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Given below are the monthly values of the S&P 500 Index. Suppose that in each month you had written an out-of-the-money put option on one unit of the index with an exercise price 5% lower than the current value of the index.   End of month S&P 500 End of month S&P 500 End of month S&P 500 End of month S&P 500 September-77 96.53 April-80 106.29 November-82 138.53 July-85 191.85 October-77 92.34 May-80 111.24 December-82 140.64 August-85 190.92 November-77 94.83 June-80 114.24 January-83 145.30 September-85 188.63 December-77 95.10 July-80 121.67 February-83 148.06 October-85 182.08 January-78 89.25 August-80 122.38 March-83 152.96 November-85 189.82 February-78 87.04 September-80 125.46 April-83 164.43 December-85 202.17 March-78 89.21 October-80 127.47 May-83 162.39 January-86 211.28 April-78 96.83 November-80 140.52 June-83 167.64 February-86 226.92 May-78 97.24 December-80 135.76 July-83 162.56 March-86 238.90 June-78 95.53 January-81 129.55 August-83 164.40 April-86 235.52 July-78 100.68 February-81 131.27 September-83 166.07 May-86 247.35 August-78 103.29 March-81 136.00 October-83 163.55 June-86 250.84 September-78 102.54 April-81 132.81 November-83 166.40 July-86 236.12 October-78 93.15 May-81 132.59 December-83 164.93 August-86 252.93 November-78 94.70 June-81 131.21 January-84 163.41 September-86 231.32 December-78 96.11 July-81 130.92 February-84 157.06 October-86 243.98 January-79 99.93 August-81 122.79 March-84 159.18 November-86 249.22 February-79 96.28 September-81 116.18 April-84 160.05 December-86 242.17 March-79 101.59 October-81 121.89 May-84 150.55 January-87 274.08 April-79 101.76 November-81 126.35 June-84 153.18 February-87 284.20 May-79 99.08 December-81 122.55 July-84 150.66 March-87 291.70 June-79 102.91 January-82 120.40 August-84 166.68 April-87 288.36 July-79 103.81 February-82 113.11 September-84 166.10 May-87 290.10 August-79 109.32 March-82 111.96 October-84 166.09 June-87 304.00 September-79 109.32 April-82 116.44 November-84 163.58 July-87 318.66 October-79 101.82 May-82 111.88 December-84 167.24 August-87 329.80 November-79 106.16 June-82 109.61 January-85 179.63 September-87 321.83 December-79 107.94 July-82 107.09 February-85 181.18 October-87 251.79 January-80 114.16 August-82 119.51 March-85 180.66     February-80 113.66 September-82 120.42 April-85 179.83     March-80 102.09 October-82 133.72 May-85 189.55       Required: a-1. What would have been the average value of your gross monthly payouts on the puts over the 10-year period October 1977–September 1987? (Do not round intermediate calculations. Round your answer to 4 decimal places.)   a-2. The standard deviation? (Do not round intermediate calculations. Round your answer to 4 decimal places.)   b-1. What would have been the average value of your gross monthly payouts on the puts if you extend the sample by one month to include October 1987? (Do not round intermediate calculations. Round your answer to 4 decimal places.)   b-2. The standard deviation? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Given below are the monthly values of the S&P 500 Index. Suppose that in each month you had written an out-of-the-money put option on one unit of the index with an exercise price 5% lower than the current value of the index.   End of month S&P 500 End of month S&P 500 End of month S&P 500 End of month S&P 500 September-77 96.53 April-80 106.29 November-82 138.53 July-85 191.85 October-77 92.34 May-80 111.24 December-82 140.64 August-85 190.92 November-77 94.83 June-80 114.24 January-83 145.30 September-85 188.63 December-77 95.10 July-80 121.67 February-83 148.06 October-85 182.08 January-78 89.25 August-80 122.38 March-83 152.96 November-85 189.82 February-78 87.04 September-80 125.46 April-83 164.43 December-85 202.17 March-78 89.21 October-80 127.47 May-83 162.39 January-86 211.28 April-78 96.83 November-80 140.52 June-83 167.64 February-86 226.92 May-78 97.24 December-80 135.76 July-83 162.56 March-86 238.90 June-78 95.53 January-81 129.55 August-83 164.40 April-86 235.52 July-78 100.68 February-81 131.27 September-83 166.07 May-86 247.35 August-78 103.29 March-81 136.00 October-83 163.55 June-86 250.84 September-78 102.54 April-81 132.81 November-83 166.40 July-86 236.12 October-78 93.15 May-81 132.59 December-83 164.93 August-86 252.93 November-78 94.70 June-81 131.21 January-84 163.41 September-86 231.32 December-78 96.11 July-81 130.92 February-84 157.06 October-86 243.98 January-79 99.93 August-81 122.79 March-84 159.18 November-86 249.22 February-79 96.28 September-81 116.18 April-84 160.05 December-86 242.17 March-79 101.59 October-81 121.89 May-84 150.55 January-87 274.08 April-79 101.76 November-81 126.35 June-84 153.18 February-87 284.20 May-79 99.08 December-81 122.55 July-84 150.66 March-87 291.70 June-79 102.91 January-82 120.40 August-84 166.68 April-87 288.36 July-79 103.81 February-82 113.11 September-84 166.10 May-87 290.10 August-79 109.32 March-82 111.96 October-84 166.09 June-87 304.00 September-79 109.32 April-82 116.44 November-84 163.58 July-87 318.66 October-79 101.82 May-82 111.88 December-84 167.24 August-87 329.80 November-79 106.16 June-82 109.61 January-85 179.63 September-87 321.83 December-79 107.94 July-82 107.09 February-85 181.18 October-87 251.79 January-80 114.16 August-82 119.51 March-85 180.66     February-80 113.66 September-82 120.42 April-85 179.83     March-80 102.09 October-82 133.72 May-85 189.55       Required: a-1. What would have been the average value of your gross monthly payouts on the puts over the 10-year period October 1977–September 1987? (Do not round intermediate calculations. Round your answer to 4 decimal places.)   a-2. The standard deviation? (Do not round intermediate calculations. Round your answer to 4 decimal places.)   b-1. What would have been the average value of your gross monthly payouts on the puts if you extend the sample by one month to include October 1987? (Do not round intermediate calculations. Round your answer to 4 decimal places.)   b-2. The standard deviation? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.4: Mathematics Of Finance
Problem 2E
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Given below are the monthly values of the S&P 500 Index. Suppose that in each month you had written an out-of-the-money put option on one unit of the index with an exercise price 5% lower than the current value of the index.
 

End of month S&P 500 End of month S&P 500 End of month S&P 500 End of month S&P 500
September-77 96.53 April-80 106.29 November-82 138.53 July-85 191.85
October-77 92.34 May-80 111.24 December-82 140.64 August-85 190.92
November-77 94.83 June-80 114.24 January-83 145.30 September-85 188.63
December-77 95.10 July-80 121.67 February-83 148.06 October-85 182.08
January-78 89.25 August-80 122.38 March-83 152.96 November-85 189.82
February-78 87.04 September-80 125.46 April-83 164.43 December-85 202.17
March-78 89.21 October-80 127.47 May-83 162.39 January-86 211.28
April-78 96.83 November-80 140.52 June-83 167.64 February-86 226.92
May-78 97.24 December-80 135.76 July-83 162.56 March-86 238.90
June-78 95.53 January-81 129.55 August-83 164.40 April-86 235.52
July-78 100.68 February-81 131.27 September-83 166.07 May-86 247.35
August-78 103.29 March-81 136.00 October-83 163.55 June-86 250.84
September-78 102.54 April-81 132.81 November-83 166.40 July-86 236.12
October-78 93.15 May-81 132.59 December-83 164.93 August-86 252.93
November-78 94.70 June-81 131.21 January-84 163.41 September-86 231.32
December-78 96.11 July-81 130.92 February-84 157.06 October-86 243.98
January-79 99.93 August-81 122.79 March-84 159.18 November-86 249.22
February-79 96.28 September-81 116.18 April-84 160.05 December-86 242.17
March-79 101.59 October-81 121.89 May-84 150.55 January-87 274.08
April-79 101.76 November-81 126.35 June-84 153.18 February-87 284.20
May-79 99.08 December-81 122.55 July-84 150.66 March-87 291.70
June-79 102.91 January-82 120.40 August-84 166.68 April-87 288.36
July-79 103.81 February-82 113.11 September-84 166.10 May-87 290.10
August-79 109.32 March-82 111.96 October-84 166.09 June-87 304.00
September-79 109.32 April-82 116.44 November-84 163.58 July-87 318.66
October-79 101.82 May-82 111.88 December-84 167.24 August-87 329.80
November-79 106.16 June-82 109.61 January-85 179.63 September-87 321.83
December-79 107.94 July-82 107.09 February-85 181.18 October-87 251.79
January-80 114.16 August-82 119.51 March-85 180.66    
February-80 113.66 September-82 120.42 April-85 179.83    
March-80 102.09 October-82 133.72 May-85 189.55    

 

Required:

a-1. What would have been the average value of your gross monthly payouts on the puts over the 10-year period October 1977–September 1987? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

 

a-2. The standard deviation? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

 


b-1. What would have been the average value of your gross monthly payouts on the puts if you extend the sample by one month to include October 1987? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

 


b-2. The standard deviation? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

 
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