Matstat Econometrics Matan - page 34

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In essence, the non-universal nature of the win rate metric means that the equity model behind it is non-universal as a discrete SB. Therefore, it is common to use a continuous-time drift SB for equity, as a more universal model. There are two parameters here, drift and variance, so two independent metrics can be made. For example, it is the ratio of drift to the root of variance (Sharpe) and the ratio of drift to variance. Sharpe is convenient in that it does not change with changes in volume (but does change with changes in time interval, so it is usually annualised). The second metric does not change when the time interval changes (but it changes when the volume changes) and it is determinant when calculating the drawdown.

This equity model is not universal either. It cannot be used when the variance of increments is not limited - martingale, oversaturation, etc.

 
Aleksey Nikolayev #:

... usually for equity, as a more universal model, use a SB with demolition, with continuous time. ...

This equity model is also not absolutely universal. ...

However, it is desirable for equity to be calculated according to this model. At the very least, it is necessary for the portfolio of systems.

This leads to the emergence of auxiliary metrics that in some sense measure the fit of equity to this model. For example, these are the significance level that the drift is positive and/or the significance level that there is no correlation between the increments.

 
Isn't it all the same whether the time is discrete or continuous?)
Continuous can always be discretised and discrete can always be interpolated.
In DSP, for example, there is no difference.
 
secret #:
Doesn't it make the same difference whether the time is discrete or continuous?)
Continuous can always be discretised and discrete can always be interpolated.
In DSP, for example, there is no difference.

Yeah, you take the daily data, interpolate it and then discretise it into minute data) Who needs those ticks?)

 
Aleksey Nikolayev #:

Yeah, take the daily data, interpolate it and then discretise it into minute data) Who needs those ticks)

If you take daily data, it means you have an average transaction duration of about several months.
 
secret #:
If you take daily data, then you have an average transaction duration of the order of a few months.

Thus, DSP interpolation and sampling do not give the possibility of obtaining from one sampling another, e.g. a finer sampling.

The point of using continuous-time models is the potential possibility of obtaining any sampling of interest. Not necessarily uniform in time - equibrium, renko, etc. etc.

 
With ticks, you can get any discretisation you want. And there is no continuous time on the market.
 
secret #:
With ticks you can get any discretization you want. And there is no continuous time in the market.

Yes, technically time is discrete, but only because of the inaccuracy (or sufficient accuracy in practice) in its measurement (just like any other continuous physical quantity in real measurements). The price per unit of an asset, for example, is, by contrast, inherently discrete.

Nevertheless, in modern financial mathematics, continuous time models are basic.

 
Market time is discrete because the market flow of events is discrete - an order, a transaction.
 
Aleksey Nikolayev #:

Nevertheless, continuous time models are basic in modern financial mathematics.

I willingly believe so, but why is it necessary? It makes no sense to interpolate anything between two ticks, since what happens between ticks is determined by a more detailed discrete stream of events at Level2 and Level3.
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