Options dividend ex date question

Assume a customer holds 1 ABC Oct 60 Put contract. The market price of ABC is currently $60. On an ex-date with a dividend of $4, the new market price is $56. The contract is still a ABC Oct 60 put correct? The strike and multiplier do not change? So what happens to the premium? Does it just jump up around $4 (there's still time value so it's probably around $4, not exactly)? Why is this? What's the logic?

Sorry I'm studying for my series 56 and my book doesn't have a clearer explanation.

I know for stock dividends, the contract stays the same. But why does it stay the same for cash dividends?

 

The strike/multiplier do not change due to a regular dividend as it is a know/antcipated event. The market will have already factored that in to the price and therefore should not jump up $4. (or decrease if a call)

If there is a special dividend announced, you will usually see a change in the strike or multiplier to adjust accordingly. Again does not result in a sudden price increase (or decrease if a call)

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