# Question: In the financial world there are many types of complex

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 $80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between $75 and $85, the derivative is worth nothing to you. If P is less than $75, the derivative results in a loss of 100*(75–P) dollars to you. If P is greater than $85, the derivative results in a gain of 100*(P–85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean $1 and standard deviation $8. Let P(big loss) be the probability that you lose at least $1000 (that is, the price falls below $65), and let P(big gain) be the probability that you gain at least $1000 (that is, the price rises above $95). Find these two probabilities. How do they compare to one another?

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