Questions tagged [parameter-estimation]
The parameter-estimation tag has no usage guidance.
0
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2answers
60 views
GARCH fit: “failure to achieve convergence”… a problem?
Sometimes when one is trying to fit a GARCH model may happen that in the estimation summary (whatever software is) there is written "failure to achieve convergence after n iteration" or similar things....
0
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0answers
46 views
What is the value for Δt term in an Ornstein Uhlenbeck process?
I am looking at O-U processes for the first time and I was wondering what is the Δt term value.
To become more specific I have a daily dataset with daily prices ...
0
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0answers
48 views
Good introduction to estimating stochastic diffusion processes?
So, in an advanced Econometrics course, the current topic relates to estimating transition densities and diffusion processes by MLE, such as this R package doc describes, for ex., and I have to admit ...
0
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0answers
502 views
Hull white 1 factor historic parameter estimation
I'm working on a script to value an option whose value is dependent on interest rate movements.
For this I'm using the Hull White 1-factor model to simulate the interest rate movements.
\begin{align}
...
2
votes
1answer
178 views
Practical way to estimate price sensitivity to unexpected earnings (i.e., post-earnings drift)?
Post-earnings announcement drift is a well documented anomaly in financial research. In 2017 May NBER paper, Replicating Anomalies, the authors found that anomalies related to standardized unexpected ...
0
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1answer
103 views
How to estimate historical implied volatility?
I want to estimate the historical price of out of the money puts on equities.
I do have about 10 years history of implied volatility (IV) but I would like more.
I had the naïve idea modeling the IV ...
8
votes
2answers
560 views
Estimation of the drift of a non-stationary process
I'd like to estimate the drift of a continuous-paths, non-stationary, stochastic process $X_t$ from a time series of values $\{X_{i\Delta t}\}_{i=1,\dots,N}$ sampled from a single realisation of that ...
3
votes
1answer
41 views
What are some reasonable parameters with three Wiener processes?
In a foreign currency model, domestic and foreign stocks + exchange rate is modelled via 3 Wiener processes.
I am trying to price options in this model, however, I am unsure what some realistic ...
0
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0answers
101 views
Problem with simulating 2 Ornstein-Uhlenbeck processes for extreme parameters
I have a problem with simulating 2 correlated Ornstein-Uhlenbeck-processes.
After estimating the parameters from some data with multivariate maximum likelihood, it seems that I cannot simulate.
I ...
2
votes
0answers
43 views
LSE GARCH Modells
currently I am working with GARCH Modells. And it came to my attention that for the parameter estimation Maximum Likelihood approaches are commonly used. However I was wondering why Least Squared ...
0
votes
1answer
154 views
EM for conditional Gaussian model
Let $$X_1\sim N(\mu_{X_1},\sigma_{X_2}^2)$$ $$X_2\sim N(\mu_{X_2},
\sigma_{X_2}^2)$$
where $\mu_{X_2}=c+aX_1$. Also, I have data $D$ (with missing values on $X_1,X_2$).
How can I update/estimate the ...
2
votes
1answer
964 views
Robust standard errors in GARCH modelling (rugarch)
I am currently conducting some GARCH modelling and I am wondering about the robust standard errors, which I can obtain from ugarchfit() in ...
4
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0answers
106 views
Volatility Parametrization Libor Market Model - Underspecified Model?
Does the volatility parametrization that I have chosen give an underspecified model? Which volatility parametrization in the Libor Market Model would suit the best for the particular case described ...
3
votes
2answers
211 views
How to transform Ornstein-Uhlenbeck parameters from hourly to daily?
I get the parameters (long-term mean, volatility, mean-reversion speed, correlation) of two correlated Ornstein-Uhlenbeck processes via a likelihood estimation from hourly data. If I want to transform ...
4
votes
1answer
628 views
How to estimate parameters for 2 correlated Ornstein-Uhlenbeck processes with maximum likelihood?
I would like to use maximum likelihood to estimate the parameters of two correlated Ornstein-Uhlenbeck processes from empirical data.
Do you have any good references for this? If you have any hints ...
0
votes
1answer
511 views
Kalman Filter in Interest Rate Models
A couple questions regarding the use of Kalman filtering in estimating parameters of short rate models:
1) In Duan & Simonato (1995), which seems to be one of the earliest applications of the ...
4
votes
2answers
877 views
Degrees of freedom in calculating significance of GARCH coefficients
I am trying to determine the significance of coefficients of a GARCH model by calculate the p-values using the following Matlab formula:
pvalues = 2*(1-tcdf(abs(t),n-v)),
where $t$ is the t-stat, $...
2
votes
1answer
341 views
GJR-GARCH with $\alpha = 0$ as parameter estimate
I am estimating a GJR-GARCH(1,1) model with variance targeting in R. As data I am using returns on some stock indices. While calculating the GARCH models I obtain $\alpha=0$ for some indices. From ...
0
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1answer
53 views
Imposing MLE restrictions by logistic mapping
I am doing some Maximum Likelihood Estimation with a density that has time-varying parameters. I am using the fmincon function in Matlab, but I do not know how to ...
1
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0answers
46 views
Texts on the Generalized Method of Moments
I was looking for a book that could explain me well the Generalized Method of Moments, its mathematical nuances, and even have a look to the empirical side, maybe with some guided exercises with Stata ...
1
vote
2answers
626 views
Calibration of non-mean-reverting OU process
I'm looking for some reference on how to calibrate a non-mean-reverting Ornstein-Uhlenbeck process to historical data using MLE or OLS. The model has the following SDE:
$d\lambda(t)=a\lambda(t)dt+\...
0
votes
1answer
143 views
Local volatility parametrization using the spot
Is it possible to estimate the local volatility using the spot price S at time t instead of the strike price K and the expiry date T ?
Any help would be appreciated.
6
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0answers
114 views
What kind of errors arise when I fit ARMA(1,1) to data generated from ARMA(1,1)-GARCH(1,1) process?
As far as I know estimates of parameters of ARMA(1,1) are asymptotically optimal when fitted to data from ARMA(1,1)-GARCH(1,1) process, and only their variance increase, so when we assume large ...
3
votes
2answers
457 views
How to get around flat likelihood function when calibrating GBM parameters?
I want to calibrate jointly the drift mu and volatility sigma of a geometric brownian motion,
$$\log(S_t) = \log(S_{t-1}) + (\mu - 0.5*\sigma^2) \Delta t + \sigma*\sqrt{\Delta t}*Z_t$$
where $Z_t$ ...
6
votes
1answer
926 views
Ornstein versus AR(1) for modeling stationary data
I've come across several posts regarding parameter estimation for O-U models given some stationary data (say, some sort of mean reverting spread), but I can't seem to find an answer as to why modeling ...
4
votes
0answers
230 views
Time series (stochastic process) estimating parameters using characteristic function
I have a time series of assets ${A_1, A_2, ..., A_n}$, which is described by a sophisticated distribution having the following characteristic function: $\phi(u; t;\theta)$, where $\theta$ is a vector ...
14
votes
1answer
524 views
Covariance estimation: shrinkage, random matrix theory, what else?
Shrinkage was much en-vogue before random matrix theory (RMT) took everybody's attention in covariance matrix estimation, however the latter also showed its limits. A plethora of other estimators has ...
17
votes
2answers
3k views
Parameter estimation of Ornstein–Uhlenbeck and CIR processes
I would like to estimate Ornstein–Uhlenbeck process' parameters via Kalman filter.
My process is the following one:
$\text{d}x_{t}=\alpha(\theta-x_{t})\text{d}t+\sigma\text{d}W_{t}$
I'm interested ...
