Learn / Risk & ALM
Scenario generation
A scenario is a path for the risk factors. Scenario generation is how you produce that path: you type it, you reuse a historical path, or a model draws many paths. The paths then reprice assets and liabilities.
Drawing a path is not the same job as pricing a derivative. One asks what might happen. The other asks what price is consistent with the market’s no-arbitrage quotes.
01
Three ways to get a path
A deterministic scenario is a path you write down. The 10-year yield goes to 5% and stays there. There is no random draw. Stress tests and the shock lab are deterministic.
A historical scenario copies a path that already happened. You are reusing a record, not asking a model to invent a new crisis.
A stochastic scenario is a draw. A model with a drift, a width, and a random shock produces one path, then another, then thousands. The distribution of outcomes is the point. One pretty path is an illustration. Mean reversion means a rate that wanders is pulled back toward a level. A regime change means the drift or the width itself switches, as in a calm market becoming a stress market.
02
Which model draws which factor
Equity paths on this site use geometric Brownian motion: a drift and a volatility applied to a positive price. That lesson is stochastic processes. The Monte Carlo tool draws many of those paths for one long option.
Interest-rate paths in this track use a short rate. Hull–White pulls the overnight rate toward a level that can change with time. CIR ties the shock to the level of the rate so the draw is less willing to go negative. Heath–Jarrow–Morton writes the shock on the whole forward curve instead of on one overnight rate. Correlated scenarios draw the equity shock and the rate shock together, using a correlation like the one on the correlation page, including a correlation that is higher in a stress regime.
03
Real world and risk neutral
A real-world, or physical, scenario keeps a drift that is meant to describe outcomes you might actually see. Asset-liability projections, stress tests, and planning ranges use that kind of path. The question is “what might happen?”
A risk-neutral scenario replaces that drift with the rate that makes the model line up with quoted prices, so a derivative price is a discounted expected payoff with no leftover free lunch. The question is “what price matches the market?” The name does not mean anyone is personally indifferent to risk. The risk-neutral pricing lesson is the longer version. Use the real-world path for the risk report. Use the risk-neutral price for the option. Do not swap the two labels.