.161.8432.3%
USD/JPY RNN test results for the validation data set
RNN(44-1-1)
RNN(44-5-1)
RNN(44-10-1)
RNN(44-10-5-1)
RNN(44-15-10-1)
8.4%0.161.8630.1%
8.5%0.161.8529.4%
8.0%0.161.8429.4%
3.2%0.161.8531.5%
3.0%0.161.8530.1%
NNR/RNN (a-b-c) represents different neural network models, where:a = number of input variables;b = number of hidden nodes;c = number of output nodes.Realised Vol(t) = f [lVol(t − 21), Realised Vol(t − 21), |r|(t − 21, . . . , t − 41), DLOIL(t − 21, . . . , t − 41)].
Figure E4.2
USD/JPY RNN (44-5-1) volatility forecast (%)
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RNN Vol. Forecast
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15
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Figure E4.1
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Forecasting and Trading Currency Volatility157
APPENDIX E
18Realised Vol.18
1616
1414
1212
1010
88
66
44
22
00
GBP/USD RNN (44-1-1) volatility forecast (%)
35Realised Vol.35
3030
2525
2020
.15
1010
55
0
0
Figure F4.2 USD/JPY volatility forecast combinations (%)
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COM1 Comb.05/05/00
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15
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GR Comb.05/01/97
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GR Comb.
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Figure F4.1
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158Applied Quantitative Methods for Trading and Investment
APPENDIX F
18Realised Vol.18
1616
1414
1212
1010
88
66
44
22
00
GBP/USD volatility forecast combinations (%)
35Realised Vol.35
3030
2525
2020
.15
1010
55
0
0
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159
APPENDIX GTable G4.11 Threshold = 0.5
GBP/USD weekly volatility trading strategy
Trading days = 5
In-sampleOut-of-sampleSample(1-1329)(1330-1610)ObservationPeriod(12/04/1999-09/05/2000)(31/12/1993-09/04/1999)ModelsNNR(44-10-5-1) RNN(44-1-1) GARCH(1,1)COM1GRNNR(44-10-5-1) RNN(44-1-1) GARCH(1,1) COM1GRP/L without gearing162.15%160.00%262.41% 189.82% 313.55%15.37%13.30%−12.85% 8.30% 30.08%P/L with gearing626.62%852.70%889.04% 597.16% 792.87%36.46%58.98%−2.39% 20.92% 53.64%Total trades2212212242102323943403533Profitable trades66.97%68.07%81.70% 72.86% 91.38%53.85%60.47%30.00% 45.71% 72.73%Average gearing2.864.202.712.542.191.722.581.821.621.632 Threshold = 1.0
Trading days = 5
Out-of-sampleIn-sampleSample(1330-1610)(1-1329)ObservationPeriod(31/12/1993-09/04/1999)(12/04/1999-09/05/2000)ModelsNNR(44-10-5-1) RNN(44-1-1) GARCH(1,1)COM1GRNNR(44-10-5-1) RNN(44-1-1) GARCH(1,1) COM1GR166.15%147.13%213.13% 167.03% 243.71%20.09%12.02%7.87% 11.11% 18.57%P/L without gearing333.20%420.39%27.01%20.87%12.80% 14.27% 23.42%P/L with gearing434.96% 300.56% 366.44%1661661471382127171314Total trades15373.49%72.00%76.19%55.56%58.82% 76.92% 85.71%Profitable trades84.31% 77.55% 94.93%1.822.351.731.611.421.241.641.311.161.21Average gearing3 Threshold = 1.5
Trading days = 5
Out-of-sampleIn-sampleSample(1330-1610)Observation(1-1329)Period(31/12/1993-09/04/1999)(12/04/1999-09/05/2000)NNR(44-10-5-1) RNN(44-1-1) GARCH(1,1) COM1GRModelsNNR(44-10-5-1) RNN(44-1-1) GARCH(1,1)COM1GR128.90%137.62%176.30% 122.22% 129.73%16.49%7.06%7.08% 7.08% 4.39%P/L without gearing198.76%278.91%268.10% 173.28% 158.83%19.49%10.52%8.56% 7.61% 5.21%P/L with gearing1131139482611018442Total trades74.34%69.70%93.62% 82.93% 95.08%90.00%50.00%100.00% 100% 100.00%Profitable trades1.491.811.451.381.211.121.271.191.071.14Average gearing4 Threshold = 2.0
Trading days = 5
In-sampleSample(1-1329)ObservationPeriod(31/12/1993-09/04/1999)ModelsNNR(44-10-5-1) RNN(44-1-1) GARCH(1,1)95.08%115.09%118.43%P/L without gearing131.34%194.33%158.35%P/L with gearing686856Total trades82.35%72.44%94.64%Profitable trades1.341.551.31Average gearing
Note: Cumulative P/L figures are expressed in volatility points.
COM162.47%79.39%3688.89%1.29
Out-of-sample(1330-1610)(12/04/1999-09/05/2000)GRNNR(44-10-5-1) RNN(44-1-1) GARCH(1,1) COM145.67%3.26%7.25%4.67% 3.26%52.97%3.99%9.27%5.65% 3.48%181102194.44%100.00%80.00%100% 100%1.141.221.141.161.07
GR0-
160
Applied Quantitative Methods for Trading and InvestmentTable G4.2
1 Threshold = 0.5SampleObservationPeriodModelsP/L without gearingP/L with gearingTotal tradesProfitable tradesAverage gearing2 Threshold = 1.0SampleObservationPeriodModelsP/L without gearingP/L with gearingTotal tradesProfitable tradesAverage gearing3 Threshold = 1.5SampleObservationPeriodModelsP/L without gearingP/L with gearingTotal tradesProfitable tradesAverage gearing4 Threshold = 2.0SampleObservationPeriodModelsP/L without gearingP/L with gearingTotal tradesProfitable tradesAverage gearing
USD/JPY weekly volatility trading strategy
Trading days = 5In-sampleOut-of-sample(1330-1610)(1-1329)(12/04/1999-09/05/2000)(31/12/1993-09/04/1999)NNR(44-1-1) RNN(44-5-1) GARCH(1,1)COM1GRNNR(44-1-1) RNN(44-5-1) GARCH(1,1) COM1GR−10.17%−11.66%208.63% 77.06% 387.38%63.95%78.77%−82.07% 39.23% 69.31%−79.31%−32.08%1675.67% 517.50% 1095.73%251.14%372.70%−359.44% 111.86% 206.43%251251242232229505053485051.00%50.60%54.13% 55.17% 78.60%76.00%86.00%18.87% 60.42% 78.00%3.763.883.672.672.423.223.735.922.182.35Trading days = 5Out-of-sampleIn-sample(1330-1610)(1-1329)(12/04/1999-09/05/2000)(31/12/1993-09/04/1999)NNR(44-1-1) RNN(44-5-1) GARCH(1,1)COM1GRNNR(44-1-1) RNN(44-5-1) GARCH(1,1)18.73%30.43%234.66% 142.37% 308.50%52.70%63.01%−75.61%0.43%102.50%88.19%135.49%−162.97%897.30% 331.50% 578.10%21321316816539435320152.11%54.17%76.92%81.40%24.53%54.23% 58.93% 82.42%2.162.162.151.681.651.771.982.96
COM1GR31.71% 76.88%49.88% 124.63%303766.67% 94.59%1.521.56
Trading days = 5Out-of-sampleIn-sample(1330-1610)(1-1329)(31/12/1993-09/04/1999)(12/04/1999-09/05/2000)NNR(44-1-1) RNN(44-5-1) GARCH(1,1)COM1GRNNR(44-1-1) RNN(44-5-1) GARCH(1,1) COM1GR34.15%54.46%251.07% 104.67% 282.96%64.00%55.83%−65.02% 5.33% 52.59%60.28%164.86%643.47% 203.58% 399.48%108.52%81.09%−102.88% 11.99% 77.99%15715714498104333550132254.78%56.21%63.89% 60.20% 86.54%81.82%80.00%24.00%69% 100.00%1.831.751.781.451.351.561.512.001.381.42Trading days = 5In-sampleOut-of-sample(1-1329)(1330-1610)(31/12/1993-09/04/1999)(12/04/1999-09/05/2000)NNR(44-1-1) RNN(44-5-1) GARCH(1,1)COM1GRNNR(44-1-1) RNN(44-5-1) GARCH(1,1) COM1−6.13%14.08%247.22% 71.30% 154.88%49.61%53.90%−43.71% 9.23%−35.86%63.43%514.30% 105.49% 202.86%71.66%86.20%−52.64% 14.94%1171171134750212347651.28%52.94%70.80% 65.96% 86.00%90.48%86.96%28%83%1.581.661.561.281.251.461.521.741.55
GR30.33%40.28%11100%1.30
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