Why Financial Price Models Use Cadlag Paths for Jumps

Summary

The document explains the intuition for modeling financial price paths as cadlag: right-continuous with left limits. Under this convention, a jump is observed as having happened at a particular time, while the path immediately before that time has a well-defined limiting value. The accepted answer presents jumps as surprises that are not known in advance, followed by a period in which another jump may not occur.

It connects this mathematical path property to discrete monitoring: observers checking prices at intervals may see the post-jump value without witnessing the transition itself. This is an intuition-building explanation, not a formal proof that all market prices follow cadlag paths. It also does not cover alternative path assumptions or the statistical evidence for jump models, so its claims should be read as a modeling rationale rather than a universal empirical law.

Key ideas

• Cadlag means a path is right-continuous and has left limits.
• The explanation treats jumps as unanticipated events rather than processes known to be underway.
• Discrete observations can reveal a jump's after-state without showing the transition.
• The discussion gives intuition for a modeling assumption rather than proving it empirically.

Tags

# Cadlag Property of Jump Proccesses


# Cadlag Property of Jump Proccesses












I've recently started studying Cont & Tankov's "financial modelling with jump processes". I'm curious as to why that this assumption of the cadlag property (also called RCLL "right continuous with left limits") for price paths is natural for the financial context?

## Answer by nbbo2 (score 7, accepted)

https://quant.stackexchange.com/a/35721

Intuitively, cadlag expresses the fact that we know a jump has occurred after the fact, but we never have advance knowledge that the jump is about to occur (i.e no knowledge of the starting point for the jump or that a jump is "under way"). Each jump is a surprise, after which we believe there will be no jumps at least for a little while.

I hear it in the trading room all the time: "WTF! I looked away from the screen for a few secs and the price just jumped up[down]!". That is exactly what discrete time monitoring of a c.t. cadlag process is like. Even if you "look very frequently" somehow you never really "see" the jump, only the after jump situation.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.