| There are two basic concepts in finance: time-value of money and uncertainty about expectations. |
在金融界有两个基本概念:资金的时间价值和预期的不确定性。 |
| The two concepts are the core of financial valuations, including futures contracts. |
这两个概念是财务估值的核心内容,涵盖期货合约。 |
| cost-of-carry model is the most widely accepted and used for pricing futures contract |
对于定价期货合约而言,持有成本模型是最被接受和广泛使用的模型 |
| Cost-of-carry Model |
持有成本模型 |
| Cost-of-carry model is an arbitrage-free pricing model. |
持有成本模型是一种无套利定价模型。 |
| Its central theme is that futures contract is so priced as to preclude arbitrage profit. |
它的中心主题是期货合同在扣除套利利润后定价。 |
| 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. |
换言之,无论投资者是在现货还是期货市场,对标的资产进行买卖将没有差别。因为他们获得的定价在实质上是相同的。 |
| Expectations do influence the price, but they influence the spot price and, through it, the futures price. |
预期确实会影响价格,但预期直接影响的是现货价格,从而影响期货价格。 |
| They do not directly influence the futures price. |
预期并不直接影响期货价格。 |
| 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,期货价格的计算公式是期货价格(Fp)=现货价格(Sp)+持有成本(Cc)-持有回报(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)是持有标的资产(购买自现货市场)直到期货合约到期日的利息成本。 |
| Carry return (CR) is the income (e.g., dividend) derived from underlying asset during holding period. |
持有回报(CR)是在持有期间从标的资产获得的收入(例如,分红)。 |
| 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)应该等价于现货价格(S)加上持有成本再减去持有回报。 |
| If it is otherwise, there will be arbitrage opportunities as follows |
否则,将出现如下的套利机会。 |
| 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,在现货市场买入标的资产并持有直到期货合约到期日。 |
| This is called "cash-and-carry" arbitrage. |
这种方式称为“买现卖期套利”。 |
| 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):买入(定价过低的)期货合约,在现货市场卖空标的资产并以卖空所得进行投资直到期货合约到期日。 |
| This is called "reverse cash-and-carry" arbitrage. |
这种方式称为“反向套利”。 |