BERND PAPE Asset Allocation, Multivariate Position Based Trading ...

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96 ACTA WASAENSIA0.8Chartist Index Parameter Set I0.60.40.200 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 10 4Chartist Index Parameter Set II0.80.60.40.200 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 10 4Chartist Index Parameter Set III0.80.60.40.200 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 10 4Chartist Index Parameter Set IV0.80.60.40.200 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 10 4Figure 4. Chartist index z over 20,000 integer time steps (Simulation II). The horizontallines indicate the threshold z max ,beyondwhichthefirst type equilibriumof (4.51) is expected to loose its stability.
ACTA WASAENSIA 97Table 2. Median estimates of the tail index over ten samples of 2,000 observationseach and the range of estimates for common choices of the tail region.Parameter 2.5%tail 5%tail 10%tailSet I min median max min median max min median maxSimulation I 1.86 3.34 4.80 1.60 2.57 3.15 1.58 2.27 2.66Simulation II 2.12 3.23 3.59 1.97 2.51 3.56 1.73 2.17 2.65Lux&Marchesi 1.61 2.04 4.50 1.51 2.11 2.64 1.26 1.93 2.44Parameter 2.5%tail 5%tail 10%tailSet II min median max min median max min median maxSimulation I 2.18 2.61 4.44 2.21 2.32 3.09 1.76 2.19 2.67Simulation II 2.34 3.43 4.08 2.12 2.96 3.46 2.11 2.35 2.95Lux&Marchesi 2.28 2.82 3.73 2.00 2.52 3.17 1.55 2.18 2.36Parameter 2.5%tail 5%tail 10%tailSet III min median max min median max min median maxSimulation I 2.02 3.34 4.58 1.81 2.93 4.43 1.46 2.28 5.09Simulation II 1.58 3.21 4.81 1.25 2.81 4.12 1.72 2.67 3.33Lux&Marchesi 2.41 4.63 6.82 2.33 3.48 8.60 1.80 2.86 4.84Parameter 2.5%tail 5%tail 10%tailSet IV min median max min median max min median maxSimulation I 2.92 3.70 7.75 1.97 2.90 4.13 1.94 2.83 3.85Simulation II 2.07 3.25 5.06 1.95 2.98 3.74 1.65 2.33 3.24Lux&Marchesi 2.11 3.08 4.06 2.13 2.46 7.68 1.65 1.97 3.18illustrates the difference between the stochastic dynamics of the state variables x, p andz, and the dynamics of their expected values t , t and t , whose dynamics isdescribed by the deterministic differential equations (4.51). If (4.51) would describe thedynamics of the state variables themselves, the case z>z max could not occur as long asz was initialized below this threshold. On the other hand, occurence of z>z max wouldnecessarily lead to market instability. Occasional violation of the stability conditionz
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ACTA WASAENSIA 52.10.1 Cross-Sectio
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ACTA WASAENSIA 7A5 Matlabcodeforerr
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10 ACTA WASAENSIAIn chapter 5 I sha
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12 ACTA WASAENSIA2 Statistical Prop
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14 ACTA WASAENSIA2.2 Absence of Ser
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ACTA WASAENSIA 17The survival or ta
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ACTA WASAENSIA 19& Scheinkman (1987
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ACTA WASAENSIA 212.6 Long Range Dep
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ACTA WASAENSIA 23A particular class
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26 ACTA WASAENSIAMultiscaling may t
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28 ACTA WASAENSIAHansen (1982) to c
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30 ACTA WASAENSIAThe leverage hypot
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32 ACTA WASAENSIAIn order to aviod
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34 ACTA WASAENSIAon a risk-adjusted
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36 ACTA WASAENSIAplanations for the
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38 ACTA WASAENSIAspeculative prices
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40 ACTA WASAENSIAindex α is howeve
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42 ACTA WASAENSIAThis approach has
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44 ACTA WASAENSIAimplying exponenti
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Page 48 and 49: 48 ACTA WASAENSIAdivisible version
Page 50 and 51: 50 ACTA WASAENSIAto check their ade
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Page 80 and 81: 80 ACTA WASAENSIAWe wish to obtain
Page 82 and 83: 82 ACTA WASAENSIAindividual markets
Page 84 and 85: 84 ACTA WASAENSIAreturn series. I l
Page 86 and 87: 86 ACTA WASAENSIASwitches between c
Page 88 and 89: 88 ACTA WASAENSIAfollowing necessar
Page 90 and 91: 90 ACTA WASAENSIATable 1. Parameter
Page 92 and 93: 92 ACTA WASAENSIAin stepwise search
Page 94 and 95: 94 ACTA WASAENSIA0.2Logreturns Para
Page 98 and 99: 98 ACTA WASAENSIATable 3. Kurtosis
Page 100 and 101: 100 ACTA WASAENSIAthe most extreme
Page 102 and 103: 102 ACTA WASAENSIATable 4. Estimate
Page 104 and 105: 104 ACTA WASAENSIATable 8. Results
Page 106 and 107: 106 ACTA WASAENSIATable 9. Results
Page 108 and 109: 108 ACTA WASAENSIATable 11. Paramet
Page 110 and 111: 110 ACTA WASAENSIA1 x 105 Aggr. Inv
Page 112 and 113: 112 ACTA WASAENSIA200Aggr. Inventor
Page 114 and 115: 114 ACTA WASAENSIA5 x 105 Aggr. Wea
Page 116 and 117: 116 ACTA WASAENSIAOverall, we can a
Page 118 and 119: 118 ACTA WASAENSIAby Lux (1998). Th
Page 120 and 121: 120 ACTA WASAENSIAwhere s is a disc
Page 122 and 123: 122 ACTA WASAENSIAprocessing valuat
Page 124 and 125: 124 ACTA WASAENSIAProof. See append
Page 126 and 127: 126 ACTA WASAENSIA2.5Logarithmice T
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Page 132 and 133: 132 ACTA WASAENSIATable 17. Probabi
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Page 136 and 137: 136 ACTA WASAENSIAIn order to test
Page 138 and 139: 138 ACTA WASAENSIAReferencesAbhyank
Page 140 and 141: 140 ACTA WASAENSIABaillie, R. T. (1
Page 142 and 143: 142 ACTA WASAENSIABlack, F. & M. Sc
Page 144 and 145: 144 ACTA WASAENSIAButler, R. J., J.
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146 ACTA WASAENSIACont, R. (2001).
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148 ACTA WASAENSIAEmbrechts, P., C.
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150 ACTA WASAENSIAFielitz, B. D. (1
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152 ACTA WASAENSIAGhysels, E., A. C
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154 ACTA WASAENSIAHeston, S. L. (19
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156 ACTA WASAENSIAKaldor, N. (1939)
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158 ACTA WASAENSIALiesenfeld, R. (1
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160 ACTA WASAENSIALye, J. N. & V. L
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162 ACTA WASAENSIAMikosch, T. (2003
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164 ACTA WASAENSIAPindyck, R. S. (1
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166 ACTA WASAENSIASethi, R. (1996).
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168 ACTA WASAENSIATesfatsion, L. &
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170 ACTA WASAENSIAAAppendixA1Matlab
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172 ACTA WASAENSIA87 % a3 = 1; %imp
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174 ACTA WASAENSIA181 nmout = max([
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176 ACTA WASAENSIA275276 figure;277
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178 ACTA WASAENSIA45 end464748 % In
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180 ACTA WASAENSIA454647 % Check wh
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182 ACTA WASAENSIAA4Matlab code for
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184 ACTA WASAENSIA888990 % create P
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186 ACTA WASAENSIA4344 nobs = 500;
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188 ACTA WASAENSIAA6Matlab code for
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190 ACTA WASAENSIA9192 for t = 1:T
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192 ACTA WASAENSIA185 fcash = fcash
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194 ACTA WASAENSIA279280281 %Output
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196 ACTA WASAENSIA(4.20), and o(τ
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198 ACTA WASAENSIAas t = n k P ˙
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200 ACTA WASAENSIA nBn˙f2 = v B n
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202 ACTA WASAENSIA f˙1−c1 = v B
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204 ACTA WASAENSIAlocal stability o
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