# Question

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?

## Answer to relevant Questions

When you sum 30 or more independent random variables, the sum of the random variables will usually be approximately normally distributed, even if each individual random variable is not normally distributed. Use this fact to ...The time it takes you to swim 100 yards in a race is normally distributed with mean 62 seconds and standard deviation 2 seconds. In your next five races, what is the probability that you will swim under a minute exactly ...Many states supplement their tax revenues with state-sponsored lotteries. Most of them do so with a game called lotto. Although there are various versions of this game, they are all basically as follows. People purchase ...A decision d is said to be dominated by another decision D if, for every outcome, the payoff from D is better than (or no worse than) the payoff from d.a. Explain why you would never choose a dominated decision using the ...Explain in words what information a two-way sensitivity chart, such as the one in Figure 6.27, provides. Demonstrate how you could provide this same information without Precision Tree’s sensitivity tools, using only data ...Post your question

0