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6

I personally use the simple Garch(1,1) for volatility filtering in the risk management area. In fact in most cases I don't even estimate the parameters, I stick 0.94 for mean reversion, 0.04 for the squared error and I get the constant by matching the series variance. My experience is that there is no point pretending to finetune parameters when vol is ...


3

$\alpha=0$ does not imply constant volatility. Consider just a simple Garch(1,1): $$\sigma^2_t = \omega + \alpha \eta_t^2 + \beta \sigma^2_{t-1}$$ Note that: $$\sigma^2_t = \omega + (\alpha + \beta) \eta_t^2 - \beta (\eta_t^2- \sigma^2_{t-1})$$ Now add $\eta_{t+1}^2$ to both sides: $$\eta_{t+1}^2 = \omega + (\alpha + \beta) \eta_t^2 - \beta (\eta_t^2-...


3

Since you're asking on a quant finance forum, the mathematical approach would be Decide on a model that the stock price follows, and Compute the expected value of the price, conditional on the most recent price. A famous model, made ubiquitous by Black, Scholes and Merton, is a geometric Brownian motion. Under this model, the stock price $S_T$ at time $...


2

Interesting question, as All the answers (including mine) could not be generalized unfortunately. As far as I am concerned, I use a univariate EGARCH for risk modelling purposes (Filtered Historical Simulation (FHS), etc.). 1 - EGARCH, merely because GARCH models do not take into account so-called leverage effects, which is crucial to me for skewed and ...


2

$v$ should be the total number of parameters (constants + AR + MA + GARCH + ARCH). I disagree with @kiwiakos, the student t(df) distribution is used because we are using standard errors which are estimates of standard deviations (and not true standard deviations) to compute the statistic. That is the reason why we use student t test eventhose the ...


2

Before you start asking about the number of dof, how do you know that the finite sample distribution of parameters is student-t? I don't think it is. In linear regression they are student-t because of linearity and under assumption for the residual distribution. In Garch you can just say that if you estimate using max-likelihood then asymptotically (not ...


2

Even in calculating VAR, you have certain assumptions / constants / random numbers being used. Hence, even your VAR calculation is not 100% correct. So, you are estimating VAR and you hedge similar portion of risk, however your Estimations aren't 100% correct. This is Estimation Risk. Estimation risk is a generic term. It could be applied to models, VAR, ...


1

Try the mgarch package, it's available at CRAN. In this link you will find an example from Prof. Zivot.


1

1- It seems to me there is a problem in the original code the variable b should be defined as b= sqrt(1 + 3*lamda^2 - a^2) 2- The likelihood is defined just after equation 8. in the paper. You have to take into account the $ \frac{1}{\sigma}$ term (in $ \frac{1}{\sigma} \times g(..) $ , ie to scale the densitie) . So the - 0.5*log(h(t)) refers to this ...


1

Here is an MLE I built that uses logistic mapping. %MLE iterator: for cxm = 1:cxmax for cxth = 1:wx; %thx %Incr. theta within asymptotic min and max. thi1 = thA1(cxth,1); mint = thA1(cxth,2); maxt = thA1(cxth,3); thix = -log((maxt - mint)/(thi1 - mint) - 1); %Logistic inverse. if rand > 0.5; signx = -1; ...


1

If $\log{(|R_t|)}$ is your first term, I'm not sure why this is a matrix. Modulus (determinant herein) applied to a matrix $R_t$ gives a scalar. If your implementation in python produces a matrix, that's likely because modulus is treated as an element-wise abs() function for each element of a matrix. It may be easier and faster to use rugarch (univariate ...


1

The $\lambda$ value used in the original paper is arbitrary, but you can estimate that by assuming (in the simplest case) 2 assets and running the following model: $\sigma^2_{12,t+1}$ $=$ $\lambda$$*$$\sigma^2_{12,t-1}$$+$$(1-\lambda)$$r_{1,t}$$*$$r_{2,t}$; given $r_{1,t}$ and $r_{2,t}$ respectively as the returns for the asset 1 and 2 and $\sigma^2_{12,t}$...


1

I can't comment yet on the topic due to my reputation level (so I will throw an answer up) but having just done my MFE capstone research on EVT implementation for VaR. According to my advisor who was a director of a quant research group at Citi before returning to academia, not many people are doing this. My research was to start collecting data comparing ...



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