1. Consider the following table displaying the bid-ask prices for all options on the OEX index passed on January 10, 2002, at 9:46. These options have February 22, 2002, expiry and at the time of data collection, the underlying was at 589.14. Calls Bid Ask Vol Puts Bid Ask Vol Feb 400 188.9 191.9 0 Feb 400 0.05 0.2 0 Feb 420 169 172 0 Feb 420 0.1 0.4 0 Feb 440 149.2 152.2 0 Feb 440 0.25 0.55 0 Feb 460 129.4 132.4 0 Feb 460 0.45 0.75 0 Feb 480 109.6 112.6 0 Feb 480 0.8 1.1 0 Feb 500 90.2 92.7 0 Feb 500 1.4 1.7 0 Feb 520 71 73.5 0 Feb 520 2.5 2.8 0 Feb 530 61.6 64.1 0 Feb 530 2.8 3.5 0 Feb 540 52.4 54.9 0 Feb 540 3.7 4.4 0 Feb 550 43.8 45.8 0 Feb 550 4.9 5.6 1 Feb 560 35.4 37.4 0 Feb 560 6.6 7.3 0 Feb 570 27.9 29.4 0 Feb 570 8.9 9.6 0 Feb 580 20.8 22 0 Feb 580 11.8 12.8 0 Feb 590 14.8 15.8 0 Feb 590 15.8 16.8 1 Feb 600 10 10.7 1 Feb 600 20.8 22 0 Feb 610 6.1 6.8 0 Feb 610 27.1 28.6 0 Feb 615 4.6 5.3 0 Feb 615 31 32 0 Feb 620 3.4 4.1 0 Feb 620 34.3 36.3 0 Feb 630 1.9 2.2 0 Feb 630 42.8 44.8 0 Feb 640 0.9 1.2 0 Feb 640 52 54 0 Feb 650 0.4 0.7 0 Feb 650 61.4 63.9 0 Feb 660 0.15 0.45 0 Feb 660 71.2 73.7 0 Feb 680 0 0.25 0 Feb 680 90.8 93.8 0 Feb 700 0 0.2 100 Feb 700 110.8 113.8 0

(a) Using the out-of-the-money ask prices for the puts, calculate the implied volatility for the relevant strikes. Plot the volatility smile against K/S.

(b) Using the out-of-the-money bid prices for the puts, calculate the implied volatility for the relevant strikes. Plot the volatility smile against K/S. Are the bid-ask spreads for these vols constant?

(c) Using the out-of-the-money ask prices for the calls, calculate the implied vol for the relevant strikes. Plot the volatility smile against K/S. When you put this figure together with the out-of-the-money put volatilities, do you obtain a smile or a skew?