Delta Hedging and the Gap Risk Market Makers Retain

Summary

The document explains why delta hedging does not eliminate a market maker’s exposure to a large overnight move in the underlying stock. A hedge offsets the option’s current directional sensitivity, but a sudden price jump can change the option’s value before the position can be adjusted. The response identifies this residual exposure as gap risk.

It describes market making as a portfolio activity: losses on an individual trade may be offset by gains across many other trades, while the desk aims to keep the book’s Greeks reasonably balanced. A takeover-related example illustrates how unusually informed or urgent option buying ahead of news can cause losses. This is an anecdotal explanation, not a guarantee that diversified trading will recover losses; rare jumps can still be costly, and the document does not quantify their likelihood or describe specific controls.

Key ideas

• Delta hedging offsets an option’s current directional exposure but cannot prevent losses from sudden price gaps.
• Market makers refer to this residual jump exposure as gap risk.
• A market maker manages risk across a portfolio of trades and seeks to keep its Greeks balanced.
• Losses on particular positions may be offset by other trades, but this does not guarantee recovery from rare events.

Tags

# Delta Hedge, does large stock move produce a loss?


# Delta Hedge, does large stock move produce a loss?












I dont understand how MM protect themselves from large moves in underlying while being delta hedged. Example: MM sels 1 ATM put and sells 100stock (delta = 1) as a hedge. Now what will happen if next day stock shoots up? I can't imagine MM losing money on every such occasion, but I don't get how can they protect from it?

## Answer by JoshK (score 1, accepted)

https://quant.stackexchange.com/a/26375

That's the risk that MM's take, generally. This is commonly referred to as "gap risk". Holistically the idea is that with the law of large numbers you will lose sometimes but overall be OK as you have a large number of these trades.

On our MM desk we have seen a few times where big takeovers were preceded by someone in the market lifting 10k call contracts on all strikes of the acquiring name. Stinks when it happens but hopefully you make it back in a thousand other places.

You've heard that expression, "picking up nickels in front of a steamroller" ?

For the book as a whole the MM tries to keep all the greeks reasonably flat.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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