When we buy a Put option, we expect the price of the underlying asset to decrease.
(Answer: Correct. As the price in the market of the underlying asset goes down, and is lower than the exercise price of the option, so our gross profit on the option goes up. In the case of a Put option, the gross profit on the option is the difference between the exercise price and the market price. The lower the market price, so the gross profit increases. Note that it is impossible to make a negative profit.. If the exercise price is lower than the market, we simply will not exercise the option, and the gross profit will be $0).
2. Dan bought an option "May 100 P H", and paid a premium of $10K for it. At the end of May, the price of houses in the market is $110K. Thus Dan makes a loss on the option of $10K + $10Kpremium. In total Dan lost $20K.
(Answer: Incorrect. Dan bought a Put option, which gives him the right to sell the house at the exercise price of $100K. At the expiry date, the price of the houses is $110K. Thus Dan will not exercise the option, and his gross profit will be $0. However, Dan paid $10K for the option, and thus his net loss on the transaction as a whole is $10K.
3. The gross profit on a Call option is the market price less the exercise price, on condition that the difference is not negative. (If it is negative, the gross profit is $0, and no exercise will take place).
The gross profit on a Put option is the exercise price less the market price, on condition that the difference is not negative. (If it is negative, the gross profit is $0, and no exercise will take place).