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Time Series Models Cointegration Granger Causality and ARCH Interbank Rates


									Stochastic Volatility Models

   Course: Applied Econometrics
   Lecturer: Zhigang Li
Why Study Stochastic Volatility?
 Heteroskedasticity can affect the standard error
  estimates of model parameters
   We can address this using robustness estimators.
 Risk is a key factor in many decision process (e.g.
  investment). Risk changes over time and this often
  reflect on instable variance in the disturbance of
  models with price measures as dependent variables.
   Capital Asset Pricing Model (CAPM) suggests a
      natural relationship between expected returns and
      volatility of returns.
   Option pricing depends critically on the risks of
 News in the financial market may reflect on changes
  in the volatility of price measures.
Autoregressive Conditional
Heteroskedasticity (pp. 416 or 438)
 First-order ARCH (or ARCH(1))model
 U is the error term of a typical regression
  model and v is the “error term of the error
  term u”.
 The model implies that the variance of the
  error term u is correlated over time, so
  called “volatility clustering”.
 ARCH is just one particular form of
Generalized ARCH Model
 GARCH(p,q)
   Yt=μ+ut
   ut=ht1/2vt
   v is i.i.d. with standard normal
   ht=α0+Σ1qαiu2t-i+Σ1pβjht-j
   GARCH(0,q) model is an ARCH (q)
Why ARCH-Type Models?
 ARCH-Type models are easy to
  estimate and interpret. (There are
  other volatility models, but the ARCH-
  Type is generally much easier to
 Knowledge of future risk is useful for
  optimal decision at the current stage.
Currency Board Reforms and Interbank
Market of Hong Kong (Tse and Yip, 2003)
 A CBS scheme is introduced in Hong Kong
  on 17 October 1983, fixing the exchange
  rates between HK$ and US$. Seven major
  reforms have been made to the CBS
  system since them.
 What are the effects of the reforms on the
  quality and stability of the financial sector
  of Hong Kong?
   The impact of the mean and variance of the
    interest rate differential between Hong Kong and
    the US.
Shocks to CBS
 Oct 1983: Account Aggrangements
  introduced to limit the ability of HSBC to
  create money.
 Jul 1992: Liquidity Adjustment Facility
  introduced to cap the variation of interest
 Mar 1994: Change target from interbank
  liquidity to interbank interest rate.
 Oct 1997: Financial Crisis
 Sept 1998: Reform packages
Empirical Strategy
 Data
   Daily observations of the HK and US
    interbank interest rates (from
 Model
Meteor showers or Heat Waves?
(Engle et al., 1990)
 Heat waves: Domestic news affects
  only local financial markets.
 Meteor showers: Domestic news can
  affect foreign financial markets.
   Market failure
   Need time to absorb news into trading
Test Framework
 N nonoverlapping markets within a day
  with market 1 open first.
 Let εi,t be the intra-day exchange rate
  change divided by the square root of
  business hours in market i on date t.
 A modified GARCH model
   Hi,t=ωαi+βjihi,t-1+Σ1i-1αijε2j,t+Σinαijε2j,t-1
   If αij=0 for i different from j, then the heat
    waves model is supported. Otherwise, the
    meteor shower model is supported.
Empirical Strategy
 Intra-day yen/dollar exchange rate from
  Oct 3, 1985 to Sep 26, 1986.
 Four markets
     Tokyo
     Pacific
     New York
     Europe
 Three tests
   Heat waves
   Meteor showers with foreign news
   Meteor showers with country-specific news
Computer Exercise
 Example 12.9 (Using NYSE weekly
  stock returns data)

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