1樓：Tonney
Good question.
The reason you would take the difference of log of price for equity is that the fundamental assumption for equity price evolving process is 'Geometric Brownian Motion'. Not the same for interest rate. (when variable x follows GBM, its log follows BM)
For interest rate (instant forward rate is the focus of modeling here), empirically, (as a commonly accepted assumption among the practitioners) the properties of its evolving process is characterized as:
When far from 0% or when 0% is not a benchmark anymore ( as in the case of Japan and Europe), interest rate tends to follow a Brownian Motion process.
As a result, the most simplistic model would be to assume it follows a * GBM + b * BM
where a and b are weights for respective process and is a function of the itself. This translates into some statistical differential functions. But this is not the only way to model it.
In trading, people use both terminologies at the same time, while specifying if the quote was 'black vol' (which is calculated using log diff) or 'normal vol' (which is calculated using difference). They are not inter-changeable but could be converted pretty easily given a curve and model parameters.
Hope it helps.
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