By Ser-Huang Poon

Monetary marketplace volatility forecasting is certainly one of brand new most vital parts of craftsmanship for pros and lecturers in funding, choice pricing, and fiscal industry law. whereas many books deal with monetary marketplace modelling, no unmarried e-book is dedicated essentially to the exploration of volatility forecasting and the sensible use of forecasting versions. a realistic consultant to Forecasting monetary marketplace Volatility offers useful tips in this important subject via an in-depth exam of a number of renowned forecasting types. information are supplied on confirmed ideas for construction volatility types, with guide-lines for truly utilizing them in forecasting functions.

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The means of the two states are ﬁxed, but there is no restriction on the timing of the switch, the duration of each regime and the probability of switching. Sometimes a three-regime switching is adopted but, as the number of regimes increases, the estimation and modelling become more complex. Technically speaking, if there are inﬁnite numbers of regimes then there is no difference between the two models. The regime-switching model and the structural break model will be described in Chapter 5. 2 Volatility Forecast Evaluation Comparing forecasting performance of competing models is one of the most important aspects of any forecasting exercise.

6) i=1 Next, we have the EWMA model for the sample standard deviations, where σ 2t = 1 1 + λ + + · · · + λn λ2 2 2 2 . + λσt−1 + · · · + λn σt−n σt−1 As n → ∞, and provided that λ < 1 σ 2t = (1 − λ) ∞ 2 λi−1 σt−i . g. the GARCH(1, 1) model), and hence it adjusts readily to changes in unconditional volatility. 2 EWMA, a sample standard deviation model, is usually estimated based on minimizing in-sample forecast errors. There is no volatility error in GARCH conditional variance. 6) has not. 4 EXPONENTIAL GARCH The exponential GARCH (denoted as EGARCH) model is due to Nelson (1991).

For higher orders of GARCH, the constraints on βi and α j are more complex (see Nelson and Cao (1992) for details). The unconditional variance equals ω σ2 = p 1− q βi − i=1 αj j=1 The GARCH( p, q) model is covariance stationary if and only if p q i=1 βi + j=1 α j < 1. Volatility forecasts from GARCH(1, 1) can be made by repeated substitutions. 1) to provide an estimate for the expected squared residuals E εt2 = h t E z t2 = h t . Arch 39 The conditional variance h t+1 and the one-step-ahead forecast is known at time t, h t+1 = ω + α1 εt2 + β1 h t .