In fact, these two problems are summarized as follows:
In the first case, when the index is higher than or equal to 10200, neither the sold put option nor the bought put option is executed, and the profit and loss is the income of the sold put option minus the cost of the bought put option;
In the second case, when the index is less than 10200, but greater than or equal to 10000, the sold put option is not executed, and the bought put option is executed. The profit and loss is the income of the put option you sell plus the option value of the put option you buy to exercise the option minus the cost of the put option you buy.
In the third case, when the index is less than 10000, the actual profit is as follows. Because the put option sold will be executed below 10000, it will offset the income of the put option originally bought below 10000 (the income between 10000 and 10200 will not be affected), that is, the index is 10000.
Obviously, according to the analysis and summary of the three situations, it is not difficult to see that when the index is equal to or less than 10000, the investor's profit is the largest, and the largest profit and loss is the actual profit and loss, that is, the option value obtained by selling the put option plus the option value obtained by exercising at 10000 minus the cost of buying the put option itself.
According to the above analysis, it is not difficult to see that the result of the first question should be150+(10200-10000)-120 = 230. Obviously, none of the four answers is correct, and the result of the second question according to the original intention is 120.
Personal estimation is that the answer to the first question is the result of B. If the value of the sold put option is 150, the cost swap of the bought put option becomes 120 of the sold put option and 150 of the bought put option. According to these data, the calculation result should be