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 wo

A First Course in Probability (10th Edition)
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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?
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