You want to give returns rather than prices to the
garch fitting function. Log returns are more
appropriate than simple returns.
Actually a negative lambda is what I would expect.
Higher volatility (across time) is usually associated
with lower returns. The risk premium is more likely
a cross-sectional phenomenon than a time series one.
Some people are not so believing in risk premia in
the first place -- see for instance, Eric Falkenstein.
This would have been better sent to the r-sig-finance
list.
Pat
On 12/03/2013 12:15, Wyss Patrick wrote:> Hey,
>
> I'm trying to implement a GARCH model with Johnson-Su innovations in
order to simulate returns of financial asset. The model should look like this:
>
> r_t = alpha + lambda*sqrt(h_t) + sqrt(h_t)*epsilon_t
> h_t = alpha0 + alpha1*epsilon_(t-1)^2 + beta1 * h_(t-1).
>
> Alpha refers to a risk-free return, lambda to the risk-premium.
>
> I've implemented it like this:
>
> #specification of the model
> spec = ugarchspec(variance.model = list(model = "sGARCH",
> garchOrder = c(1,1), submodel = NULL, external.regressors > NULL,
variance.targeting = FALSE), mean.model = list(
> armaOrder = c(0,0), include.mean = TRUE, archm = TRUE, archpow = 1,
> arfima = FALSE, external.regressors = NULL, archex = FALSE),
> distribution.model = "jsu", start.pars = list(), fixed.pars =
list())
>
> #fit the model to historical closing price (prices)
> fit = ugarchfit(data = prices, spec = spec)
>
> #save coefficients of the fitted model into 'par'
> par <- coef(fit)
> m = coef(fit)["mu"]
> lambda = coef(fit)["archm"]
> gamma = coef(fit)["skew"]
> delta = coef(fit)["shape"]
> #GARCH parameter
> a0 = coef(fit)["omega"]
> a1 = coef(fit)["alpha1"]
> b1 = coef(fit)["beta1"]
>
> My problem is that I often get negative values for lambda, i.e. for the
intended risk-premium. So I'm wondering if I've made a mistake in the
implementation, as one would usually expect a positive lambda.
> And a second question is about the Johnson-Su distribution: Am I right by
extracting the Johnson-Su parameters gamma (delta) by the keywords
"skew" ("shape")?
>
> Many thanks in advance,
>
> Patrick
>
>
> [[alternative HTML version deleted]]
>
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--
Patrick Burns
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