Q4. In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stock's current price is 100 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let S be the price

of the stock in a month. If S is between 90 and 110, the derivative is worth nothing

to you. If S is less than 90, the derivative results in a loss of 100*(90-S) to you.

(The factor of 100 is because many derivatives involve 100 shares.) If S is greater

than 110, the derivative results in a gain of 100*(S-110) to you. Assume that the

distribution of the change in the stock price from now to a month from now is normally

distributed with a mean 2 and a standard deviation 10. Let P(big loss) be the

probability that you lose at least 1,000 (that is, the price falls below 90), and let

P(big gain) be the probability that you gain at least 1,000 (that is, the price rises

above 110).

Find these two probabilities. How do they compare to one another?

[Instruction] In this exercise, describe the process of calculation. You should include

Excel functions used for the calculation. One thing to keep in mind is not to insert the screenshot

of the Excel screen.