”, Weather Risk Management Association, available at:http://wrma.cyberserv.com/library/public/ﬁle346.ppt.Raspé, A. (2001), “Legal and Regulatory Issues”, in E. Banks (ed.), Weather Risk Management:Market, Products and Applications, Palgrave, New York, pp. 224–245.Schafer, J. L. (1997), Analysis of Incomplete Multivariate Data, Series Monographs on Statisticsand Applied Probability, Vol. 72, Chapman and Hall, London.
Indexafﬁne models 73–5econometric methodology/applications87–106estimation results 106–26identiﬁcation 84–6AR 130ARCH 193, 245, 258ARCH-LM 385Arbitrage Pricing Theory (APT) 45, 73, 282,283, 391ARIMA 130ARMA modelling 3, 4, 10, 32, 38ARMA (1,1) process 248ARMA (p, q) 157in EUR/USD forecasting in trading models13–17ARSV model 267, 275artiﬁcial neural networks 166–7artiﬁcial random-walk series 43asset pricing background issues 77–8at-the-money forward (ATMF) 134, 145at-the-money forward volatility 355, 356Augmented Dickey–Fuller (ADF) test statistic6, 7, 385autoregression 240average gain/loss 31, 32axis-parallel trees 172backpropagation networks 25, 26, 37backpropagation neural networks (BPNNs)166‘basis’ 48Bayes’ formula 196Bayesian approach to stochastic volatility259–60Bayesian estimator 262benchmark models 10–20Berndt, Hall, Hall and Hausman (BHHH)200Bernoulli model 357betaARCH 240Applied Quantitative Methods for Trading and Investment. 2003 John Wiley & Sons, Ltd ISBN: 0-470-84885-5
bilogistic sigmoid 138Black–Scholes formula 243, 275–6, 277, 278Breusch–Godfrey Serial Correlation LM Test18buy signal, EUR/USD 31C4.5 algorithm 174, 178Capital Asset Pricing Model (CAPM) 45changing volatility, models of 244–5Classiﬁcation Tree in Excel 172–8, 191decision trees 172–5technical implementation 175–8cointegrating regression 44Cointegrating Regression Durbin–Watson(CRDW) 44cointegrating vector 44cointegrationadvantages and disadvantages 67application to international equities 54–66in a controlled simulation 50–4deﬁnition 41–2modelling 41–2time series modelling and 42–5conditional correlations 350Consumption Capital Asset Pricing Model(CCAPM) 73contingent assets, pricing 242–3contrarian strategies 340cooling degree days (CDDs) 383correct directional change (CDC) 31, 32, 143,144prediction 130Data Augmentation (DA) algorithm, missingdata and 381, 382, 388–9delta rule 166de-trending of time series 43diagonal GARCH model 326–7with variance targeting 327–8Dickey–Fuller (DF) statistics 44, 53–4,126Edited by C.L. Dunis, J. Laws and P. Naı̈m
402difference stationary time series 43Dufﬁe–Kan (exponential-afﬁne) afﬁne modelsof the term structure 78–83Efﬁcient Method of Moments (EMM) 256,257–8EGARCH 258error-correction model (ECM) 41estimation bias in rolling estimation 221EUR/USD exchange rate 5–10Expectation Maximisation (EM) algorithm,missing data and 381, 382expectation maximisation algorithm 386–8E-step and M-step 387–8imputation accuracy 394maximum-likelihood estimation 387expectations theoryforward rate test 83–4non-pure version 83explained variance (EV) 26–7explicit factor modelling 66–7exponential-afﬁne models of the term structure78–83exponential smoothing 3exponentially weighted moving averages(EWMA) 202, 203–4, 360–1extrapolation, deﬁnition 42factor sensitivities, deﬁnition 215–16fallback methodology to missing weather data385–6imputation accuracy 394feedforward neural network 22feedforward neural network, three-layer 167Fisher hypothesis 75forecasting accuracyout-of-sample accuracy measures 31out-of-sample forecasting accuracy results32–4out-of-sample trading performance measures31–2out-of sample trading performance results34–6forecasting and trading currency volatilityexchange rate series databank and 132–4historical volatility 132–4implied volatility series databank 134–5foreign exchange volatility trading models145–9currency volatility trading models 145–7trading simulation results 147–9volatility trading strategies 145forward rate regression 75F -test 14GARCH model 130, 131, 193, 258, 318–20diagonal 326–8
Indexorthogonal 313scalar, with variance targeting 328–9GARCH (1,1) model 4, 144, 350choice of benchmark model 135GARCH (1,1) volatility forecasts 135–7cf NNR/RNN in trading simulation 147–9Garman–Kohlhagen pricing formula 130, 353Gauss code for maximum likelihood forvariance switching models 208–11Gaussian kernel regression 131Generalised Method of Moments (GMM)255–6estimation of long-memory stochasticvolatility model 262estimator 262–3geometric Brownian motion 357German Yield curve, afﬁne modelling of71–126Gibbs algorithm 259Gini Index 174Glosten, Jagannathan and Runkle (GJR) model320–2Granger causality test 86, 124Granger–Ramanathan optimal weightingregression-based approach 38, 131,142–3Hamilton ﬁlter 251, 252, 255, 264, 265, 275,282for maximum likelihood estimation ofdiscrete stochastic volatility models253heating degree days (HDDs) 383–4hedging, implicit, of unknown common riskfactors, cointegration and 45–7Hinton graph 28Historical Burn Analysis (HBA) 384historical volatility 132–4, 243homoskedastic model, one-factor 74hyperbolic tangent 138implicit factor modelling 66, 67implied standard deviation 130implied volatility 134–5, 243importance sampling 258–9impulse-response analysis 86“impurity” index 173–4independent components analysis (ICA)index arbitrage 47–8indirect inference method 256, 257–8inﬂation measure 84Information Index 174interpolation, deﬁnition 42
67
Jarque–Bera statistic 6, 9, 199, 200, 202,241, 242, 385Jensen inequality 81
Indexjump models 261jump process 357–8Kalman ﬁlter 76, 223–36, 251, 255, 275applied to German yield 87–106imputation accuracy 394missing data 381, 382, 389–90for quasi-maximum likelihood estimation ofcontinuous stochastic volatility models252–3Kalman gain matrix 22Kalman smoother 269for continuous stochastic volatility models254–5Kim smoother 272for discrete stochastic volatility models255Kolmogorov–Smirnov test 199, 200, 202latent factor models 84likelihood ratio (LR) test 14linear cross-correlation analysis 26Ljung–Box test 199, 202log-normal stochastic volatility model 245log-periodogram estimator, semi parametric262, 263logit estimation 10, 17–20logit1 model 18, 19–20, 21, 22, 23, 32–6long-memory stochastic volatility model 262market risk, VaR applied to 244Markov chain 246–7ergodic 248Markov Chain Monte Carlo (MCMC) 256maximum likelihood estimation and 260–1Markovian switching models 193, 194–5,246application to foreign exchange rates197–205descriptive statistics 199empirical results 200evaluation strategy 200evaluation with a simple hedging strategy202–5moving average deﬁnitions 203–4trading results 204–5trading rules of EMA trading models withvolatility ﬁlters 204trading rules with EMA trading models204trend-following moving average (MA)models 202features of foreign exchange interbankmarket 197–9residuals analysis 200–2Markovitz model of portfolio risk in Excel293–311
403alternative optimisation targets 308–10matrix algebra in Excel with increasingassets 303–8matrix approach 301–3simple model 294–300Max Minority 174maximum drawdown 31maximum likelihood estimation 195–7, 387maximum likelihood procedure applied toGerman yield 87–106Mean Absolute Error (MAE) 31, 32, 130,143, 144, 393mean absolute percentage error (MAPE) 29,31, 32, 130, 393mean error (ME) 393mean squared error (MSE) 216–17method of moments 255–6Metropolis–Hastings steps 259, 260, 261missing data, ﬁlling analysis for 381–98Monte Carlo simulation 244, 281Monte Carlo variance 258–9Moving Average Convergence/Divergence(MACD) technical models 32, 34,36, 37in EUR/USD forecasting and trading models10–11long-term (LMA) 11short-term (SMA) 11multilayer feedforward neural networks(MLNNs) 166multilayer perceptron 22, 137multivariate continuous stochastic volatilitymodels 264multivariate discrete stochastic volatilitymodels 264–5Multivariate Switching Regime Beta Model282naı̈ve approachin EUR/USD forecasting and trading models10imputation accuracy 394to missing data 385nearest neighbours 4neural network modelsactivation function 24advantages/disadvantages 21in forecasting FX time series 2–3fully connected 24in FX forecasting and trading currencyvolatility 129, 130–2imputation accuracy 394issue affecting performance 25–6literature evaluation 3–4logistic function 24, 26missing data 381, 382, 390–1, 394post-training weights analysis 28
404neural network models (continued)procedure 26–31technical implementation, for classiﬁcationin Excel 167–72, 191theory and methodology 20–31transaction costs 36Neural Network Regression (NNR) models 1,2–3, 4, 129forecasting accuracy results 32, 35, 36, 37transfer function and 138volatility forecasting and 137–9Neural Network Regression/Recurrent NeuralNetwork (NNR/RNN)cf GARCH (1,1) in trading simulation147–9out-of-sample forecasting accuracy 143–5volatility forecasts 140–2Newey–West standard errors 108Newey–West standard deviations 106no-arbitrage approach 47nonlinear error-correction modelling 131nonlinear nonparametric models 139nonstationarity 42–3oblique decision trees 172observation-driven models 244–5Occam’s Razor 25one-factor homoskedastic model 74optimal decay model 316–18, 324–6optimisation error 24option pricing, stochastic volatility pricingapplied to 275–80ordinary least squares (OLS) estimation 46in factor sensitivities estimation 216–22Ornstein–Uhlenbeck process 245, 276orthogonal GARCH 313overﬁtting of models 25over-the-counter currency optionsadvantages of 349–50at-the-money forward volatility 355, 356empirical applications 365–77estimation of RND functions using optionspreads 365–70implied correlations/credibility tests371–7indicators of credibility of an exchange rateband 361–5measures of correlation and prices 359–61risk neutrality function estimation 349,350, 351risk-reversals 353–4, 356RND estimation using option spreads355–9strangles 353, 354, 356valuation of currency options spreads353–5
Indexpairs trading 42, 49parameter-driven models 244–5Pentanomial model 284–6Pentanomial tree 279, 280Phillips–Perron (PP) test statistic 6, 7, 385principal components analysis (PCA) 67, 73,74–5algorithm 396–8computation 391–2drawback of 395imputation accuracy 394missing data and 381, 382, 391–3pure risk premium 81quadrinomial tree 278, 279quasi-maximum likelihood (QML) estimator253, 256, 262–3Ramsey’s RESET test 14random coefﬁcient model 226random trend model 226random walk forecasting accuracy 3random walk model 3, 4, 225–6Recurrent Neural Network (RNN) 3, 29, 38in forecasting and trading currency volatility129, 131volatility forecasting and 139–40relative value analysis 67Ricatti equation 92risk-adjusted measures of return 2risk neutrality (risk-neutral density; RND)function estimation 349, 350, 351using option spreads 365–70riskless arbitrage 47, 48, 49RiskMetricsTM model 315–16, 324, 350rnn1 29–31robust regression analysis 391rolling regression 218–22root-mean-squared error (RMSE) 1, 25, 31,32, 130, 138, 143, 144, 393scalar GARCH model with variance targeting328–9SEE5 classiﬁer 178–91advanced options 189boosting 184–6categorical value subsets 186–8construct classier 189–91costs ﬁle 189cross-validation trials 188–9data inputs 178–80implementing for windows 180–1rulesets 182–3softening thresholds 188winnowing attributes 186sell signal, EUR/USD 31
Indexsemi parametric log-periodogram estimator262, 263serial correlation LM test 385shadow effect in rolling estimation 221Sharpe ratio 19, 31–2, 34, 37, 130sigmoid function 138Simulated Expectation Maximisation (SEM)260Simulated Likelihood Ratio (SLR) 260–1simulated method of moments 256‘smile effect’ 134, 276‘sneer effect’ 276SRSV model 267“statarb” strategy 50statistical arbitrage 47–50statistical modelling 67stochastic parameter regression model223–36stochastic variance 130stochastic volatility (SV) models 240,246–50with continuous volatility 247–8extensions 261–3Kalman ﬁlter for quasi-maximumlikelihood (QML) estimation252–3Kalman smoother for 254–5with discrete volatility 248–50extensions 263Hamilton ﬁlter for maximum likelihoodestimation of 253Kim smoother for 255estimation 250–61, 255–61extensions of 261–3ﬁlter for 250–3simulation-based methods 256–61smoother for 254–5Student-t-based 261stock beta estimation 219stopping rule 174Student-t-based stochastic volatility model261Student-t-distribution 136Sum Minority 174supervised learning 164tau-period variance ratio 44Theil inequality coefﬁcient (Theil-U) 31, 32,130, 143, 144, 393three-layer feedforward neural network167Index compiled by Annette Musker
405time series modelling, cointegration and 42–5time-varying factor sensitivities estimation213–36ordinary least squares (OLS) 216–22stochastic parameter regression model223–36weighted least squares (WLS) 222–3trading rulesapplied example 344–6correlation of linear forecasters 340–1data 333–5equivalence 336–8expected return of linear forecasters 342–4expected transactions cost under assumptionof random walk 338–40expected volatility of moving averages341–2moving averages 335–6trading simulation performance measures 33,34transaction costs 36trend-stationary time series 43Twoing Rule 174Value at Risk (VaR) 72, 243–4stochastic volatility pricing applied to280–3, 286variance ratio analysis 50variance ratio function (VRF) 45variance ratio tests 44–5volatility and correlation modelling using Excel313–32basics 314–15model comparison 322–3, 331multivariate models 324–31univariate models 315–23volatility and forecasting accuracy modelcombinations 142–3volatility forecast classiﬁcation 146Volatility program 265–75estimation 267–73forecasting 275simulation 273–5volatility smile 356Wald statistic 136weather data and weather derivatives 383–5weather databank 384–5weighted least squares (WLS) 222–3yield curve, evolution of 140
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