Simple Covariance Models: Historical and Implied
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Ch9 slides
‘Introductory Econometrics for Finance’ © Chris Brooks 2013 In exactly the same fashion as for volatility, the historical covariance or correlation between two series can be calculated from a set of historical data Implied covariances can be calculated using options whose payoffs are dependent on more than one underlying asset The relatively small number of such options that exist limits the circumstances in which implied covariances can be calculated Examples include rainbow options, ‘crack spread’ options for different grades of oil , and currency options. Implied Covariance Models ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 To give an illustration for currency options, the implied variance of the cross-currency returns is given by where and are the implied variances of the x and y returns respectively, and is the implied covariance between x and y So if the implied covariance between USD/DEM and USD/JPY is of interest, then the implied variances of the returns of USD/DEM and USD/JPY and the returns of the cross-currency DEM/JPY are required. EWMA Covariance Models ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 A EWMA specification gives more weight in the covariance to recent observations than an estimate based on the simple average The EWMA model estimates for variances and covariances at time t in the bivariate setup with two returns series x and y may be written as hij,t = λhij,t −1 + (1 − λ )xt −1yt −1 where i j for the covariances and i = j ; x = y for the variances The fitted values for h also become the forecasts for subsequent periods λ (0 < λ < 1) denotes the decay factor determining the relative weights attached to recent versus less recent observationsThis parameter could be estimated but is often set arbitrarily (e.g., Riskmetrics use a decay factor of 0.97 for monthly data but 0.94 for daily). Dostları ilə paylaş:
