Questions tagged [parameter-estimation]
The parameter-estimation tag has no usage guidance.
50
questions
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46 views
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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24 views
Estimating parameters using Lasso Regression in Python
I'm a begginer and my goal is to estimate these parameters (a0, a1, a2, a3) from the following model:
SPXret(h) = a0 + a1*SPX(t) + a2*VIX(t) + a3*IVTS(t)
where:
...
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0answers
56 views
MPT pitfalls and solutions
I am a master student in finance and I am looking for a (literature) review paper (or book) about the pitfalls of MPT and the potential solutions. Specifically, I am interested in the sensitivity of ...
3
votes
1answer
110 views
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 ...
2
votes
0answers
72 views
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 ...
3
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145 views
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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0answers
77 views
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 ...
1
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1answer
166 views
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) ...
3
votes
1answer
145 views
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 ...
3
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81 views
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 ...
2
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0answers
247 views
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 ...
2
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0answers
50 views
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 ...
1
vote
1answer
260 views
Can someone explain the particle filter algorithm in detail with intuition
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 ...
2
votes
1answer
95 views
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 ...
1
vote
2answers
208 views
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 ...
2
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0answers
69 views
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 ...
3
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0answers
73 views
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 ...
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3answers
255 views
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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0answers
36 views
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.
...
3
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0answers
310 views
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:
$dM(t)=rM(t)dt$
$dS_1(t)=S_1(t)(\mu_1dt+\...
1
vote
1answer
73 views
Calibrate a model parameter with an error function
Suppose I want to find the implied volatility using an option model from market prices. Surely I can find the implied volatility for each strike price ($k$ different strike prices) for a given ...
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0answers
62 views
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 ...
3
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0answers
103 views
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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0answers
77 views
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 ...
0
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2answers
960 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
57 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 ...
2
votes
1answer
217 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
255 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
897 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 ...
2
votes
1answer
48 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 ...
2
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0answers
48 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
184 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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3answers
2k 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
142 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 ...
2
votes
2answers
309 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 ...
2
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0answers
123 views
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, $\nu$...
4
votes
1answer
1k 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
739 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 ...
3
votes
2answers
2k 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
672 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
60 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 ...
2
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0answers
51 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 ...
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vote
2answers
1k 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
198 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.
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0answers
129 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
727 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
1k 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
248 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 ...
15
votes
1answer
814 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 ...
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2answers
4k 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 ...
