A trader with a net long position in a call option is not required to post margin by the Chicago Board Options Exchange (CBOE). This is because when a trader holds a net long position in an exchange-traded stock option, they have no potential future liability. These positions are often purchased upfront, and the option may or may not be exercised. Consequently, there is no reason for the exchange to require margin from a trader who holds a long position in a call option or a long position in a put option. The trader has already paid the premium for the option, which is the maximum amount they can lose. Therefore, the exchange does not require any additional margin from these traders.

Choice B is incorrect. A trader with a net short position in a put option is required to post margin according to the rules of the CBOE. This is because when you sell (or "write") a put option, you are obligated to buy the underlying asset at the strike price if the option holder decides to exercise their right. This exposes you to potential losses if the price of the underlying asset falls below the strike price, hence, margin is required as collateral for this risk.

Choice C is incorrect. Similarly, a trader with a net short position in a call option must also post margin according to CBOE rules. When selling call options, traders are obligated to sell an underlying asset at an agreed-upon price (the strike price) if called upon by an options holder. If market prices rise above this level, sellers face potential losses and therefore need to provide margin as security against these risks.

Choice D is incorrect. A trader who shorts stocks also needs to post margin according to CBOE regulations. Shorting involves borrowing shares and selling them with hopes that they can be bought back later at lower prices for profit; however, if share prices increase instead of falling as anticipated by short sellers, they would incur losses and thus need margins as protection against such adverse movements.