| There are two basic concepts in finance: time-value of money and uncertainty about expectations. |
金融学有两个基本概念——货币的时间价值和对于期望的不确定性。 |
| The two concepts are the core of financial valuations, including futures contracts. |
这两个概念是金融估值的核心，其中包括期货合约。 |
| cost-of-carry model is the most widely accepted and used for pricing futures contract |
持有成本模型最被广泛接受，并用于期货合约的定价。 |
| Cost-of-carry Model |
持有成本模型 |
| Cost-of-carry model is an arbitrage-free pricing model. |
持有成本模型是一种无套利的定价模型。 |
| Its central theme is that futures contract is so priced as to preclude arbitrage profit. |
其原理是使期货合约的定价足以排除套利利润。 |
| In other words, investors will be indifferent to spot and futures market to execute their buying and selling of underlying asset because the prices they obtain are effectively the same. |
换句话说，投资者将对现货和期货市场无动于衷，执行其相关资产的买卖，因为他们获得的价格实际上是相同的。 |
| Expectations do influence the price, but they influence the spot price and, through it, the futures price. |
期望会影响价格，但它们影响的是现货价格，因而影响期货价格。 |
| They do not directly influence the futures price. |
它们不会直接影响期货价格。 |
| According to the cost-of-carry model, the futures price is given by Futures price(Fp) = Spot Price(Sp) + Carry Cost(Cc) - Carry Return(Cr) (1) |
根据持有成本模型，期货价格是按照以下计算：
期货价格（Fp）=现货价格（Sp）+持有成本（Cc）-持有收益（Cr）（1） |
| Carry cost (CC) is the interest cost of holding the underlying asset (purchased in spot market) until the maturity of futures contract. |
持有成本（CC）是持有（在现货市场上购买的）资产直至期货合约到期之前的利息成本。 |
| Carry return (CR) is the income (e.g., dividend) derived from underlying asset during holding period. |
持有收益（CR）是持有资产期间从相关资产获得的收入（如：股息）。 |
| Thus, the futures price (F) should be equal to spot price (S) plus carry cost minus carry return. |
因此，期货价格（F）应等于现货价格（S）加上持有成本，减去持有收益。 |
| If it is otherwise, there will be arbitrage opportunities as follows |
不然就会出现以下的套利机会: |
| When F > (S + CC - CR): Sell the (overpriced) futures contract, buy the underlying asset in spot market and carry it until the maturity of futures contract. |
当F>（S + CC - CR）：卖出（定价过高的）期货合约，在现货市场买入相关资产，并持有至期货合约到期日。 |
| This is called "cash-and-carry" arbitrage. |
这被称为“现货持有”套利。 |
| When F < (S + CC - CR): Buy the (under priced) futures contract, short-sell the underlying asset in spot market and invest the proceeds of short-sale until the maturity of futures contract. |
当 F < (S + CC - CR)：购买（定价过低的）期货合约，在现货市场卖空相关资产，并投资卖空收益至期货合约到期。 |
| This is called "reverse cash-and-carry" arbitrage. |
这被称为“反向现货持有”套利。 |
