A Poisson process models rare, random events occurring at a constant average rate — like market crashes that strike unpredictably at roughly the same annual probability regardless of when the last one occurred. Retirement Lab uses this to layer discrete black swan events on top of normal market volatility.
A Poisson process is a statistical model for events that occur randomly and independently at a constant average rate over time. In retirement simulation, it models black swan events — sudden, severe market shocks that occur at a fixed annual probability, independent of previous occurrences.
How It Works
The defining property of a Poisson process is memorylessness: the probability of an event occurring in any given period is constant, regardless of when the last event happened. A crash last year doesn't make a crash this year more or less likely.
In Retirement Lab's engine:
- A fixed annual probability is set for black swan events (e.g., 3%)
- Each simulated month, the engine generates a random number from the PRNG
- If the number falls below the monthly probability threshold, a crash event is triggered
- The crash applies a configurable negative shock to portfolio returns for that period
- Normal volatility continues independently
This approach layers discrete jump events on top of the continuous return distribution (normal or Student-t), capturing a different dimension of market risk than fat tails alone.
Why It Matters for Retirement Planning
The Poisson model captures an important feature of market crashes: they are discrete, sudden events rather than gradual moves. A 2008-style crisis isn't just a fat tail — it's a qualitatively different event that unfolds over weeks, not the kind of large monthly return that a fat-tailed distribution generates.
By combining Poisson-process crashes with fat-tailed return distributions, Monte Carlo simulation captures both types of tail risk: the general tendency of markets to produce larger moves than expected and the possibility of sudden, catastrophic shocks that can devastate a retirement portfolio through sequence-of-returns risk.
Frequently Asked Questions
- How does Retirement Lab model black swan events?
- Black swan events are modeled as a Poisson process with a configurable annual probability (e.g., 3-5% chance per year). In each simulated month, the engine rolls against this probability. If triggered, a large negative shock (e.g., -30% to -50%) is applied to the portfolio on top of normal market volatility. The events are independent — a crash this year doesn't change the probability next year.
- Why use a Poisson process instead of just making the distribution more fat-tailed?
- Fat tails and Poisson crashes capture different phenomena. Fat tails (via the Student-t distribution) model the general tendency of markets to produce larger moves than expected. Poisson events model discrete, identifiable shocks — sudden crashes that are qualitatively different from normal volatility. Combining both produces the most realistic simulation.