远期与期货

期货（futures）是交易所交易的标准化合约；远期（forwards）是场外定制合约，因此更灵活。期货每天盯市结算，而远期通常在到期时一次性结算。

如果利率是确定的，二者的理论价格相同：

$$F = Se^{(r+u-y)\tau}$$

其中 $u$ 表示持有或储存成本，$y$ 对投资资产表示股息率、对商品表示便利收益、对外汇表示外币无风险利率。

当利率是随机的时，期货的每日盯市会使它和远期的价值出现差异。如果期货价格与利率正相关，那么做多期货时，盈利往往发生在利率较高的时候，这些盈利可以立刻按更高利率再投资；亏损则往往发生在利率较低的时候，融资成本也更低。

因此，当标的价格与利率强正相关且利率随机时，期货合约比远期合约更有价值，所以期货价格更高。

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Original Explanation

Futures contracts are exchange-traded standardized contracts; forward contracts are over-the-counter agreements so they are more flexible. Futures contracts are marked-to-market daily; forwards contacts are settled at the end of the contract term.

If the interest rate is deterministic, futures and forwards have the same theoretical price: $F = Se^{(r+u-y)\tau}$, where $u$ represents all the storage costs and $y$ represents dividend yield for investment assets, convenience yield for commodities and foreign risk-free interest rate for foreign currencies.

The mark-to-market property of future makes their values differ from forwards when interest rates vary unpredictably. As the life of a futures contract increases, the differences between forward and futures contracts may become significant. If the futures price is positively correlated with the interest rate, the increases of the futures price tend to occur the same time when interest rate is high.

Because of the mark-to-market feature, the investor who longs the futures has an immediate profit that can be reinvested at a higher rate. The loss tends to occur when the interest rate is low so that it can be financed at a low rate. So a futures contract is more valuable than the forward when its value is positively correlated with interest rates and the futures price should be higher.