Scenarios · 7 min read
Why path dependence matters
The same starting and ending price can produce different perpetual-option economics.
Most payoff diagrams place final underlying price on the horizontal axis and profit or loss on the vertical axis. That view is useful, but it compresses an entire journey into one endpoint. For a path-dependent premium model, the missing journey can be the main economic event.
A strike is also a region of activity
In a theta-streaming approximation, premium accumulates fastest where option time value is most sensitive. For an at-the-money option, that often means the neighborhood around the strike. A path that repeatedly crosses or lingers in that region can accumulate more premium than a path that jumps through it quickly.
Imagine two 30-day paths:
- Path A rallies far above the strike, sells off, then returns to finish 8% higher.
- Path B slowly oscillates around the strike and also finishes 8% higher.
Their ending intrinsic value can be identical. Their streamed premium need not be.
Sampling is an assumption
A modeled path is discrete even when the intended mechanism is continuous. The distance between points determines which movements the model can observe. A daily path cannot see intraday crossings; an hourly path can. More samples improve resolution but do not turn a model into recorded market history.
The Lab's canned paths are deliberately illustrative. Direct point editing changes the path immediately, and Monte Carlo explores a distribution of synthetic paths using a reproducible seed. Neither should be interpreted as a forecast.
What to experiment with
Start with a streaming call at the strike. Choose Spike and revert, note cumulative premium, then drag the middle points away from the strike. Next choose Volatile chop and tighten the modeled range. The final price might barely change, while the cost profile changes substantially.
That gap between endpoint and journey is not a charting detail. It is the defining risk of a path-dependent instrument.