back start next[start] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [ 16 ] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] 16 edge points and 7mat, where the forward period meets the forward periods of the neighbor contracts. The value of q at the meeting point 7exp is determined from the four implied forward rates nearest to 7exp (in a regular sequence of 3-month futures contracts) by polynomial interpolation, 9 (q2 + q3) -q\ -04 ,07.e(Te)tp) = -- C27)where q is computed by Equation 2.5 and its index (1,2,3,4) indicates the position in the series of the four nearest forwards. For instance, qt, refers to the forward from rcxp to Tmat. Equation 2.7 can be interpreted as the interpolation of a cubic polynomial going through the values Qi ... qa, located at the midpoints of the corresponding forward periods. The same equation if shifted by one forward period leads to e(7mat). If a contract at the edge (q\ or 04 in Equation 2.7) is not available from the data source, we extrapolate3 q2 - q3 - cQi =--- (2-8)and analogously for Q4. The numerical impact of an extrapolation error is small, as qi and Q4 have little impact in Equation 2.7. By fulfilling all the mentioned requirements, the coefficients of the polynomial q(T) of Equation 2.6 can be formulated asa = [