5 4 3 2 1 st) 0 - 1 -2 -3 -4 -5 0 1 2 3 4 5 6 7 8 9 10 11 t FIGURE 1. Graph of S'(t) for Problem 3 Problem 3. (20 points) Let S(t) be the price of a certain stock at time t. Figure 1 above is the graph of the rate of change of the stock price over 11 seconds. At time t = 0 the stock price was $10 (per share). (a) Over what time sub-interval(s) is the stock dropping? (b) Find the stock price at the end of the 11 second time interval. You are free to calculate this as you wish but, as for everything, you must clearly show your reasoning. (c) We are interested in the volatility of the stock, that is, how much the stock is changing over this 11 second time interval- whether moving up or down. Define the Volatility of the stock, V(t), at time t, to be the amount the stock price has gone up plus the amount the stock price has gone down over the first t seconds. For example, if over the first t seconds the stock moved up by 2 points and then down by 3, then V(t) = 2+3 = 5. Find V(11), the Volatility at the end of the 11 second time interval, for the stock described by Figure 1. Again, you are free to calculate this as you wish, but you must clearly explain your reasoning. 5 4 3 2 1 st) 0 - 1 -2 -3 -4 -5 0 1 2 3 4 5 6 7 8 9 10 11 t FIGURE 1. Graph of S'(t) for Problem 3 Problem 3. (20 points) Let S(t) be the price of a certain stock at time t. Figure 1 above is the graph of the rate of change of the stock price over 11 seconds. At time t = 0 the stock price was $10 (per share). (a) Over what time sub-interval(s) is the stock dropping? (b) Find the stock price at the end of the 11 second time interval. You are free to calculate this as you wish but, as for everything, you must clearly show your reasoning. (c) We are interested in the volatility of the stock, that is, how much the stock is changing over this 11 second time interval- whether moving up or down. Define the Volatility of the stock, V(t), at time t, to be the amount the stock price has gone up plus the amount the stock price has gone down over the first t seconds. For example, if over the first t seconds the stock moved up by 2 points and then down by 3, then V(t) = 2+3 = 5. Find V(11), the Volatility at the end of the 11 second time interval, for the stock described by Figure 1. Again, you are free to calculate this as you wish, but you must clearly explain your reasoning