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 £100per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, letSbe the price of the stock in a month. IfS is between £90and £110, the derivative is worth nothing to you. IfS 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 £2and 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?
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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 £100per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, letSbe the price of the stock in a month. IfS is between £90and £110, the derivative is worth nothing to you. IfS 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 £2and a standard deviation £10. Let P(big loss) be the
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