(a) Suppose that stock XYZ is trading at \(\$ 80.00\) on February 12 , and its price increases to \(\$ 83.00\) on February 14. This \(\$ 3.00\) increase will affect the price of options on the stock. Consider six different call options on the stock: the February 80 call, the February 95 call, the May 80 call, the May 95 call, the August 80 call, and the August 95 call. The prices of all of these call options will increase, but by different amounts. Which of these options will increase the most, which the second most, and so on? List these six options in the order of their price increases, from most increase to least. (Some of these will be indeterminate, but rank them anyway and state why you think the relative increases would be in the order you specify.)

(b) The "Greeks" are quantitative measures of the price movements of an option; in particular, the delta of an option is the relative change in price of an option to a small change in the price of an underlying. The delta of an at-the-money call option is usually of the order of 0.5, and the delta of an at-the-money put option is usually around -0.5 . A delta of a deep in-the-money option is usually close to 1 or -1 . Furthermore, as the time to expiry decreases, the delta of in-the-money options approach 1 in absolute value.

Suppose that stock XYZ is trading at \(\$ 80.00\) on February 12 . Suppose on February 12 that the price of the May 80 call is \(\$ 3.62\) (which gives an implied volatility of 0.23 ) with a delta of 0.533 (according to \(\mathrm{E}^{*}\) Trade), and suppose that the price of the May 80 put is \(\$ 3.50\) (which also gives an implied volatility of 0.23 ) with a delta of -0.475 (again according to E*Trade).

i. On February 14, the price of the stock increases to \(\$ 83.00\). What is the implied price of the May 80 call and the price of the May 80 put on February 14? Comment on the delta.

ii. On February 15 , the price of the stock drops to \(\$ 79.00\). What is the implied price of the May 80 call and the price of the May 80 put on February 14? Comment on the computational method.