Only statement II is correct. In the context of options trading, the terms 'long' and 'short' are used to describe the positions that traders can take. A trader who buys an option is said to be 'long' on that option, while a trader who sells an option is said to be 'short' on that option. Therefore, the individual who holds a short position in a put option is indeed referred to as the seller of the option. This is because they have sold the right to sell the underlying asset at a specified price (the strike price) within a specified period. The seller of the option, therefore, has the obligation to buy the underlying asset if the option is exercised by the buyer. This statement accurately reflects the roles and terminologies associated with put options in financial markets.

Choice A is incorrect. The first statement is not accurate. The individual who holds a long position in a call option is known as the buyer, not the writer of the option. The writer or seller of an option is the one who has a short position.

Choice C is incorrect. As explained above, statement I is incorrect which makes this choice invalid as it suggests both statements are correct.

Choice D is incorrect. Statement II accurately describes that an individual holding a short position in a put option can be identified as the seller of the option, hence this choice suggesting none of the statements are correct, becomes invalid.