Questions tagged [distribution]

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29
votes
4answers
24k views

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: ...
24
votes
3answers
4k 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
1answer
780 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 ...
8
votes
3answers
346 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 ...
10
votes
8answers
4k 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 ...
10
votes
1answer
443 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
1answer
462 views

Use NIG distribution to model stock path

I would like to use Monte Carlo simulation to price some options. First I use standard approach where stock price is discribed by the following process: $$S_T = S_0\exp \left[(r - 0.5\sigma^2)T + \...
2
votes
1answer
164 views

Is it always better to use the entire distribution of a financial returns series, not just $\mu$ and $\sigma$?

In finance models that use historical returns for inputs, including option pricing models, forecasting and portfolio optimization, only the statistical moments of the returns distribution, $\mu$ and $\...
2
votes
1answer
319 views

Quantile normal and lognormal

Let's assume we have a normal distribution $X\sim \mathcal{N}(\mu,\sigma^2)$. In a normal distribution the quantile can be calculated as follows: \begin{equation} \Phi_X ^{-1}(p)=\mu +\sigma {\sqrt {...
1
vote
0answers
417 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 ...
3
votes
1answer
309 views

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

What are the formulae for d1 & d2 using a Laplace distribution?
2
votes
2answers
170 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 ...
0
votes
0answers
53 views

Is asset return skewness hard to estimate?

The asset mean is known to be difficult to estimate, incurring more estimation error than estimates of asset return variance. How about asset return skewness, is it hard to estimate and how can that ...