为什么要使用连续复利？

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关键词：连续复利 复利

连续复利是指在期数趋于无限大的极限情况下得到的利率，此时不同期之间的间隔很短，可以看作是无穷小量。

我只知道算期权定价的时候用的比较多。比如B-S模型假设要求无风险利率必须是连续复利形式。

我们一般比较熟悉的是以年为单位计算的利率，但在期权以及其它复杂的衍生证券定价中，连续复利得到广泛的应用。因而，熟悉连续复利的计算是十分必要的。

有时候 在股票投资中，我们也以连续复利计息。

2# licheng47 你说的没错 可是老师出了个考试题目 为什么要使用连续复利 你说二不二 我该怎么回答

呵呵 这种题目一般是找找英文有没有答案

没有的话 先把定义答上 然后说下连续福利和离散福利的区别 所适用的模型等。

帮你找了专家答案了 来自 大牛David Harper, CFA, FRM, CIPM的回答：

This might be a very basic question but while valuing the forward contract why to use continuous compounding?



- It’s a good question. We don’t *need* to, really. But it is convenient for us, esp. in derivatives pricing, due to its properties; e.g., it is often easier to differentiate with the easy properties of the LN() and EXP() functions. Linda Allen (assigned Quant chapter) alludes to this when she notes continuous returns are “time consistent.” That is, they can be easily added. For example, 2% return in year 1, then 3% in year 2 = 5% over 2 years because EXP(2%)*EXP(3%)=EXP(5%). But, if those were instead annual compound frequency, (1.02)(1.03)>1.05. It goes a little further, as the product of the continuous returns, if normal, is also normal. But it is not the case for non-continous.

That said, for the FRM, we still want to be able to translate from continuous to the various compound frequencies. Hull does perform the forward/cost of carry models in continuous, as you suggest, but also to your point, the forward contract can alternatively be done in discrete compounding. Nothing wrong with that. Specifically, Hull computes implied forward interest rates with continuous but the FRM assigned on this topic is Tuckman and he uses semi-annual compounding b/c he does that for all bonds. So, our ideal (IMO) is to be able to switch from one to another, seeing them as but different frequencies (where continuous is the convergence).

Hope that helps, thanks truly for liking the videos.

David

4# licheng47 不会把 只要1句话到2句话就行啦 那人写的看不懂啊 这个是小概念题 写出关键就有分了 不用那么复杂的

眼角的伤痕 发表于 2011-4-5 12:12
4# licheng47 不会把 只要1句话到2句话就行啦 那人写的看不懂啊 这个是小概念题 写出关键就有分了 不用那么复杂的

you can summarize in one or two sentences..

因為時間是連續的不是間斷的 所以報酬也會是連續的話就會變成複利

就是说原因很简单，连续框架好处在于其模型容易用数学工具分析（随机积分），否则的话没人用这种“过于理想化”的模型

因为可以分到的钱更多，这是通过计算得出的