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]]
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
--
Patrick Burns
pbu...@pburns.seanet.com
twitter: @burnsstat @portfolioprobe
http://www.portfolioprobe.com/blog
http://www.burns-stat.com
(home of:
'Impatient R'
'The R Inferno'
'Tao Te Programming')
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
