| There are two basic concepts in finance: time-value of money and uncertainty about expectations. |
金融學中有兩個基本概念：貨幣的時間價值和預期的不確定性。 |
| The two concepts are the core of financial valuations, including futures contracts. |
這兩個概念是金融估值的核心，其中包括期貨合約。 |
| cost-of-carry model is the most widely accepted and used for pricing futures contract |
持有成本模型是最被廣泛接受和使用於期貨合約定價的模型。 |
| Cost-of-carry Model |
持有成本模型 |
| Cost-of-carry model is an arbitrage-free pricing model. |
持有成本模型是一種無套利定價模型。 |
| Its central theme is that futures contract is so priced as to preclude arbitrage profit. |
它的中心主旨是期貨合約的定價應該排除套利淨收益 |
| 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. |
換句話說，投資者對於在現貨和期貨市場來執行標的資產的買賣是中立的，因為他們獲得的價格實際上是相同的。 |
| Expectations do influence the price, but they influence the spot price and, through it, the futures price. |
預期確實會影響價格，但它們會影響現貨價格，並以此影響期貨價格。 |
| They do not directly influence the futures price. |
預期不會直接影響期貨價格 |
| 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) |
根據持有成本模型，期貨價格為： 期貨價格(Fp) = 現貨價格(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）是持有在現貨市場購買的標的資產直至期貨合約到期的利息成本。 |
| Carry return (CR) is the income (e.g., dividend) derived from underlying asset during holding period. |
持有收益（CR）是持有期間從標的資產中獲得的收入（例如股息）。 |
| Thus, the futures price (F) should be equal to spot price (S) plus carry cost minus carry return. |
因此，期貨價格（F）應等於現貨價格（S）加上持有成本減去持有收益。 |
| If it is otherwise, there will be arbitrage opportunities as follows |
否則，將存在如下套利機會 |
| 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. |
當F>(S+CC-CR)時：賣出（被高估的）期貨合約，在現貨市場買入標的資產並持有至期貨合約到期。 |
| This is called "cash-and-carry" arbitrage. |
這被稱為“正向套利”。 |
| 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. |
當F<(S+CC-CR)時：買入（被低估的）期貨合約，在現貨市場賣空標的資產，並將賣空收益投資至期貨合約到期。 |
| This is called "reverse cash-and-carry" arbitrage. |
這被稱為“反向套利”。 |
