Questions tagged [parameter-estimation]
The parameter-estimation tag has no usage guidance.
58
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Likelihood of least squares estimates of Vasicek model
I want to compare some short-rate models based on likelihood and AIC. I will use least squares estimates.
Let's take the Vasicek model as an example and its discretized version:
$$
dr = \alpha(\beta-r)...
- 211
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74
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Maximum likelihood estimation of system of correlated SDEs
I have the following system of SDEs (which you can think of as 3 different stocks)
$$dX_t^1 = \mu_t X_t^1 dt + \sigma_t X_t^1 dW_t^1$$
$$dX_t^2 = \mu_2 dt + \sigma_2 dW_t^2$$
$$dX_t^3 = \mu_3 dt + \...
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0
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23
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Empirical estimation of the rate parameter in exponential distribution of time arrivals
I am recording the execution time of aggregated trades on the BTCUSDT market on Binance. The websocket server delivers messages of the following form
{"e":"aggTrade","E":...
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2
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154
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What is the process for using OLS on time series models (HAR like)
I am reading about HAR models for realised variance and they all seem to use WLS or OLS to calculate the parameters. Now I understand how that works if you just use say the 10 years of AAPL intraday ...
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104
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ESSVI calibration problem in translating parameter bounds
I am trying to implement the calibration algorithm presented in the "ESSVI Implied Volatility Surface" white paper from Factset by Akhundzadeh et al.
The eSSVI model includes 2 variables ...
- 11
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72
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Calibration for CIR Model Discretization for Predictor Corrector and Milstein method
I'm new to Quantitative Finance. I've data which I need to fit a CIR model and estimate its parameters.
$ dX_{t+1} = a(b-X_{t})dt + \sigma \sqrt{X_t}dW_{t} $
While I can fit and obtain ...
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125
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how to estimate Geometric Brownian Motion parameters on long timeseries [closed]
I'm working on a 50-years financial timeseries and I would like to simulate GBM paths from it.
The first thing I'm supposed to do is to estimate the drift $\mu$ and the volatility $\sigma$ parameters.
...
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118
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How can I estimate value-at-risk of a long/short portfolio without making simplifying assumptions?
I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am ...
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55
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Nonlinear Constrained optimization for a CIR model
I want to calibrate a CIR model which is commonly used to model the evolution of interest rates. Briefly speaking, we know that its dynamics is of the form
\begin{equation}
dr_t = \kappa (\theta - r_t)...
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1
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339
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Estimating volatility of a geometric Brownian motion at different sample rates
I have troubles estimating volatility (= standard deviation of log returns) when the data is re-sampled at different sample frequencies.
Problem
I have generated a time series data using a geometric ...
- 285
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70
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Option pricing when stock price follows binomial tree
Assume that the stock price is currently trading at $S_0$. It is known that the stock price follows a binomial tree, such that its price will be either $S_0e^{\theta_u}$ or $S_0e^{−\theta_d}$ over the ...
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1
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184
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How to parameterising Greek Surfaces?
I'm currently working on my master thesis, where I have data on option trading volume and flow (number of shares bought minus sold; i.e., net position), divided among three kinds of market ...
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0
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79
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Robust standard errors OLS for term structure
Suppose i have estimated the following model with OLS: $y_{1,t+1} - y_{1,t} = \alpha + \beta y_{1,t} + \epsilon_{t+1}$. Where $y_{1,t}$ is the 1 month zero-coupon yield at time t. What would be an ...
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Initial forward variance curve $\xi_0(t)$ in the Rough Bergomi model
The rough Bergomi model is defined as
\begin{cases}
\frac{dS_t}{S_t} = \sqrt{v_t}dW_t^1 \\
v_t=\xi_0(t)\exp(\eta \tilde{W}_t^H-\frac{1}{2}\eta^2t^{2H}) \\
\tilde{W}_t^H = \int_0^t \sqrt{2H}(t-s)^{H-\...
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MatLab code does not work for Heston model calibration
I am trying to calibrate Heston model on some data and I have the following code. Code is supposed, after it reads the data, to give back 5 parameters. However, I get an empty answer from MatLab. Does ...
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1
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200
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Long-Term Energy Price Modelling: Log Returns, Distributions, Time-Weighting
I wish to forecast energy prices in the long-term (ca. 20 years) for energy-efficiency investments. While I understand that the energy carriers are particularly sensitive to external (geo-political) ...
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1
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Which references would be useful as an introduction to econometrics as it pertains to CONTINUOUS TIME models?
It seems like the problem of trying to estimate model parameters for continuous time models is not commonly covered in standard econometric textbooks, even those focusing on time series. I certainly ...
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120
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How often to tune the regularisation parameter in LASSO?
I'm trying to implement the following paper: Avellaneda & Lee (2010), Statistical Arbitrage in the US equities market.
To build the strategy, the idea is to trade a stock and hedge using a basket ...
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414
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James-Stein estimator for superior estimates of returns in m.v. portfolio optimization
I am currently learning about statistical techniques to enhance the estimation of input parameters in a m.v. optimization. Specifically I have some doubts about the James-Stein estimator applied as an ...
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57
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Correcting high AR(1) coefficients in dynamic Gordon model
I have just finished my thesis on a heterogeneous dividend expectations model applied to the COVID-19 crisis. However after receiving some feedback there is one last issue I want to resolve. I'm using ...
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2
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855
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Can someone explain the particle filter algorithm in detail with intuition [closed]
I am trying to understand particle filters and their application but i am not able to understand the underlying methodology.
I have read a few sources but either the language is not clear or they dive ...
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1
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249
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Cornish Fisher VaR Parameters Calibration
I am trying to calculate Cornish-Fisher (modified VaR), but I am in a trouble because when I am reading some articles, some authors calculate the Cornish-Fisher expansion taking parameters S and K, as ...
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2
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268
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What to do if certain parameters are not market observable?
Lets say I have no clue on correlation between 2 equities in the market (i.e. i don't have an observable market price). What is the best way to go about marking this correlation for lets say the best ...
- 1,875
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80
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Beta estimates of Regressions on AR(1) Process
I am currently working through the paper The Myth of Long-Horizon Predictability [1] and I got stuck in reproducing the empirical results in Section 1.4.
It is my understanding that time series of ...
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94
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Are the increments of a stochastic process driven by fractional Brownian motion independent?
I'm studying the following equation
$$\tag1
dX_t = \mu X_t dt + \sigma X_t dB^H_t
$$
where $B^H$ is the fractional Brownian motion (fBm) of Hurst parameter $H\in(0,1)$, that is a continuous ...
- 147
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3
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404
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maximum likelihood pdf
I am looking at the topic maximum likelihood, and I cannot understand why we set the pdf of $y_{t}$ equal to 1. It is with regards to a OLS example.
The information i got is this:
Model: $y_{t}=\...
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Likelihood increases on increasing variance of measurement error in kalman filter
I tried to fit a local trend model to daily data of a currency. I used the "dlm" package and tried to estimate the parameters V (measurement noise) and W (the process noise) via maximum likelihood.
...
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343
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Estimating Market Price of Risk
I need help with estimating market price of risk. Assume money market account and two risky assets which exposed to same two sources of risks follow process:
$dM(t)=rM(t)dt$
$dS_1(t)=S_1(t)(\mu_1dt+\...
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1
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Calibrate a model parameter with an error function
Suppose I want to find the implied volatility using an option model from market prices. Surely I can find the implied volatility for each strike price ($k$ different strike prices) for a given ...
- 1,396
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103
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Brownian motion from price-series, what is the time step?
If I assume a given empirical price-series is a brownian motion, I can estimate the drift and standard deviation as long as I know what the time step was when the process was 'generated'.
But since ...
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Inverse Problems in Finance
Are there any canonical references for inverse problems in finance? For example, if I have a measure that evolves with Fokker-Planck dynamics, are there standard approaches used by the community to ...
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Parameter Estimation of any model
I am new to time series modelling.I cant get my head around parameter estimation and its methods. My question consists of 3 parts :
1st : Lets say i have a model like Garch or Heston model or a SVJD ...
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2
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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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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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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 ...
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323
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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 ...
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2
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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 ...
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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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52
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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 ...
- 31
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1
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191
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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 ...
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3k
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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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161
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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 ...
- 353
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2
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358
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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 ...
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Simulating t-distributed returns by calibrating degrees of freedom $\nu$ from variance or kurtosis
A slight twist (I hope) on the familiar problem of simulating log returns from a t-distribution. My two questions concern calibration to sample data.
First, one can infer the degrees of freedom, $\nu$...
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1
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1k
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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 ...
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853
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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 ...
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2k
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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, $...
- 491
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votes
1
answer
818
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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 ...
- 491
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1
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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 ...
- 491
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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 ...
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