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5
votes
2answers
73 views

Is it possible to deal with non-normal distribution in Black-Litterman model?

Suppose that I know that the normality assumption about my data is unrealistic (as it is very frequently): is it possible to apply any distribution that I judge the right one to the Black-Litterman ...
0
votes
1answer
21 views

Creating the histogram for the distribution of the portfolio returns

Given log returns for some stocks $A$ and $B$, which are the constituents of our hypothetical portfolio in equal weights, how does one actually come up with a distribution of the log returns of the ...
0
votes
0answers
10 views

Obtaining non-central moments from the central moments

I have a question regarding moments of the Gaussian and t distributions. I am working in the GARCH framework with Gaussian/t distributed innovations. I need to know the forecasts of the first four ...
1
vote
2answers
51 views

Normal Inverse Gaussian distribution - any consensus on an accurate quantile function?

I am making use of the Normal Inverse Gaussian distribution in my work to model underlying interest rate implied volatility risk drivers. What is particularly nice about this distribution for my ...
0
votes
0answers
65 views

Large deviations theory and extreme value theory

I'll enter into details of both, sooner or later, but for the moment I'm concerned about the differences (and relationships, if any) between these two theories. Can someone give me a brief, but still ...
1
vote
1answer
60 views

Calculate VaR for a liabilty taking a exponential distribution?

An insurance company faces the liability loss off $L = \begin{cases} 0, & \mbox{with probability } 0.75 \\ Z, & \mbox{with probability } 0.25\end{cases}$ where $Z\sim Exp(\mu)$. I want to ...
2
votes
2answers
51 views

Problem with obtaining densities

For my research I need to obtain a series of densities, however, I am encountering some problems. The first problem is perhaps very simple, but the answer eludes me. Let's say I have an observation ...
1
vote
0answers
49 views

Skewed Generalized Error Distribution's (SGED) pdf

I want to use the SGED distribution of Theodossiou for GARCH estimation, however, I am struggling to understand which is the correct pdf function of the distribution. Let me just say that the ...
0
votes
0answers
34 views

Skewed Generalized Error Distribution in GARCH modelling

I am trying to estimate GARCH models with the use of Theodossiou's (2000) Skewed Generalized Error Distribution. I am modifying matlab's ARMAX-GARCH-K toolbox to calculate this model. I am calculating ...
3
votes
1answer
58 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: ...
0
votes
1answer
19 views

Error using ghyp-distribution function

I want to fit multivariate GH distribution on my data, and then generate simulations for that distribution. Using the instructions given in ghyp package, I wrote following lines of code in R. ...
1
vote
1answer
30 views

Fitting (marginal/multivariate) distributions to financial return data

I have calculated the simple arithmetic return on a number of different financial securities and am fitting both a Student-T and Generalised Pareto Distribution. My question is can I just use the ...
1
vote
0answers
54 views

Cross-sectional moments

I got a seminar topic named Forecasting risk from cross sectional moments? Could at least someone tell me what should I write about and if there is any paper that I could read. Thank you very much in ...
4
votes
1answer
329 views

Is volatility for the next day forecastable? To any extent?

In a more general way: is there 1) a methodological approach to quantify the correctness of a model that produces a probability distribution for the, say, S&P 500 index return for the next ...
5
votes
2answers
132 views

Do futures follow physical or risk-neutral distributions

I've spent a while looking for an answer to this question and while I feel it is a simple question I have not found an answer. I know prices of option contracts follow an implied, risk-neutral ...
3
votes
1answer
63 views

VaR calculation accuracy/comparison/effectiveness through different R packages

My question is what would be the better( in terms of estimation accuracy) method of VaR calculation among below two:, also any small code snippet will be great as a starting point for me. 1st method: ...
6
votes
3answers
227 views

Can Gaussianity of returns depend on the time frame?

I would be interested in knowing if the fact that returns are Gaussian is disproved on all time frames, or if, for example, the 5 minute intra-day time frame could exhibits Gaussian returns assuming ...
2
votes
1answer
104 views

Density of Geometric BM via Fokker-Planck

Attempting to derive density of a GBM (which we know is log-normal) the long way, using the Fokker Planck-equation. Can't figure out where I went wrong - would appreciate a few sets of extra eyes! ...
1
vote
1answer
75 views

Inferences with non-normal data

I have data of index closing values. I later will use to run some regressions on the percent changes. When examining the data, I find heteroscedastic residuals and that the distribution is non-normal. ...
3
votes
2answers
151 views

Stock Returns Distribution in Heston Model

There is a paper by Dragulescu and Yakovenko (DY) in 2002 proposing a pdf for the stock returns in the Heston model. However, in a paper by Daniel, Bree and Joseph, they actually perform statistical ...
3
votes
4answers
1k views

Copulas simply explained

I try to understand the basic idea of copulas, however I am still struggling and hope that someone can help me. I understood that in general a copula is a function which links several marginal ...
0
votes
1answer
71 views

Is the value also log-normally distributed?

My book assumes many times that $log(1+R)$ is normally distributed, so R is log-normal. But does this also mean that the value process is log-normal? Since $V=V_0(1+R)\rightarrow V/V_0=1+R$, and since ...
7
votes
2answers
247 views

Kolmogorov-Smirnov test for Generalized Pareto Distribution

I've fitted my data to a generalized pareto distribution as to model the returns in the tails more accurately. The interior is fitted with kernel distributions. I would like to now test whether the ...
1
vote
2answers
54 views

Distribution of the value of a portfolio

Suppose there are k different stocks in a stock market. All of their prices are independent from each other. One year from now the price of the i-th stock will be $X_i^2$, where $X_i \sim ...
1
vote
2answers
268 views

How to combine Gaussian marginals with Gaussian copula to obtain multivariate normals?

in the book "Numerical Methods and Optimization in Finance" I red the following: "Combining the Gaussian copula with Gaussian marginal gives a fancy way of expressing multivariate normals. However, ...
3
votes
1answer
106 views

Ito integrals and copulas

Let $X_{t}$ and $Y_{t}$ be two brownian motions and let their joint distribution be given by $F$. So in regularly correlated BM's where $dX_{t}dY_{t}=\rho dt$, we have a bivariate normal distribution ...
3
votes
1answer
281 views

Brownian Bridge's first passage time distribution

Let's say we have a Brownian Bridge $Y_{b,T}(t)$ such that $Y_{b,T}(0)=0$, $Y_{b,T}(T)=b$. Let's say we are interested in the first passage time of $Y_{b,T}(t)$ at level $b$: $\tau_b = \{\min \tau; ...
3
votes
1answer
184 views

Fitting stochastic variance distributions to index return data

I want to calculate option prices based on a realistic distribution of the underlying. The underlying is a liquid index such as Eurostoxx50. I think of two aproaches, both of them incorporate ...
2
votes
4answers
262 views

How to model hedge fund returns?

I know that a lot of work has been done characterizing the first four moments of monthly hedge fund returns across a variety of fund types and strategies, and that work indicates that the higher ...
2
votes
1answer
135 views

Is there an easily implementable alternative to lognormal growth (something with fatter tails)?

I have a toy model in Excel for the growth of a investment portfolio. I assume iid lognormal annual growth factors: =EXP(mu+sigma*NORM.S.INV(RAND())) where mu and ...
2
votes
2answers
146 views

ITM Puts under negatively skewed return distribution (volatility skew)

I read Hull (2009) on implied volatilies. I understand that (given a negatively skewed return distribution) an OTM-Put is more worth than under a normal distribution and that a OTM-Call is worth less ...
5
votes
0answers
281 views

Fitting Student t-distributions to log-returns

It seems that some tail-risk centric groups are bent on using Paretian and t-distributions to account for tail risk when fitting log-returns. It has been observed, however, that with and without ...
2
votes
1answer
280 views

Closed form european option prices for a variance gamma process with a randomly distributed drift, volatility, and variance rate

Does an option pricing model with a closed form European option price exist that takes into account randomly distributed drift, volatility, and variance rate? I prefer a modification to the variance ...
0
votes
1answer
147 views

Parameters for numerically fitting t-distribution to log-returns

I am fitting the t-distribution to log-returns numerically (not using R, MATLAB, Stata, etc.), but rather using general programming. Assuming the log-return values are $r_t$, and the $t$-variates are ...
4
votes
5answers
901 views

Consensus on Cauchy distribution for stock prices

What is the general consensus for using a Cauchy distribution to model stock prices? I can't find much after researching online and wonder if it has been tried and discarded. My motivation is to find ...
1
vote
0answers
73 views

How to choose a window for curve fitting and prediction?

I am using Pareto distribution to fit a serie of survival rates (with least square). My ultimate goal is to use this fitting curve for prediction. Thus I would mainly focus on the tail of the ...
2
votes
2answers
119 views

how to make a distribution model tolerable of trend?

I'm building an model on different loans' NPL rate. The problem is NPL rates are always affected by the market. When NPL rates move in trend, my model will fail the back-testing. Assuming $x(t)$ is a ...
3
votes
2answers
323 views

Transformation to reduce standard deviation without changing median

Consider some negative skew and high kurtosis return time-series $X_t$. I do not know the functional form of the pdf of $X_t$ and have about 150,000 data points. Suppose that I was to create an ...
4
votes
2answers
929 views

Fitting distributions to financial data using volatility model to estimate VaR

I want to fit a distribution to my financial data using a volatility model to estimate the VaR. So in case of a normal distribution, this would be very easy, I assume the returns to follow a normal ...
2
votes
1answer
1k views

Value at Risk Monte-Carlo using Generalized Pareto Distribution(GPD)

I have created a VBA program to calculate VaR by using Monte Carlo, I have simulated Brownian Motion. This method might be ok for 100% equity portfolio, but let's say this portfolio may have fixed ...
3
votes
1answer
233 views

What are $d_1$ and $d_2$ for Laplace?

What are the formulae for d1 & d2 using a Laplace distribution?
5
votes
1answer
527 views

Benfords law and quantitative finance

Benford's law has been applied in various ways for detecting fraud (e.g. elections or accounting). But what are the most useful applications of Benford in quantitative finance? Are there any? I have ...
7
votes
1answer
393 views

What distribution should I apply to estimate the likelihood of extreme returns?

Say I have a limited sample, a month of daily returns, and I want to estimate the 99.5th percentile of the distribution of absolute daily returns. Because the estimate will require extrapolation, I ...
3
votes
2answers
604 views

Distribution for High Kurtosis

Can you please advise which distribution to follow when your skewness is 0.28 and Kurtosis value is 51. Since it's leptokurtic and positively skewed I would like to fit distribution and also wanted to ...
3
votes
0answers
130 views

What is the relation between return volatility and return rank volatility, and how can I control the latter?

I have no experience in finance, but I've been playing around with a virtual portfolio. I'm trying to control the "rank volatility" distribution - that is, the volatility of a stock's daily rank in ...
8
votes
6answers
2k views

What distribution to assume for interest rates?

I am writing a paper with a case study in financial maths. I need to model an interest rate $(I_n)_{n\geq 0}$ as a sequence of non-negative i.i.d. random variables. Which distribution would you advise ...
4
votes
1answer
159 views

What are some common models for one-sided returns?

One typically models the log returns of a portfolio of equities by some unimodal, symmetric (or nearly symmetric) distribution with parameters like the mean and standard deviation estimated by ...
20
votes
3answers
2k 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 ...
10
votes
2answers
3k views

How can I compare distributions using only mean and standard deviation?

I only have means and standard deviations of samples of two random variables. What technique can I use to determine how similar the distributions these describe are? Assume that the values are built ...
1
vote
0answers
335 views

Probability distributions in quantitative finance [closed]

What are the most popular probability distributions in quantitative finance and what are their applications?