关于期货价格收敛到现货价格

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我在看Hull的第二章,里面说 期货价格收敛到现货价格, 他是用在"交割期"内用反证法 构造组合 套利得到的这个结论.
可是我怎么觉得他的推理"在任何时刻"都是成立的呢.

比如说现在是$t$, 资产价格 $S_t$, 期货价格 $F_t$.
那么$S_t=F_t$, 否则如果$S_t<F_t$, 那么卖出期货,买入资产,在到期日交割就可以,这样不就有套利了吗??

感觉有点荒谬, 但是不知道问题在哪里..

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关键词：期货价格 现货价格 期货价 资产价格 hull 反证法

The problem is you ignore the financing cost. At t<T, if you borrow St at r and buy St and hold it to T, your debt at time T will accumulate to Stexp(r*(T-t)), while you can only get Ft from selling St to the long party. Which means you loss Stexp(r*(T-t))-Ft (given r>0 and St=Ft). You can only say while Ft>Stexp(r*(T-t)) you will have arbitrage opportunity.

While doing arbitrage, you can not ignore the financing cost because you either borrow the money or you have the opportunity cost because you can earn r by just putting the money in the bank. Only when the arbitrage profit is higher than your financing cost, we consider this is an arbitrage because you take no risk but earn more than the risk free rate.

Chemist_MZ 发表于 2015-11-4 11:39
The problem is you ignore the financing cost. At t0 and St=Ft). You can only say while Ft&gt;Stexp(r*(T ...

谢谢 明白了