Models

The models behind every simulation

Every Prometheus run is assembled from the models below, each calibrated to decades of real history and built to capture the skew and fat tails that ordinary bell-curve models miss. Here is the full roster, in plain English. For the end-to-end method, see the methodology.

Market & economic factors

Each tradable or economic driver gets its own model, calibrated to decades of history and built to capture the skew and fat tails that a plain bell curve misses.

Equity returns

A year of stock-market returns for the index you hold.

An AR-GARCH process reproduces real markets, volatility that clusters, and fat, skewed crash-and-rally tails. The shock distribution is chosen as the best fit among several fat-tailed distributions using statistical tests (e.g. BIC).

In the methodology →

Yield curves & bonds

How the government-bond yield curve can shift over a year, and the bond P&L that follows.

Principal-component analysis distils the whole curve into three interpretable moves - overall level, steepness, and curvature - each driven by a fat-tailed distribution fit to history. The reconstructed curve shock revalues your bonds by their duration.

In the methodology →

Inflation

How market-implied inflation can move, and what it does to your cost of living.

Two factors, level and slope, on the market-implied inflation curve, each with a fat-tailed distribution. The simulated one-year inflation level scales your household running costs in every path.

In the methodology →

Property

What a home could be worth a year from now.

A flexible fat-tail-aware distribution (EGB2) is fit to decades of regional house-price history, separating property’s excess return from the prevailing risk-free rate so the two move together as they do in reality.

In the methodology →

Private equity

How a private-equity holding moves over a year, beyond what listed markets do.

PE is projected onto the engine’s simulated equity factor with a higher beta in down markets than up markets, plus an idiosyncratic skewed shock for write-down risk, then recentred so its long-run return matches published private-equity benchmarks.

In the methodology →

Currencies (FX)

How a foreign-currency exposure can swing over a year.

The same AR-GARCH machinery as equities, applied to exchange-rate moves, capturing the volatility clustering and fat, sometimes one-sided tails of currency swings, then simulating thousands of month-by-month paths on your foreign holdings.

In the methodology →

The statistical core

Two building blocks sit under the factor models: the distributions that give them their fat tails, and the engine that ties every factor together.

Heavy-tailed distributions

The lopsided, fat-tailed shock distributions behind rates, inflation and property.

Rather than assume a bell curve, shocks are drawn from a fat-tailed distribution, for example an EGB2 or a Student’s t, with the family chosen per factor by how well it fits. It is why extreme moves aren’t quietly underestimated.

In the methodology →

Correlation engine

The web of dependence that links every factor in a single run.

Iman-Conover rank correlation locks the factors together, so a market crash and a job loss can strike together about as often as history says, while leaving each factor’s own distribution exactly intact. If you hand-edit the correlation matrix, a PSD repair quietly snaps it to the nearest mathematically valid one so the simulation never breaks.

In the methodology →

Risk & the simulation

The operational layer turns plain-language risk estimates into loss distributions; the wealth engine runs everything together a million times.

Operational & life risks

One-off shocks - job loss, fraud, a major bill - and the insurance that offsets them.

You give two plain-language estimates per risk, a typical bad event, a really bad one, and how often it happens. Those become a Monte-Carlo loss distribution (compound Poisson or Bernoulli for how often, lognormal or normal for how large). Your real policy limits and deductibles are then netted off, path by path, to leave the loss you’d actually bear.

In the methodology →

Wealth simulation engine

Your whole balance sheet, replayed a million times over the year ahead.

On top of every factor model sits the wealth engine: one million one-year paths of your finances - salary in (invested month by month via dollar-cost averaging), markets up or down, a possible shock - producing your full outcome distribution, your chance of ruin, your chance of simply ending behind, and your average worst-case (expected shortfall).

In the methodology →