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
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)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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