SECOND CITY OPTIONS: A Case Study on Index Options[1]

Don M. Chance and Michael L. Hemler

(Version: August 30, 2011)

Second City Options (SCO) is a small firm that specializes in option trading. Employing 35 people, SCO is located on LaSalle Street in the Chicago financial district. It is a member firm of the Chicago Board Options Exchange (CBOE), where it trades options on stocks and stock indices. It is also a member firm of the Chicago Mercantile Exchange Group (CME Group), where it trades options on futures and the underlying futures contracts.

SCO trades for itself and a number of corporate and individual clients. In addition, it provides general advice to other clients who trade for themselves. SCO was founded in 1975, two years after the CBOE opened. It was very successful for its first 25 years, but its profits have declined steadily since 2000. SCO's founder and principal owner, Joseph Jensen, is 67 years old and has been a life-long student of the stock market. Jensen has traded since he was a teenager. By the age of 30 he was a millionaire and an acknowledged expert on analyzing market trends.

Throughout his career Jensen has relied primarily on technical analysis, the evaluation of trends in past market data such as prices and volumes. He has consistently devised option strategies to take advantage of his stock market forecasts. Over the last several years, however, his techniques have grown less profitable. Jensen attributes his declining success to the growing competitiveness of the options market, which has made it increasingly difficult for SCO to implement its trading strategies at attractive prices.

Worried that his firm's techniques were becoming outmoded, Jensen has conferred recently with his chief trading executive, Bill Harrison, to analyze the situation and discuss possible solutions. Harrison believes that better implementation of option pricing techniques would improve SCO's trading profits. In particular, there would be two potential benefits for SCO: it could improve its historical strategy of trading based on stock market forecasts, and it could explore other trading opportunities related to option mispricing. Consequently, SCO has significantly upgraded and modernized its computer system. Furthermore, it has hired Carla Shilling, a derivatives specialist who recently graduated from a major Midwestern business school. Her mandate is to improve the firm's trading profits by utilizing her expertise in option valuation.

The Market Outlook

Before making any recommendation regarding strategies, Shilling must finalize her opinion of how the economy and stock market will perform over the next few months. The date is July 2, 2007. Over the last six months the S&P 500 has ranged from 1374.12 to 1539.18, closing at 1503.35 at the end of June. Investors seem worried about an impending credit crunch, even though problems at two Bear Stearns hedge funds that own collateralized debt obligations (CDOs) based on subprime mortgage debt appear to be contained. The economy has slowed with consumer pessimism high, reflecting a weak housing market combined with credit worries. For the last two months personal income has declined after adjusting for inflation. The Federal Reserve has focused on rising inflation. The Federal Open Market Committee, the Fed's policy-setting arm, left interest rates unchanged in its June 27?28 meeting, keeping the Fed funds target level at 5.25% for the ninth time in the past twelve months. Despite inflation fears, the Federal Reserve did not raise interest rates due to concern that rate hikes would ripple out to home mortgages and hurt borrowers already struggling to make mortgage payments. Economists differ widely in their optimism or pessimism regarding the overall economy. There is no consensus, for example, on whether the stock market will increase or decrease during the next few months. Economists do agree in one key respect, however ? they believe there is a large and increasing degree of uncertainty regarding future economic and market behavior.

SCO's Trading Committee meets weekly to determine the firm's outlook regarding the overall economy and the stock market. Shilling attended the most recent meeting, and she left that meeting holding the same opinion as the vast majority of her colleagues. There was a strong general belief that market volatility was relatively high, yet it might climb even higher than expected in the near future.

Analysis of Index Option Strategies

For her first task, Shilling must investigate option strategies that can exploit her firm's consensus opinion regarding stock market uncertainty.

Part I

Identify two option strategies that take advantage of high or increasing market volatility. Examine each strategy for both S&P 500 index (SPX) and S&P 100 index (OEX) options. Use data provided in Table 1 of SCO-Data.xls.[2] At this stage consider only strategies in which all options are held to expiration. If more than one expiration date is possible, use only options with the nearest expiration date, which is August 18, 2007. Also, use options that are at-the-money or closest to at-the-money. Discuss the advantages and disadvantages of each strategy.

Provide profit diagrams for each strategy and index using the spreadsheet Stratlyz8e.xls. Let Exhibits 1 and 2 correspond to the first strategy and Exhibits 3 and 4 correspond to the second strategy. These exhibits should contain basic information such as the name of the strategy and index, the maximum profit and maximum loss, and breakeven points.

Shilling knows that if she presents these results to SCO's management without further analysis, she will be told to come back later when she can provide something more useful. She realizes that she must use valuation methods to strengthen her analysis and support her recommendation. She knows that she can use the Black-Scholes-Merton model for SPX options, which are European-style options. She must use another approach, however, to price OEX options, which are American-style options. Moreover, she will need a volatility estimate for each index.

Part II

Table 2 of SCO-Data.xls contains daily data for the first six months of 2007 for both the SPX and OEX indices.[3] Using this data estimate historical volatility for each index to four decimal places, e.g., 0.1234 or 12.34%. For your base estimates, calculate volatility using daily observations for the entire six month period. Then for comparison purposes, calculate historical volatilities over the first three months, the last three months, and all six months combined using both daily and weekly data.[4] Using the Excel spreadsheet Hisv9e.xls, report these estimates in Exhibit 5. Are these estimates sensitive to the choice of time period or observational frequency?

Estimate implied volatility for each index to four decimal places. For these estimates use data in Tables 1 and 3 of SCO-Data.xls.[5] Restrict your attention to the six call and put options expiring on August 18, 2007, that are at-the-money or closest to at-the-money. Use Excel spreadsheets such as BSMbin9e.xls or BSMImpVol9e.xls. Give your implied volatility estimates in Exhibit 6. Recall that the Black-Scholes-Merton model can be used for the SPX estimate, but not for the OEX estimate. Thus, you must use your best judgment in order to estimate implied volatility for OEX. Whatever methodology you use, explain it clearly.

Discuss the advantages and disadvantages of historical estimates versus implied estimates. Then provide one final volatility estimate for each index and explain your reasoning.

Shilling knows that she will ultimately have to use an American option pricing model for the OEX index. She has software for the Binomial model that allows up to 1000 time periods. She knows that this model will capture the early exercise value of an American option. She also knows that if both the Binomial and Black-Scholes-Merton models are appropriate in a given situation, then the price from the Binomial model will converge to the price from the Black-Scholes-Merton model as the number of time periods increases to infinity.

Part III

Consider the S&P 500 call option that has the shortest time to expiration and is closest to at-the-money. Calculate the theoretical option price based on the Black-Scholes-Merton model. Define n as the number of time periods in the Binomial model, and let n equal 1, 5, 10, 25, 50, 100, 500, and 1000. For each value of n, calculate the corresponding theoretical option price from the Binomial model. Use BSMbin9e.xls to obtain the prices for both models.

To obtain a call price C from the Binomial model, one needs five parameters: n, u, d, r, and p. These represent the number of periods, the binomial up factor, the binomial down factor, the risk-free rate, and the risk neutral probability, respectively. Construct a table that shows how the values of u, d, r, p, and C change as n varies. Note that the software BSMbin9e.xls does not report values for u, d, r, and p as n varies; it reports only values of C. Calculate the changing values of u, d, r, and p using the formulae in Chapter 4 of An Introduction to Derivatives and Risk Management, 8^th edition or higher, by Don M. Chance and Robert Brooks, which also contains a table, Table 4.2, similar to the one requested here. Call this table Exhibit 7 and discuss your findings.

Shilling must now identify which individual options appear overpriced or underpriced. She must then use that information to determine whether her recommended strategies are priced attractively.

Part IV

Using appropriate pricing models and final volatility estimates from Part II, calculate theoretical prices for all options utilized in the strategies recommended in Part I. Determine whether each individual option is overpriced, underpriced, or fairly priced. Present your results in Exhibit 8.

Using the information just obtained for individual options, determine which, if any, strategies recommended in Part I are mispriced. Present your results in Exhibit 9.

Identify the one strategy and index that seems most attractive of the four possibilities considered. Explain your reasoning.

Harrison, who has been monitoring Shilling's work, has been impressed by her analysis. He knows, however, that the firm rarely holds a position until all options in the strategy expire. Noting that Shilling has concentrated on strategies held to expiration, he mentions that there is another strategy ? one in which not all options expire ? commonly used in situations where one expects high or increasing volatility.

Part V

Identify the strategy to which Harrison refers. Examine this strategy using SPX and OEX options that are at-the-money or closest to at-the-money. Some, but not all, of the options used in this strategy can expire on the nearest expiration date, which is August 18, 2007. Provide Exhibits 10 and 11 for this strategy similar to Exhibits 1 and 2 in Part I.

In terms of pricing, how does this strategy compare to the two strategies analyzed in Part IV? If you must recommend one strategy and index from all those investigated in Parts IV and V, what do you recommend and why?

[1]This case is an updated and revised version of Second City Options Case, by Don M. Chance (1997). Although it can easily be used with virtually any derivatives text, it has been written to accompany the 8^th and higher editions of An Introduction to Derivatives and Risk Management, by Don M. Chance and Robert Brooks. The computer software files Stratlyz9e.xls, Hisv9e.xls, BSMbin9e.xls, and BSMImpVol9e.xls (8e = 8^th edition, 9e = 9^th edition, etc.) mentioned in this case are available at the www.cengage.com website for this text. Instructors and students who adopt this text can use them freely.

[2]The option data in Table 1 of SCO-Data.xls are from Market Data Express.

[3]The stock index data in Table 2 of SCO-Data.xls are from the Chicago Board Options Exchange (CBOE) at www.cboe.com/LearnCenter/pricehistory.xls.

[4]In calculating volatilities use the following conventions: For daily calculations use all 124 daily index observations over six months. This yields 123 daily returns. Use the first 60 returns to estimate volatility for the first three months. Use the last 63 returns to estimate volatility for the last three months. For weekly calculations begin with the first Friday in the data, January 5, 2007, and go to the last Friday in the data, June 29, 2007. This yields 25 weekly returns. The first 12 returns correspond to the first three months, and the last 13 returns correspond to the last three months. Because there is no observation on Friday, April 6, replace it with the preceding day?s observation.

[5] The stock index return data in Table 3 of SCO-Data.xls are from the Center for Research in Security Prices (CRSP). The interest rate data are from Federal Reserve Economic Data (FRED) at www.research.stlouisfed.org. The daily dividend estimates calculated in Table 3 are not actual forecasts of daily dividends that could be made on July 2, 2007, which are what one should use as inputs for the option pricing models. One reason is that the SPX dividend estimates in Table 3 consist of realized, not estimated, dividends for the dates in question. They are calculated using SPX returns from CRSP. Another reason is that when estimating the OEX dividends in Table 3, the percentage of total return due to dividends for SPX proxies for the analogous percentage of total return due to dividends for OEX. The rationale is that SPX returns, unlike OEX returns, are directly available from CRSP. To obtain accurate dividend estimates in practice, proprietary market making firms such as Chicago Trading Company (a lead market maker for SPX and OEX options at the CBOE) utilize financial information services companies such as Markit. For the illustrative purposes of this case, however, the dividend estimates in Table 3 suffice.

SECOND CITY OPTIONS: A Case Study on Index Options1 Don M. Chance and Michael L. Hemler (Version: May 28, 2015) Second City Options (SCO) is a small firm that specializes in option trading. Employing 35 people, SCO is located on LaSalle Street in the Chicago financial district. It is a member firm of the Chicago Board Options Exchange (CBOE), where it trades options on stocks and stock indices. It is also a member firm of the Chicago Mercantile Exchange Group (CME Group), where it trades options on futures and the underlying futures contracts. SCO trades for itself and a number of corporate and individual clients. In addition, it provides general advice to other clients who trade for themselves. SCO was founded in 1975, two years after the CBOE opened. It was very successful for its first 25 years, but its profits have declined steadily since 2000. SCO's founder and principal owner, Joseph Jensen, is 67 years old and has been a life-long student of the stock market. Jensen has traded since he was a teenager. By the age of 30 he was a millionaire and an acknowledged expert on analyzing market trends. Throughout his career Jensen has relied primarily on technical analysis, the evaluation of trends in past market data such as prices and volumes. He has consistently devised option strategies to take advantage of his stock market forecasts. Over the last several years, however, his techniques have grown less profitable. Jensen attributes his declining success to the growing competitiveness of the options market, which has made it increasingly difficult for SCO to implement its trading strategies at attractive prices. Worried that his firm's techniques were becoming outmoded, Jensen has conferred recently with his chief trading executive, Bill Harrison, to analyze the situation and discuss possible solutions. Harrison believes that better implementation of option pricing techniques would improve SCO's trading profits. In particular, there would be two potential benefits for SCO: it could improve its historical strategy of trading based on stock market forecasts, and it could explore other trading opportunities related to option mispricing. Consequently, SCO has significantly upgraded and modernized its computer system. Furthermore, it has hired Carla Shilling, a derivatives specialist who recently graduated from a major Midwestern business school. Her mandate is to improve the firm's trading profits by utilizing her expertise in option valuation. The Market Outlook Before making any recommendation regarding strategies, Shilling must finalize her opinion of how the economy and stock market will perform over the next few months. The date is July 2, 2007. Over the last six months the S&P 500 has ranged from 1374.12 to 1539.18, closing at 1503.35 at the end of June. Investors seem worried about an impending credit crunch, even though problems at two Bear Stearns hedge funds that own collateralized debt obligations (CDOs) based on subprime mortgage debt appear to be contained. The 1This case is an updated and revised version of Second City Options Case, by Don M. Chance (1997). Although it can easily be used with virtually any derivatives text, it has been written to accompany the 8th and higher editions of An Introduction to Derivatives and Risk Management, by Don M. Chance and Robert Brooks. The computer software files BlackScholesMertonBinomial10e.xlsm, BlackScholesMertonImpliedVolatility10e.xlsm, OptionStrategyAnalyzer10e.xlsm, and HistoricalVolatility10e.xlsm mentioned in this case are available at the www.cengage.com website for this text. Instructors and students who adopt this text can use them freely. Version: 5/28/15 SCO Case (Chance-Hemler) p. 1 of 4 economy has slowed with consumer pessimism high, reflecting a weak housing market combined with credit worries. For the last two months personal income has declined after adjusting for inflation. The Federal Reserve has focused on rising inflation. The Federal Open Market Committee, the Fed's policy-setting arm, left interest rates unchanged in its June 27-28 meeting, keeping the Fed funds target level at 5.25% for the ninth time in the past twelve months. Despite inflation fears, the Federal Reserve did not raise interest rates due to concern that rate hikes would ripple out to home mortgages and hurt borrowers already struggling to make mortgage payments. Economists differ widely in their optimism or pessimism regarding the overall economy. There is no consensus, for example, on whether the stock market will increase or decrease during the next few months. Economists do agree in one key respect, however they believe there is a large and increasing degree of uncertainty regarding future economic and market behavior. SCO's Trading Committee meets weekly to determine the firm's outlook regarding the overall economy and the stock market. Shilling attended the most recent meeting, and she left that meeting holding the same opinion as the vast majority of her colleagues. There was a strong general belief that market volatility was relatively high, yet it might climb even higher than expected in the near future. Analysis of Index Option Strategies For her first task, Shilling must investigate option strategies that can exploit her firm's consensus opinion regarding stock market uncertainty. Part I a) Identify two option strategies that take advantage of high or increasing market volatility. Examine each strategy for both S&P 500 index (SPX) and S&P 100 index (OEX) options. Use data provided in Table 1 of SecondCityOptionsCase_Data10e.xlsx. 2 At this stage consider only strategies in which all options are held to expiration. If more than one expiration date is possible, use only options with the nearest expiration date, which is August 18, 2007. Also, use options that are at-the-money or closest to at-themoney. Discuss the advantages and disadvantages of each strategy. b) Provide profit diagrams for each strategy and index using the spreadsheet OptionStrategyAnalyzer10e.xlsm. Let Exhibits 1 and 2 correspond to the first strategy and Exhibits 3 and 4 correspond to the second strategy. These exhibits should contain basic information such as the name of the strategy and index, the maximum profit and maximum loss, and breakeven points. For consistency in these diagrams (and elsewhere throughout this case), use the average of the last bid and ask prices for a given option as the price for that option. Discuss the advantages and disadvantages of using bid-ask midpoints versus bids, asks, or transaction prices. Shilling knows that if she presents these results to SCO's management without further analysis, she will be told to come back later when she can provide something more useful. She realizes that she must use valuation methods to strengthen her analysis and support her recommendation. She knows that she can use the BlackScholes-Merton model for SPX options, which are European-style options. She must use another approach, however, to price OEX options, which are American-style options. Moreover, she will need a volatility estimate for each index. Part II a) Table 2 of SecondCityOptionsCase_Data10e.xlsx contains daily data for the first six months of 2007 for both the SPX and OEX indices.3 Using this data estimate historical volatility for each index to four decimal places, e.g., 0.1234 or 12.34%. For your base estimates, calculate volatility using daily observations for the 2The option data in Table 1 of SecondCityOptionsCase_Data10e.xlsx are from Market Data Express. stock index data in Table 2 of SecondCityOptionsCase_Data10e.xlsx are from the Chicago Board Options Exchange (CBOE) at www.cboe.com/LearnCenter/pricehistory.xls. 3 The Version: 5/28/15 SCO Case (Chance-Hemler) p. 2 of 4 entire six month period. Then for comparison purposes, calculate historical volatilities over the first three months, the last three months, and all six months combined using both daily and weekly data.4 Using the Excel spreadsheet HistoricalVolatility10e.xlsm, report these estimates in Exhibit 5. Are these estimates sensitive to the choice of time period or observational frequency? b) Estimate implied volatility for each index to four decimal places. For these estimates use data in Tables 1 and 3 of SecondCityOptionsCase_Data10e.xlsx. 5 Restrict your attention to the six call and put options expiring on August 18, 2007, that are at-the-money or closest to at-the-money. Use Excel spreadsheets such as BlackScholesMertonBinomial10e.xlsm or BlackScholesMertonImpliedVolatility10e.xlsm. Give your implied volatility estimates in Exhibit 6. Recall that the Black-Scholes-Merton model can be used for the SPX estimate, but not for the OEX estimate. Thus, you must use your best judgment in order to estimate implied volatility for OEX. Whatever methodology you use, explain it clearly. c) Discuss the advantages and disadvantages of historical estimates versus implied estimates. Then provide one final volatility estimate for each index and explain your reasoning. Shilling knows that she will ultimately have to use an American option pricing model for the OEX index. She has software for the Binomial model that allows up to 1000 time periods. She knows that this model will capture the early exercise value of an American option. She also knows that if both the Binomial and BlackScholes-Merton models are appropriate in a given situation, then the price from the Binomial model will converge to the price from the Black-Scholes-Merton model as the number of time periods increases to infinity. Part III a) Consider the S&P 500 call option that has the shortest time to expiration and is closest to at-the-money. Calculate the theoretical option price based on the Black-Scholes-Merton model. Define n as the number of time periods in the Binomial model, and let n equal 1, 5, 10, 25, 50, 100, 500, and 1000. For each value of n, calculate the corresponding theoretical option price from the Binomial model. Use the Excel spreadsheet BlackScholesMertonBinomial10e.xlsm to obtain the prices for both models. b) To obtain a call price C from the Binomial model, one needs five parameters: n, u, d, r, and p. These represent the number of periods, the binomial up factor, the binomial down factor, the risk-free rate, and the risk neutral probability, respectively. (In this scenario, however, one must also incorporate dividends.) Construct a table that shows how the values of u, d, r, p, and C change as n varies. Note that the software BlackScholesMertonBinomial10e.xlsm does not report values for u, d, r, and p as n varies; it reports only 4In calculating volatilities use the following conventions: For daily calculations use all 124 daily index observations over six months. This yields 123 daily returns. Use the first 60 returns to estimate volatility for the first three months. Use the last 63 returns to estimate volatility for the last three months. For weekly calculations begin with the first Friday in the data, January 5, 2007, and go to the last Friday in the data, June 29, 2007. This yields 25 weekly returns. The first 12 returns correspond to the first three months, and the last 13 returns correspond to the last three months. Because there is no observation on Friday, April 6, replace it with the preceding day's observation. 5 The stock index return data in Table 3 of SecondCityOptionsCase_Data10e.xlsx are from the Center for Research in Security Prices (CRSP). The interest rate data are from Federal Reserve Economic Data (FRED) at www.research.stlouisfed.org. The daily dividend estimates calculated in Table 3 are not actual forecasts of daily dividends that could be made on July 2, 2007, which are what one should use as inputs for the option pricing models. One reason is that the SPX dividend estimates in Table 3 consist of realized, not estimated, dividends for the dates in question. They are calculated using SPX returns from CRSP. Another reason is that when estimating the OEX dividends in Table 3, the percentage of total return due to dividends for SPX proxies for the analogous percentage of total return due to dividends for OEX. The rationale is that SPX returns, unlike OEX returns, are directly available from CRSP. To obtain accurate dividend estimates in practice, proprietary market making firms such as Chicago Trading Company (a lead market maker for SPX and OEX options at the CBOE) utilize financial information services companies such as Markit. For the illustrative purposes of this case, however, the dividend estimates in Table 3 suffice. Version: 5/28/15 SCO Case (Chance-Hemler) p. 3 of 4 values of C. Calculate the changing values of u, d, r, and p using the formulae in Chapter 4 of An Introduction to Derivatives and Risk Management, 10th edition, by Don M. Chance and Robert Brooks, which also contains a table, Table 4.2, similar to the one requested here. Call this table Exhibit 7 and discuss your findings. Shilling must now identify which individual options appear overpriced or underpriced. She must then use that information to determine whether her recommended strategies are priced attractively. Part IV a) Using appropriate pricing models and final volatility estimates from Part II, calculate theoretical prices for all options utilized in the strategies recommended in Part I. Determine whether each individual option is overpriced, underpriced, or fairly priced. Present your results in Exhibit 8. b) Using the information just obtained for individual options, determine which, if any, strategies recommended in Part I are mispriced. Present your results in Exhibit 9. c) Identify the one strategy and index that seems most attractive of the four possibilities considered. Explain your reasoning. Harrison, who has been monitoring Shilling's work, has been impressed by her analysis. He knows, however, that the firm rarely holds a position until all options in the strategy expire. Noting that Shilling has concentrated on strategies held to expiration, he mentions that there is another strategy one in which not all options expire commonly used in situations where one expects high or increasing volatility. Part V a) Identify the strategy to which Harrison refers. Examine this strategy using SPX and OEX options that are at-the-money or closest to at-the-money. Some, but not all, of the options used in this strategy can expire on the nearest expiration date, which is August 18, 2007. Provide Exhibits 10 and 11 for this strategy similar to Exhibits 1 and 2 in Part I. b) In terms of pricing, how does this strategy compare to the two strategies analyzed in Part IV? If you must recommend one final strategy and index from all six of the combinations investigated in Parts IV and V, what do you recommend and why? Version: 5/28/15 SCO Case (Chance-Hemler) p. 4 of 4 Table 1: STOCK INDEX OPTION DATA FOR JULY 2, 2007 OBSERVATION DATE EXPIRATION DATE STOCK INDEX CALL OR PUT STRIKE PRICE VOLUME 20070702 20070702 20070702 20070702 20070702 20070702 20070818 20070818 20070818 20070818 20070818 20070818 OEX OEX OEX OEX OEX OEX C P C P C P 695 695 700 700 705 705 12 26 50 21 2 0 20070702 20070702 20070702 20070702 20070702 20070702 20070922 20070922 20070922 20070922 20070922 20070922 OEX OEX OEX OEX OEX OEX C P C P C P 690 690 700 700 710 710 0 113 61 0 0 0 20070702 20070702 20070702 20070702 20070702 20070702 20070818 20070818 20070818 20070818 20070818 20070818 SPX SPX SPX SPX SPX SPX C P C P C P 1515 1515 1520 1520 1525 1525 205 87 82 108 1615 2256 20070702 20070702 20070702 20070702 20070702 20070702 20070922 20070922 20070922 20070922 20070922 20070922 SPX SPX SPX SPX SPX SPX C P C P C P 1515 1515 1520 1520 1525 1525 0 2 108 85 11077 10381 LAST TRADE LAST BID LAST ASK INDEX VALUE 17.9 11.9 14.3 13.1 10.0 17.3 10.6 14.1 12.6 11.3 14.5 18.7 11.6 15.2 13.4 12.3 15.6 699.49 699.49 699.49 699.49 699.49 699.49 26.7 13.2 20.2 16.8 14.5 20.7 28.4 14.1 21.6 17.7 15.7 22.1 699.49 699.49 699.49 699.49 699.49 699.49 33.6 27.0 34.5 30.4 30.0 30.0 36.1 25.2 32.9 27.0 29.9 28.9 38.1 27.2 34.9 29.0 31.9 30.9 1519.43 1519.43 1519.43 1519.43 1519.43 1519.43 36.6 46.4 41.0 41.0 41.0 49.8 33.8 46.6 35.5 43.5 37.3 51.8 35.8 48.6 37.5 45.5 39.3 1519.43 1519.43 1519.43 1519.43 1519.43 1519.43 14.1 19.8 Table 2: DAILY STOCK INDEX VALUES FOR FIRST HALF OF 2007 DATE 3-Jan-2007 4-Jan-2007 5-Jan-2007 8-Jan-2007 9-Jan-2007 10-Jan-2007 11-Jan-2007 12-Jan-2007 16-Jan-2007 17-Jan-2007 18-Jan-2007 19-Jan-2007 22-Jan-2007 23-Jan-2007 24-Jan-2007 25-Jan-2007 26-Jan-2007 29-Jan-2007 30-Jan-2007 31-Jan-2007 1-Feb-2007 2-Feb-2007 5-Feb-2007 6-Feb-2007 7-Feb-2007 8-Feb-2007 9-Feb-2007 12-Feb-2007 13-Feb-2007 14-Feb-2007 15-Feb-2007 16-Feb-2007 20-Feb-2007 21-Feb-2007 22-Feb-2007 23-Feb-2007 26-Feb-2007 27-Feb-2007 28-Feb-2007 1-Mar-2007 2-Mar-2007 5-Mar-2007 6-Mar-2007 7-Mar-2007 8-Mar-2007 9-Mar-2007 12-Mar-2007 13-Mar-2007 14-Mar-2007 15-Mar-2007 16-Mar-2007 19-Mar-2007 20-Mar-2007 21-Mar-2007 22-Mar-2007 23-Mar-2007 26-Mar-2007 27-Mar-2007 28-Mar-2007 29-Mar-2007 30-Mar-2007 2-Apr-2007 3-Apr-2007 4-Apr-2007 5-Apr-2007 9-Apr-2007 10-Apr-2007 11-Apr-2007 12-Apr-2007 13-Apr-2007 16-Apr-2007 17-Apr-2007 18-Apr-2007 19-Apr-2007 20-Apr-2007 23-Apr-2007 SPX 1416.60 1418.34 1409.71 1412.84 1412.11 1414.85 1423.82 1430.73 1431.90 1430.62 1426.37 1430.50 1422.95 1427.99 1440.13 1423.90 1422.18 1420.62 1428.82 1438.24 1445.94 1448.39 1446.99 1448.00 1450.02 1448.31 1438.06 1433.37 1444.26 1455.30 1456.81 1455.54 1459.68 1457.63 1456.38 1451.19 1449.37 1399.04 1406.82 1403.17 1387.17 1374.12 1395.41 1391.97 1401.89 1402.85 1406.60 1377.95 1387.17 1392.28 1386.95 1402.06 1410.94 1435.04 1434.54 1436.11 1437.50 1428.61 1417.23 1422.53 1420.86 1424.55 1437.77 1439.37 1443.76 1444.61 1448.39 1438.87 1447.80 1452.85 1468.47 1471.48 1472.50 1470.73 1484.35 1480.93 OEX 660.29 661.00 657.50 659.15 657.89 658.35 661.64 665.67 666.03 665.20 664.04 665.38 662.41 664.12 669.94 661.34 660.35 659.55 662.79 666.78 668.89 669.59 669.21 668.91 668.46 667.16 663.18 661.02 665.82 670.21 669.73 668.84 670.05 668.40 667.22 664.01 663.38 639.71 643.74 642.05 635.28 630.47 639.96 638.16 642.28 642.42 644.19 631.17 635.15 636.74 633.94 640.69 644.71 655.51 656.07 655.98 656.92 653.07 647.87 650.93 649.89 650.65 656.66 657.77 659.73 660.13 662.08 658.13 662.38 665.35 672.01 673.56 674.10 673.99 680.82 677.59 24-Apr-2007 25-Apr-2007 26-Apr-2007 27-Apr-2007 30-Apr-2007 1-May-2007 2-May-2007 3-May-2007 4-May-2007 7-May-2007 8-May-2007 9-May-2007 10-May-2007 11-May-2007 14-May-2007 15-May-2007 16-May-2007 17-May-2007 18-May-2007 21-May-2007 22-May-2007 23-May-2007 24-May-2007 25-May-2007 29-May-2007 30-May-2007 31-May-2007 1-Jun-2007 4-Jun-2007 5-Jun-2007 6-Jun-2007 7-Jun-2007 8-Jun-2007 11-Jun-2007 12-Jun-2007 13-Jun-2007 14-Jun-2007 15-Jun-2007 18-Jun-2007 19-Jun-2007 20-Jun-2007 21-Jun-2007 22-Jun-2007 25-Jun-2007 26-Jun-2007 27-Jun-2007 28-Jun-2007 29-Jun-2007 1480.41 1495.42 1494.25 1494.07 1482.37 1486.30 1495.92 1502.39 1505.62 1509.48 1507.72 1512.58 1491.47 1505.85 1503.15 1501.19 1514.14 1512.75 1522.75 1525.10 1524.12 1522.28 1507.51 1515.73 1518.11 1530.23 1530.62 1536.34 1539.18 1530.95 1517.38 1490.72 1507.67 1509.12 1493.00 1515.67 1522.97 1532.91 1531.05 1533.70 1512.84 1522.19 1502.56 1497.74 1492.89 1506.34 1505.71 1503.35 677.16 684.37 683.66 684.42 680.65 683.22 686.42 689.40 690.95 692.79 692.05 693.43 683.73 690.04 689.31 689.18 695.95 695.16 699.80 699.91 699.12 699.01 693.47 697.27 697.70 702.99 702.43 704.71 705.57 702.28 696.57 685.33 693.11 693.73 686.16 696.06 699.82 704.53 704.18 705.79 696.78 700.78 690.77 689.72 687.78 693.94 693.86 692.77 TABLE 3: INPUTS FOR OPTION PRICING FORMULAE (1) On July 2, 2007, the values of the stock indices were SPX=1519.43 and OEX=699.49. (2) On July 2, 2007, the 3-month T-bill rate (quoted as a bank discount yield) was 4.81. (3) On July 2, 2007, the days to expiration are 47 and 82 days for the August and September option contracts, respectively. (4) On July 2, 2007, one can get estimates of daily dividends for SPX and OEX using CRSP S&P 500 returns, although the estimates for OEX are admittedly "quick and dirty" estimates and less accurate than those for SPX. The second and third columns are data for the S&P 500 from CRSP, including the total return with dividends (CSP500_RET) and the return without dividends (CSP500_RETX) for the CRSP Value-Weighted Index of the S&P 500 Universe. The fourth column is the difference obtained by subtracting returns in the third column from returns in the second column. This difference equals the dividend component of the S&P 500 return exactly, but it only approximates the dividend component of the OEX return. (Analogues of the two S&P 500 return variables are unavailable from CRSP, which is why this approximation is used.) Given this difference, one can estimate dividends at time t+1 by multiplying the value of the index at time t by the value of the difference variable at time t+1. DATE 20070629 20070702 20070703 20070705 20070706 20070709 20070710 20070711 20070712 20070713 20070716 20070717 20070718 20070719 20070720 20070723 20070724 20070725 20070726 20070727 20070730 20070731 20070801 20070802 20070803 20070806 20070807 20070808 20070809 20070810 20070813 20070814 20070815 20070816 20070817 20070820 20070821 20070822 20070823 20070824 20070827 20070828 20070829 20070830 20070831 20070904 20070905 20070906 20070907 20070910 20070911 20070912 20070913 20070914 20070917 20070918 20070919 20070920 20070921 20070924 CSP500_RET -0.0016 0.0108 0.0038 0.0003 0.0037 0.0009 -0.0143 0.0058 0.0190 0.0031 -0.0019 -0.0001 -0.0021 0.0046 -0.0123 0.0048 -0.0195 0.0046 -0.0233 -0.0159 0.0101 -0.0126 0.0073 0.0047 -0.0264 0.0241 0.0061 0.0146 -0.0291 0.0000 -0.0003 -0.0183 -0.0135 0.0033 0.0244 -0.0003 0.0012 0.0117 -0.0012 0.0118 -0.0085 -0.0234 0.0222 -0.0042 0.0112 0.0104 -0.0111 0.0044 -0.0168 -0.0013 0.0137 0.0003 0.0085 0.0003 -0.0052 0.0292 0.0062 -0.0065 0.0047 -0.0052 CSP500_RETX -0.0016 0.0108 0.0036 0.0003 0.0034 0.0009 -0.0143 0.0057 0.0190 0.0031 -0.0019 -0.0001 -0.0022 0.0046 -0.0123 0.0048 -0.0195 0.0045 -0.0233 -0.0160 0.0101 -0.0126 0.0073 0.0045 -0.0265 0.0241 0.0060 0.0143 -0.0293 0.0000 -0.0005 -0.0184 -0.0139 0.0033 0.0244 -0.0003 0.0012 0.0117 -0.0012 0.0116 -0.0085 -0.0234 0.0218 -0.0042 0.0112 0.0104 -0.0115 0.0042 -0.0168 -0.0014 0.0137 0.0000 0.0084 0.0003 -0.0052 0.0292 0.0062 -0.0067 0.0047 -0.0052 DIFFERENCE 0.0000 0.0000 0.0002 0.0000 0.0003 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0001 0.0002 0.0001 0.0000 0.0000 0.0003 0.0002 0.0000 0.0002 0.0001 0.0003 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0001 0.0000 0.0000 0.0004 0.0001 0.0000 0.0000 0.0004 0.0002 0.0000 0.0000 0.0000 0.0003 0.0001 0.0000 0.0000 0.0000 0.0000 0.0002 0.0000 0.0000 SPX 1503.35 1519.43 1524.87 1525.40 1530.44 1531.85 1510.12 1518.76 1547.70 1552.50 1549.52 1549.37 1546.17 1553.08 1534.10 1541.57 1511.04 1518.09 1482.66 1458.95 1473.91 1455.27 1465.81 1472.20 1433.06 1467.67 1476.71 1497.49 1453.09 1453.64 1452.92 1426.54 1406.70 1411.27 1445.94 1445.55 1447.12 1464.07 1462.50 1479.37 1466.79 1432.36 1463.76 1457.64 1473.99 1489.42 1472.29 1478.55 1453.55 1451.70 1471.49 1471.56 1483.95 1484.25 1476.65 1519.78 1529.03 1518.75 1525.75 1517.73 OEX 692.77 699.49 702.93 702.82 704.50 705.58 696.21 700.60 714.74 717.17 717.01 717.22 714.92 718.11 709.92 714.76 701.20 705.94 689.84 679.14 685.09 675.75 681.85 684.51 667.42 683.66 687.82 698.14 676.02 675.62 674.51 663.96 655.83 658.30 674.53 674.12 673.85 681.28 681.84 689.47 684.74 668.99 683.02 680.46 687.47 694.23 686.63 688.91 677.74 678.04 687.65 688.42 695.00 694.38 691.12 710.08 713.53 709.81 713.35 710.14 SPX EST DIV OEX EST DIV 0.01202680 0.30236657 0.01677357 0.43473900 0.00918264 0.00459555 0.18272452 0.01366884 0.01857240 0.00000000 0.00000000 0.16113448 0.03710808 0.14443644 0.01994330 0.00000000 0.01511040 0.00303618 0.21795102 0.03355585 0.00884346 0.09313728 0.34739697 0.08833200 0.02722814 0.05577146 0.49617456 0.26805071 0.00290618 0.22240692 0.16127412 0.43509470 0.05626800 0.00000000 0.00000000 0.00578220 0.08972144 0.01903291 0.15648750 0.00887622 0.06600555 0.53570264 0.08489808 0.02769516 0.02358384 0.66874958 0.25470617 0.00000000 0.05378135 0.00290340 0.39877379 0.08535048 0.00296790 0.01038975 0.01771980 0.04407362 0.32568339 0.00000000 0.00000000 0.00554216 0.13919851 0.00773223 0.20030370 0.00422700 0.00211674 0.08424141 0.00630540 0.00857688 0.00000000 0.00000000 0.07459088 0.01715808 0.06678423 0.00922896 0.00000000 0.00701200 0.00141188 0.10140648 0.01562022 0.00411054 0.04324800 0.16159845 0.04107060 0.01268098 0.02597908 0.23110752 0.12496706 0.00135204 0.10336986 0.07487061 0.20250780 0.02623320 0.00000000 0.00000000 0.00269648 0.04177870 0.00885664 0.07295688 0.00413682 0.03081330 0.25020226 0.03961516 0.01292874 0.01099952 0.31170927 0.11878699 0.00000000 0.02507638 0.00135608 0.18635315 0.03992836 0.00139000 0.00486066 0.00829344 0.02059232 0.15198189 0.00000000 0.00000000 20070925 20070926 20070927 20070928 -0.0004 0.0055 0.0040 -0.0030 -0.0004 0.0053 0.0039 -0.0030 0.0000 0.0002 0.0000 0.0000 1517.21 1525.42 1531.38 1526.75 710.52 714.06 716.46 714.49 0.02731914 0.27764943 0.05796596 0.01990794 0.01278252 0.13002516 0.02713428 0.00931398 This data accompanies Second City Options: A Case Study on Index Options, by Don M. Chance and Michael L. Hemler. (C (Current Draft: September 7, 2009)