Dan has written an option “July 200 P H”, for $10K.

1. Does Dan expect an upward trend in the price of houses, or a downward trend?

2. What is the maximum amount that Dan can profit from the transaction? What is the maximum amount that Dan can lose from the transaction?

3. At what price of houses at the end of July (the expiry date) which will bring Dan into balance?

**Solution**

- From Graph 4, it can be seen that the lower the price at expiry, the writer of the Put option loses more. Both Graph A and Graph B go down, in other words lose, as the price at expiry falls (leftwards along the horizontal axis). The lower the price of the underlying asset at expiry, so the buyer of the Put option will sell the underlying asset to the writer of the option at a relatively high price. The buyer of the Put option profits and the writer of the Put option loses. (Options are a zero-sum game).

The writer of a Put option expects an increase in the price of the underlying asset

2. The writer of an option can make a profit on the transaction at the value of the premium, at a maximum, that he received for writing the option.

The writer’s profit is at a maximum, if the option is not exercised, at the value of the premium. Dan’s maximum profit on the transaction is $10K.

The writer of a Put option loses more as the price of the underlying price at expiry is lower. The maximum loss for the writer of a Put option is when the price of the underlying asset is 0, and the buyer of the option can sell it to Dan for $200K. Dan will lose $190K on the transaction as a whole. (The gross loss of $200K less the $10K received as the premium).

The maximum profit from writing the option is $10K, and the maximum loss from writing the option is $190K.

3. The break-even point is where Dan’s net profit on the transaction is zero. This happens when a gross loss is created at the exact level of the premium received. The premium was $10K, and thus for a market price at expiry of $190K, Dan will be in balance. For this market price for the house, Dan will make a gross loss on the option of $10K, which is exactly the premium he received. Dan’s total net profit from the transaction is 0.