Options trading and wash rule

However my understanding is that the wash rule applies here since the underlying security is the same for both.

The above is not correct. A wash sale occurs if you sell securities at a loss and buy substantially identical replacement shares within 30 days before or after the sale. A long put and a long call are not substantially identical because they are in directional opposition.

A long call would be substantially identical to long stock sold at a loss.

Selling a short put after selling long stock at a loss is a nebulous area since tax law is not clear. But suffice it to say that if it's deep in-the-money, it's a problem.

Last of all, if you incur a wash sale but close all of the positions within the same year, it's of no consequence. Yes, you have to adjust the cost basis of the replacement shares but all gains and losses are allowed in that tax year.

You need to have an open position for the wash sale rule to matter at all. The whole rationale for the wash sale rule is gains are taxed now, losses might be deductible now.

If you close a position with a loss, the loss can be deducted as long as you don't reopen the position within 30 days. If you do reopen the position within 30 days the loss, rather than being a tax loss, is used to adjust the cost basis of the open position.

A wash sale "disallowed" loss doesn't mean you never get to deduct the loss, it means you have to wait until the position has been closed for 30 days before you can deduct the loss.

In your situation, even if you assume these are substantially similar securities, the wash sale rule doesn't change your outcome. You lost $1,000, then you opened a new position within 30 days. The wash sale rules say you adjust the cost basis on the new position, from $3,000 to $4,000, so when you sold that position for $4,000 you have a gain of $0.

The primary reason that this rule exists is to stop people from selling a position that's being carried for a loss that they otherwise would keep in order to book a tax loss then immediately rebuying. So the rule makes you wait 30 days out of a position before you get to take a tax loss.