# Tagged Questions

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### Is the value also log-normally distributed?

Sorry if this is a stupid question. 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### What are $d_1$ and $d_2$ for Laplace?

What are the formulae for d1 & d2 using a Laplace distribution?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### Probability distributions in quantitative finance [closed]

What are the most popular probability distributions in quantitative finance and what are their applications?
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### Getting the actual distribution of a stock price at time T using implied volatility [duplicate]

Possible Duplicate: How to derive the implied probability distribution from B-S volatilities? Let's assume a stock price S, with volatility $\sigma$ constant, no dividend, and risk free ...
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### How to derive the implied probability distribution from B-S volatilities?

The general problem I have is visualization of the implied distribution of returns of a currency pair. I usually use QQplots for historical returns, so for example versus the normal distribution: ...
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### 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 ...