A stock is priced at $48 per share. The volatility is 36% per year and the interest rate is 7% per year. Consider the following information on one-year options with a strike price of $45. Price Delta Gamma Theta Vega Rho Call Put 9.88 3.84 0.71 -0.29 0.0198 0.0198 -0.0130 -0.0047 0.1643 0.1643 0.2420 -0.1775 The theta is measured on a per day basis. The Greeks that measure the change in option price per change in interest rate or volatility are expressed in values per 1 percentage point change. a) Suppose a trader sold 50 calls. Assuming the stock price remained unchanged for one week, estimate the dollar profit on the position. (3 marks) b) Suppose a trader buys 50 put options. Estimate the change in the value of the position if the volatility increased from 36% to 40%