EVT Crash Gauge - indicator for MetaTrader 5

Overview

Almost every risk tool in the standard MetaTrader 5 toolbox shares one hidden assumption: that the worst loss worth planning for is roughly the worst loss you have already seen. Average True Range sizes positions from recent volatility. A Monte Carlo resampler reshuffles the trades you actually took. Historical Value at Risk reads a percentile straight off your return history. All of them look at the body of the distribution and quietly hope the future produces nothing more extreme than the past.

Financial returns are fat-tailed, so that hope is misplaced. Large moves happen more often and reach further than a normal distribution allows, and the single worst day in a sample is almost never the worst day the market is capable of. Any method that can only see losses as bad as the ones already in its window will systematically understate a rare crash.

The normal model (curve) versus real fat-tailed returns (histogram). The shaded left tail is the loss it misses.

This indicator brings the branch of statistics built for that gap into MQL5 natively. Extreme Value Theory does not model the whole distribution; it models only the tail, and it does so with a shape justified by a limit theorem rather than assumed. The fitted model can then extrapolate beyond anything in the sample: a 99.9% loss, a move seen roughly once every three years, a number your history never actually produced.

The method. The indicator implements Peaks-Over-Threshold. It converts the chart's closes into a one-sided downside-loss series, keeping the magnitude of every down move and mapping every up move to zero. It picks a high threshold u at a quantile of that series, discards everything below it, and studies only the exceedances, the amounts by which losses cross the threshold. The Pickands-Balkema-de Haan theorem states that for a wide class of underlying distributions those excesses converge, as the threshold rises, to a single family: the Generalized Pareto Distribution. So the tail's shape does not have to be guessed, only fitted.

Peaks-Over-Threshold: a threshold is set on the loss series, the exceedances above it are peeled off, and a Generalized Pareto Distribution is fitted to those excesses alone.

The fit is a genuine maximum-likelihood optimisation of the GPD's shape and scale, run through the ALGLIB constrained optimiser shipped with the terminal. There is no Python bridge, no DLL, and no external dependency of any kind.

What It Reports

Three numbers are computed on a rolling window and shown on an on-chart panel, with the first of them also plotted as a line in a sub-window so the tail can be watched tightening and loosening over time.

The two estimators are the standard GPD-POT forms, so what the panel reports is exactly:

VaR_p = u + (sigma / xi) * [ ( (Nu / n) / (1 - p) )^xi - 1 ]
ES_p  = VaR_p / (1 - xi) + (sigma - xi * u) / (1 - xi)

Here u is the threshold, sigma and xi are the fitted scale and shape, and Nu / n is the exceedance rate. Both have an exponential limit that is used automatically when the fitted shape sits close to zero, which keeps the arithmetic stable in exactly the regime where dividing by the shape would not be.

The tail traffic light. The panel colours the shape so the regime can be read without interpreting a number:

Those cutoffs are reading aids rather than statistical thresholds, and they can be shifted to taste. What matters is that the same shape driving the colour is the shape driving the formulas, so the panel cannot show green while the arithmetic is quietly computing a fat-tailed VaR.

The gauge on a chart: the panel reports VaR, Expected Shortfall, and the colour-coded tail shape, while the sub-window plots the EVT VaR over time.

It Refuses to Guess

This is the design decision worth knowing before you attach it, because it changes what a blank reading means. A two-parameter tail fit needs a real number of exceedances to be trustworthy, and the EVT literature treats roughly thirty to fifty tail points as the practical floor. The engine enforces thirty. Below that it reports its status rather than a figure, and the panel says so in plain words:

A concrete example of this in action: at the default 0.95 threshold, a 500-bar lookback yields only about twenty-five exceedances, and the gauge reports insufficient tail data (25/30 exceedances) instead of a number. At 800 bars it clears the floor and fits cleanly. That is not a bug to work around, it is the model declining to guess, which is precisely the behaviour you want from a tool whose entire purpose is honesty about rare events.

The same principle applies at the other end. When the fitted shape reaches one the mean of the tail diverges and Expected Shortfall stops existing, so the engine returns zero there rather than a fabricated figure. Wherever a fit does not earn the OK status the plotted line is left blank for that bar rather than carrying a stale value forward, so the line is empty exactly where the model declined to commit.

Recommended Setup

Input Parameters

Using the Engine in Your Own Code

The tail model is a standalone header-only class, CGPDModel, with no dependency on charts or indicator buffers. It fits an array of losses where larger simply means worse, so the sign convention stays the caller's, and any strategy that can produce a loss series can use it directly:

#include <EVT\GPDModel.mqh>

CGPDModel model;
model.SetThresholdQuantile(0.95);

if(model.Fit(losses,count) && model.IsReliable())
  {
   double var = model.VaR(0.99);
   double es  = model.ExpectedShortfall(0.99);
   double xi  = model.Xi();
  }
else
   Print("tail not usable: ",model.StatusText());

Alongside those, the class exposes the fitted scale, the threshold it selected, the exceedance count, and the status enumeration, so a consumer can log or display exactly why a reading was withheld. To read the indicator instead of the class, acquire a handle with iCustom on EVT\EVTCrashGauge and copy buffer 0, which carries the EVT VaR and holds zero on any bar where the fit was not reliable.

Limitations

EVT earns its place in a risk toolkit, but it is a specialised instrument and using it well means knowing where it does not apply:

• It is hungry for tail data. A two-parameter tail fit needs a meaningful number of exceedances. On a thinly traded symbol or a short window the right answer is "insufficient data", and the design honours that rather than inventing a number.
• It is sensitive to the threshold. The 0.95 default is standard, but the fitted shape and scale do shift with it. A serious deployment would study that sensitivity rather than trust one setting, which is why the quantile is exposed as an input.
• It measures magnitude, not timing. Worth repeating because it is the most common misuse. A rising tail index is not a directional signal.
• The tail can stop being well defined. As the fitted shape approaches one, Expected Shortfall ceases to exist, and a zero in that regime is itself information rather than a failure.

File Structure

One indicator and one header. The header is included as <EVT\GPDModel.mqh>, so it must sit in its EVT subfolder under Include.

The engine seeds the optimiser with a method-of-moments estimate before running maximum likelihood, and constrains the shape to a sane box, so a pathological window pushes it toward a rejected fit rather than toward a plausible-looking wrong one.

Research Basis

The implementation follows the standard Peaks-Over-Threshold treatment of Extreme Value Theory: the Pickands-Balkema-de Haan theorem for the convergence of threshold excesses to the Generalized Pareto Distribution, maximum-likelihood estimation of its shape and scale, and the usual GPD-POT expressions for Value at Risk and Expected Shortfall.

A companion article derives the method, walks through the engine and the indicator line by line, and wires the tail estimate into a position-sizing Expert Advisor to measure what it does in the Strategy Tester: Extreme Value Theory in MQL5: Building a Tail-Risk Crash Gauge Beyond Monte Carlo VaR.