.5 \times e ^ { - ( 0.06 \times \frac { 12 }{ 12 } ) } = \$0.471 \\ \end{aligned} $$$0.5 \times e ^ { - ( 0.06 \times \frac { 12 }{ 12 } ) } = \$0.471 \\ \end{aligned}

这些现值的总和为1.927美元。然后将该金额代入调整股息的远期价格公式中：

$$ \begin{aligned} &F = ( $100 - $1.927 ) \times e ^ { ( 0.06 \times 1 ) } = $104.14 \ \end{aligned} $$$100 - $

此处，q为持有成本。

如果基础资产在合约存续期间支付股息，则远期价格的公式为：