Stochastic methods in applied finance:

Question 3 (10 marks) Capsule Corp wants to see if their daily sales values affect their share price (with a one-week delay). In some chosen week, the daily sales revenues were Z23m, Z4m, Z18m, Z17m, and Z25m (in millions of Zeni Z, the local currency). The daily share prices for Capsule Corp in the following week were Z57.3, Z50.0, Z49.81, Z53.7, and Z60 (again, Z denotes Zeni) a) Calculate Kendall's Tau for this given data. [3 marks] b) Calculate Spearman's Rho for this data. You may use the fact that (i - 3)2 = 2.5 4 i 1 [3 marks] c) The Pearson's correlation coefficient for this data has been calculated to be p = 0.783606. Give a brief explanation of the difference between what p is measuring and the two results of your calculations in parts a) and b) are measuring. you do NOT need to perform any calculations for this part Note [2 marks] d) The market is now in a slump. Capsule Corp's main competitor, ShEnron, has recently filed for bankruptcy. Capsule Corp, fearing bankruptcy as well, wants to compare their daily share returns over the past year with those of ShEnron In particular, Capsule Corp is interested in modelling the lower tail dependence between the two sets of daily share returns. Name 2 copulas that could be used for this analysis. Give a brief explanation of your answer. Note: you do NOT need to perform any calculations for this part [2 marks] Question 3 (10 marks) Capsule Corp wants to see if their daily sales values affect their share price (with a one-week delay). In some chosen week, the daily sales revenues were Z23m, Z4m, Z18m, Z17m, and Z25m (in millions of Zeni Z, the local currency). The daily share prices for Capsule Corp in the following week were Z57.3, Z50.0, Z49.81, Z53.7, and Z60 (again, Z denotes Zeni) a) Calculate Kendall's Tau for this given data. [3 marks] b) Calculate Spearman's Rho for this data. You may use the fact that (i - 3)2 = 2.5 4 i 1 [3 marks] c) The Pearson's correlation coefficient for this data has been calculated to be p = 0.783606. Give a brief explanation of the difference between what p is measuring and the two results of your calculations in parts a) and b) are measuring. you do NOT need to perform any calculations for this part Note [2 marks] d) The market is now in a slump. Capsule Corp's main competitor, ShEnron, has recently filed for bankruptcy. Capsule Corp, fearing bankruptcy as well, wants to compare their daily share returns over the past year with those of ShEnron In particular, Capsule Corp is interested in modelling the lower tail dependence between the two sets of daily share returns. Name 2 copulas that could be used for this analysis. Give a brief explanation of your answer. Note: you do NOT need to perform any calculations for this part [2 marks]