The following option prices were observed for a stock on July 6 of a particular year. Use this information for the following problems. Unless otherwise indicated, ignore dividends on the stock. The stock is priced at: 165.13 The expirations and associated risk free rates for each term are: Date Rate 17-Jul 0.0516 21-Aug 0.055 16-Oct 0.0588 Calls Puts Strike Jul Aug Oct Jul Aug Oct 155 10.50 11.80 14.00 0.20 1.25 2.75 160 6.00 8.10 11.10 0.75 2.75 4.50 165 2.70 5.20 8.10 2.35 4.70 6.70 170 0.80 3.20 6.00 5.80 7.50 9.00 Compute the interinsic values, time values and lower bounds of the following calls. Identify any profit opportunities that may exist. Treat these as American options for purposes of determining the interinsic vlaues and time values and European options for the purposes of determining lower bounds. T (1 + r)^-T Intrinsic Value Time Value Lower bound of European Call July 160 0.0301 0.998 5.13 0.87 5.130 October 155 0.2795 0.984 10.13 3.87 12.585 August 170 0.1260 0.993 - 3.20 - NOTE: add extra columns as you see fit, however, please make the last 3 columns of your work the ones as shown for intrinsic value, time value and lower bound. Compute the interinsic values, time values and lower bounds of the following puts. Identify any profit opportunities that may exist. Treat these as American options for purposes of determining the interinsic vlaues and time values and European options for the purposes of determining lower bounds. (1 + r)^-T Intrinsic Value Time Value Lower bound of European Put July 165 0.9985 - 2.35 - August 160 0.9933 - 2.75 - October 170 0.9842 4.87 4.13 2.18 NOTE: add extra columns as you see fit, however, please make the last 3 columns of your work the ones as shown for intrinsic value, time value and lower bound. Check the following combinations of puts and calls, and determine whether they conform to the put-call parity rule for European options. If you see any violations, suggest a strategy. P + S C + PV(X) Difference July 155 165.330 165.265 0.06 August 160 167.880 167.024 0.86 October 170 174.130 173.307 0.82 NOTE: add extra columns as you see fit, however, please make the last 3 columns of your work the ones as shown for P+S, C + PV(X) and Difference You do not need a complex strategy explanation. Simply observe if there is an arbitrage opportunity. If the opportunity exists, use one of the strike prices as an example and explain what you would do to make a risk free profit, and say what that risk free profit would be. CE + X(1+r)-T= PE + S0 165.33 is not equal to 165.265 Thus the parity equation is not equal for all options. Examine the following paies of calls, which differ only by exercise price. Determine whether any violate the rules regarding relationships between American options that differ only by exercise price. State the rule(s), then examine whether the pair of calls violates the rule(s) a) August 155 and 160 b) October 160 and 165 Rules: Examine the following pairs of puts, which differ only by exercise price. Determine if any violate the rules regarding relationships between American options that differ only by exercise price. a) August 155 and 160 b) October 160 and 170 Rules

The following option prices were observed for a stock on July 6 of a particular year. Use this information for the following problems. Unless otherwise indicated, ignore dividends on the stock. The stock is priced at: 165.13 The expirations and associated risk free rates for each term are: 11 102 46 Date 17-Jul 21-Aug 16-Oct Strike 155 160 165 170 1 Rate 0.0516 0.055 0.0588 Jul 10.50 6.00 2.70 0.80 Calls Aug 11.80 8.10 5.20 3.20 Oct 14.00 11.10 8.10 6.00 Jul 0.20 0.75 2.35 5.80 Puts Aug 1.25 2.75 4.70 7.50 Oct 2.75 4.50 6.70 9.00 Compute the interinsic values, time values and lower bounds of the following calls. Identify any profit opportunities that may exist. Treat these as American options for purposes of determining the interinsic vlaues and time values and European options for the purposes of determining lower bounds. Points 2 2 2 T (1 + r)^-T 0.0301 0.998 0.2795 0.984 0.1260 0.993 July 160 October 155 August 170 Intrinsic Value 5.13 10.13 - Time Value 0.87 3.87 3.20 8.75 Lower bound of European Call 5.130 12.585 - There is no profitable oppurtunity NOTE: add extra columns as you see fit, however, please make the last 3 columns of your work the ones as shown for intrinsic value, time value and lower bound. 2 Compute the interinsic values, time values and lower bounds of the following puts. Identify any profit opportunities that may exist. Treat these as American options for purposes of determining the interinsic vlaues and time values and European options for the purposes of determining lower bounds. 2 2 2 July 165 August 160 October 170 (1 + r)^-T 0.9985 0.9933 0.9842 Intrinsic Value 4.87 Lower bound Time of European Value Put 2.35 2.75 4.13 2.18 The is no profitable oppurtunity NOTE: add extra columns as you see fit, however, please make the last 3 columns of your work the ones as shown for intrinsic value, time value and lower bound. Check the following combinations of puts and calls, and determine whether they conform to the put-call 3 parity rule for European options. If you see any violations, suggest a strategy. 2 2 2 1 2 3 July 155 August 160 October 170 P + S C + PV(X) 165.330 165.265 167.880 167.024 174.130 173.307 Difference 0.06 0.86 0.82 NOTE: add extra columns as you see fit, however, please make the last 3 columns of your work the ones as shown for P+S, C + PV(X) and Difference You do not need a complex strategy explanation. Simply observe if there is an arbitrage opportunity. If the opportunity exists, use one of the strike prices as an example and explain what you would do to make a risk free profit, and say what that risk free profit would be. 3 CE + X(1+r)-T= PE + S0 4 165.33 is not equal to 165.265 Thus the parity equation is not equal for all options. Examine the following paies of calls, which differ only by exercise price. Determine whether any violate the rules regarding relationships between American options that differ only by exercise price. State the rule(s), then examine whether the pair of calls violates the rule(s) a) August 155 and 160 b) October 160 and 165 2 Rules: 5 Examine the following pairs of puts, which differ only by exercise price. Determine if any violate the rules regarding relationships between American options that differ only by exercise price. a) August 155 and 160 b) October 160 and 170 2 25 Rules 1 2 3 Buy Call & Bond, Short Put & Stock Buy Call & Bond, Short Put & Stock Buy Call & Bond, Short Put & Stock