ADMS4504-Assignment2-Sample1-Sol

ADMS4504-Assignment2-Sample1-Sol - AP/ADMS4504A Assignment...

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AP/ADMS4504A Assignment #2 Solutions Fall 2009 Question 1 (Yield volatility and binomial model) (22 marks) This question has the following two independent parts, (a) and (b). (a) Use the daily yields in the table on next page to compute a daily standard deviation of yields. Next annualize the daily standard deviation just calculated first using 365 calendar days, then using 250 trading days in a year. Finally, construct a 10-day moving average equal weight volatility forecast for each day in the period from Day 15 to Day 30, assuming that the expected value of the daily change in yield is zero. Please note: for this question 1) if you use Excel please attach your Excel worksheet to your assignment and 2) keep at least 6 decimal places in both your calculations and your final answers . Please show your calculations. (12 marks) Day Yield (%) 0 4.380 1 4.393 2 4.430 3 4.428 4 4.522 5 4.648 6 4.656 7 4.595 8 4.562 9 5.208 10 4.454 11 4.404 12 4.659 13 4.904 14 4.820 15 3.933 16 4.907 17 4.650 18 4.814 19 4.766
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AP/ADMS4504A Fall 2009 Assignment #2 Solutions 20 4.692 21 4.687 22 4.521 23 4.435 24 4.424 25 4.440 26 4.516 27 4.448 28 4.427 29 4.390 30 4.457 Answer In the table below: in Column (3), X t = 100 × [Ln(y t /y t-1 )], where y t is the daily yield recorded in Column (2); and Column (4) contains the values of 2 t ) X X ( , where X , the sample mean, is calculated as: (1.742717)/30 = 0.058091 (there are 30 observations in our sample, so T, the sample size, is equal to 30). (1) Day (2) Yield (%) (3) X t (%) (4) (Percentages squared) 0 4.380 1 4.393 0.296364 0.056774 2 4.430 0.838722 0.609385 3 4.428 -0.045157 0.010660 4 4.522 2.100636 4.171990 5 4.648 2.748265 7.237034 6 4.656 0.171969 0.012968 7 4.595 -1.318795 1.895816 8 4.562 -0.720763 0.606614 9 5.208 13.243478 173.854437 10 4.454 -15.639334 246.409144 11 4.404 -1.128935 1.409031 12 4.659 5.628761 31.032369 13 4.904 5.125037 25.673938 14 4.820 -1.727727 3.189146 Page 2
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AP/ADMS4504A Fall 2009 Assignment #2 Solutions 15 3.933 -20.337144 415.965597 16 4.907 22.126027 486.993782 17 4.650 -5.379554 29.567981 18 4.814 3.466112 11.614607 19 4.766 -1.002096 1.123997 20 4.692 -1.564845 2.633921 21 4.687 -0.106621 0.027130 22 4.521 -3.605951 13.425205 23 4.435 -1.920559 3.915057 24 4.424 -0.248335 0.093897 25 4.440 0.361011 0.091761 26 4.516 1.697227 2.686767 27 4.448 -1.517209 2.481570 28 4.427 -0.473240 0.282313 29 4.390 -0.839293 0.805297 30 4.457 1.514667 2.121613 Total 1.742717 1,469.9998 Sample mean 0.058091 It follows that the variance of daily yields is: squared. s percentage 689648 . 50 1 30 9998 . 469 , 1 iance var = = The standard deviation of daily yields is thus: %. 119666 . 7 689648 . 50 = The annual standard deviation is either: %. 021032 . 136 365 % 119666 . 7 = × Or %. 571807 . 112 250 % 119666 . 7 = × Finally, as to the 10-day moving-average volatility forecast, we will use Day 15 to illustrate the calculations. The volatility forecast for Days 16 - 30 can be obtained similarly. To compute the daily volatility on Day 15 using a 10-day moving-average
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This note was uploaded on 12/17/2010 for the course ATKINSON adms 4504 taught by Professor Nabil during the Fall '10 term at York University.

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ADMS4504-Assignment2-Sample1-Sol - AP/ADMS4504A Assignment...

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