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远期合约,期货,期权等定价为什么要用连续复利?

2015-05-27 17:35阅读:
以前碰到远期合约,期货,期权等定价都要用连续复利,一直没去细想,最近在论坛看到个解释挺有意思。
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 contin
uous 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

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