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Questions tagged [parameter-estimation]

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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....
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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 ...
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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
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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
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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
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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 ...
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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
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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
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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
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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 ...
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...