Questions tagged [estimation]

The calculated approximation of a result which is usable even if input data may be incomplete or uncertain.

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1answer
121 views

Arithmetic Brownian Motion in Market Making papers

We often consider high-frequency market maker and suppose that the reference price is the arithmetic Brownian Motion: $dS_{t} = \sigma d W_t$ What is the difference $t_n - t_{n-1}$ in this case? Is ...
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3answers
2k views

Estimating Parameters - Vasicek

The Vasicek model for the short rate $r_t$ is given by the SDE $$ dr_t = \alpha(\beta - r_t)dt + \sigma dW_t, $$ where $W_t$ is a Brownian motion under the physical measure. I'd like to compute bond ...
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1answer
2k views

Estimating correlation using EWMA

I am using an EWMA model to evaluate the correlation between yearly time series. I know Riskmetrics uses $\lambda=0.94$ for daily data and $\lambda=0.97$ for monthly data. Is there a value ...
2
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1answer
180 views

How to compute a single Value-at-Risk (a single quantile) of portfolio returns taking into account correlation between individual returns?

Introduction My goal is to retrieve a single Value-at-Risk (VaR) of a N(0, H) random variable $X$ at the $\alpha \in (0,1)$ confidence level where H is a known d-dimensional positive definite matrix ...
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127 views

Model-Free Option Pricing

From Breeden and Litzenberger (1978) and subsequent work, we may find the risk-neutral density $q_{S_T}$ of $S_T$ from European option prices - assuming there are enough traded options (e.g. SPX) via ...
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3answers
3k views

Tools in R for estimating time-varying copulas?

Are there libraries in R for estimating time-varying joint distributions via copulas? Hedibert Lopes has an excellent paper on the topic here. I know there is an existing packaged called copula but ...
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59 views

How is Kalman Filter used to estimate Term structure Models

I am implementing "The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments" . This paper is using kalman filter to estimate the state and the mean variance and a parameters on ...
3
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1answer
120 views

Mean-variance portfolio optimization: methods for superior estimates of returns

Leaving aside the aspects related to the estimation of the variance component (all the latest techniques to compute a stable covariance matrix of a given set of assets such as simple shrinkage, Ledoit-...
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49 views

ARMA-GARCH estimation with EGB2 distribution

I want to estimate a ARMA-GARCH model by using the EGB2 distribution instead of the normal distribution. The model I want to estimate is: $$y_t = \mu + \phi_1 y_{t-6} + \phi_2 y_{t-8} + \theta_1 \...
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16 views

fiscal period end date

If a quarterly report is released tomorrow, is there any way to figure out the date the quarterly period ended without manually researching? Such as an API? I think there is a deadline of 35/60 ...
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1answer
538 views

MLE error in R: initial value in 'vmmin' is not finite

I am trying to fit an ARIMA(1,1)-GARCH(1,1) model. I changed the starting values a lot but still its returning the same error. Below is my code which contains two functions ...
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1answer
132 views

Neural Networks for Estimation of Unmarked Private Asset Returns from Market Data

Let's assume it is March and my illiquid private assets portfolio is only 50% marked for 12/31, but I want to get the most accurate estimate of my final return for the quarter ended on 12/31. What is ...
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65 views

Estimating an GARCH(1,1) model? Long hand method

I am really trying to invest some time to estimate a GARCH(1,1) method, I know there is many statistical packages that will do this for me (Eviews, MATLAB, R), but I am trying to do this by hand, so ...
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78 views

How rapidly should estimated volatility and volume change for estimating market impact in small markets?

The cost of market impact is usually modeled as: $$ \Delta{P} = \delta \sigma (\frac{Q}{V})^{1/2} $$ Where: $ \Delta{P} $ is the change in price of the asset caused by the transaction size $Q$ $\...
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2answers
142 views

Estimating realised gains given growth rate and churn

If one can estimate that the value of an investment portfolio will grow at $g$% per annum, and can estimate that approximately $c$% of that portfolio will be churned each year (sold and reinvested), ...
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1answer
311 views

Which program for a DCC-MIDAS model?

for a thesis research, I plan to use a DCC-MIDAS model. The program I was working with (STATA) is not able to run this. Do you have any suggestions as to which program is best for this analysis? ...
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3answers
6k views

How can I estimate the degrees of freedom for a Student's T distribution?

I am doing research estimating the value at risk for non-normally distributed assets. I need help in the process of estimating the parameters of Student's t distribution and which method to use. I ...
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23 views

Sample distribution of cross-sectional statistics of returns

Currently doing an application of VaR on sample of industry portfolios in the US. I have a matrix of $n$ industry portfolios with $m$ time-series observations. I calculate cross-sectionally (for each ...
3
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1answer
193 views

Electric power price parameter estimation

currently I am working through the paper of Tino Kluge "Pricing Swing Options and other Electricity Derivatives" to get a better understanding about the power markets. The author establishes methods ...
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193 views

How accurate are Black-Scholes estimates of Vega, Volga, Vanna

Wikipedia provides analytical formulas for calculating Greeks. I can get Delta, Gamma, Theta all from Bloomberg. I need Vega, Volga, Vanna for my research. Should I use these analytical formulas for ...
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290 views

Fama French- typical time lag

I have daily prices of 400 stocks for the last 10 years. I have to create each month a portfolio of 20 stocks that minimizes variance with 2 approaches: 1) Estimate volatility with a GARCH(1,1) model ...
3
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1answer
589 views

How to have an unbiased estimation of the standard deviation when using rolling returns?

I want to estimate the weekly standard deviation of a lognormal process in a usual setup. $$ \frac{dS}{S} = (\dots) dt + \sigma dW $$ where $\sigma$ is a constant and $W$ a brownian motion. The ...
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1answer
220 views

Estimating implied volatility of an index component with no vanilla options market

There are liquid vanilla options trading on an index of 20 equity components. The question is how to price an option on one of the index components, knowing that there are no options trading on that ...
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2answers
351 views

Estimation Risk-Neutral Variance of Returns

I am trying to find a method which allows me to estimate $Var_{\mathbb{Q}}\left(\frac{S_{t_{i+1}}}{S_{t_i}}\right)$ where $S$ denotes the price process of an underlying stock (which has to be assumed ...
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2answers
359 views

How are Quandl monthly S&P500 earnings estimates derived?

Can someone explain how the monthly earnings estimates are derived for S&P500? Quandl sources multpl.com, who state: ...
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1answer
551 views

How to estimate lambda for Jump-Diffusion Process from Empirical data?

So, I have really no idea how to go about this, but how would I go about choosing sensible parameter values for a basic jump-diffusion simulation, namely $\lambda$ ? For example, getting the average ...
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108 views

Estimation of right truncated poisson process

I have following problem: Imagine I generate large number of homogenous poisson process sample paths (by sample path I mean a sequence of arrival times $\tau_i$ all with the same intensity. However ...
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412 views

Estimating parameters of the Cox-Ingersoll-Ross model using CLS in R

I'm working on a project where I need to estimate the parameters of the CIR model. In the particular case, the CIR model is used to model cumulated capital calls for a private equity fund. The data ...
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28 views

Understanding pooled VAR model

I encountered a paper by Vuolteenaho (2002) in which he uses pooled VAR model. I have some troubles understanding the idea. He uses firm level variables (log returns, ROE, etc.) and ultimately he ...
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2answers
329 views

How to estimate the variance of this stochastic process?

I have an unobservable stochastic quantity $\lambda(t)$, which I analytically know the variance of, that is $$\text{Var}(\lambda(t))= \frac{\theta \sigma^2}{2\kappa}$$ My goal is to get an estimate ...
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1answer
129 views

Estimate American-style option delta from similar options

I have a data set which looks something like this, referring to American-style put and call options: ...
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1answer
89 views

Bond yield to maturity vs current interest yield

How close is yield to maturity usually to current interest yield? Can I use yield to maturity to approximate current interest yield of a bond index? I am trying to calculate bond index price returns ...
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46 views

How to estimate bond price returns via an index?

Let's say I have a corporate bond, for which I know current yield, modified duration, coupon and maturity. I want to estimate how it would have performed under certain market conditions by looking at ...
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2answers
260 views

How do I estimate the volatiliy of my portfolio with an estimator that requires High, Low, Open, etc

I have obtained the daily returns of my portfolio $R^{port}_t$ using a certain strategy. Now I want to estimate the realized volatility $\sigma^{port}_t$ using the past 60 days. An obvious way to do ...
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1answer
305 views

Joint estimation of GARCH models with ARMA terms in the conditional mean: a necessity?

Supposing I am using the following models to forecast conditional volatility of index returns, whereby In-sample data is 1996-2007 and out of sample data is 2007-2012, using GARCH type models. I have ...
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110 views

Monte Carlo volatily

I was wondering if we could do a forecast on volatility using monte carlo on an underlying asset. For example EUR/USD : Simulating a lot of possible paths on 1 year then calculate the volatilty for ...
3
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1answer
817 views

Log-likelihood of skew-t distribution

I am trying to estimate GARCH models with the use of Hansen's (1994) skew-t distribution. I am using matlab's ARMAX-GARCH-K toolbox, where the log-likelihood is calculated as: ...
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81 views

Approximating an SDE for Volatility Estimation

Consider the SDE $$ dT(t) = ds(t) + a(s(t) - T(t))dt + \sigma dW(t) $$ where $s(t)$ is a deterministic function that turns out to be the long-term mean (this SDE is used to model daily temperature, so ...
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1answer
583 views

How to approximate the Carr-Madan decomposition formula?

I have came across the excellent answer. I'm looking for a dicrete approximation of the Carr-Madan decomposition formula of the function $f(F_T)$ of the terminal futures price by taking a static ...
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1answer
181 views

Combine EWMA or ARCH model with estimator other than squared returns

Currently I use the EWMA model with the squared logarithmic returns as proxy estimator for the volatility, in order to forecast the volatility one step ahead in an intraday scenario (time frame is a ...
3
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4answers
272 views

Compare two time series with different frequencies

Lets say I have two time series $X_t$ and $Y_{t,q}$. As an examples, lets say $X_t$ is a series that measures year over year changes in the level of output of a good (say number of widgets). So $X_t = ...
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1answer
146 views

What volatility estimator for continuous data and small time window?

I want to know which volatility estimator should I use for the following scenario: I am implementing a market making bot and therefore I need to make estimations of the volatility of the price in ...
2
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1answer
120 views

Streaming update of the GARCH(1,1) model

Given the estimate of GARCH(1, 1) model parameters I observe the new price. How to update the estimate with this new information. Let's assume I know the coefficients that maximize the likelihood ...
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0answers
233 views

Relationship between in-sample and out-sample periods length

I have two general questions regarding "in-sample fitting vs. out-of-sample backtesting" kind of analyses. Is there any relationship between the length of the data collected for in-sample fitting ($a$)...
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1answer
1k views

Package for multivariate Garch Vech model for R?

I`m new to programming and searching a package for R which inherents the estimation for a Vech Garch(1,1). This is a multivariate Garch model which forms the residuals and the covariance matrix from a ...
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1answer
606 views

What is Estimation Risk - VAR Backtest

Simple Question. Can someone explain please: What is Estimation Risk in Value at Risk Backtesting
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1answer
379 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 ...
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2answers
1k 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, $...
22
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3answers
2k views

How are distributions for tail risk measures estimated in practice?

Let's say you want to calculate a VaR for a portfolio of 1000 stocks. You're really only interested in the left tail, so do you use the whole set of returns to estimate mean, variance, skew, and shape ...