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35 votes
4 answers
29k 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: ...
Thomas Browne's user avatar
24 votes
3 answers
5k 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 ...
Ram Ahluwalia's user avatar
17 votes
8 answers
7k 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 ...
rwolst's user avatar
  • 347
11 votes
1 answer
1k 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 ...
mt_christo's user avatar
10 votes
1 answer
466 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 ...
user2303's user avatar
  • 537
8 votes
3 answers
389 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 ...
Monolite's user avatar
  • 367
3 votes
1 answer
371 views

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

What are the formulae for d1 & d2 using a Laplace distribution?
user avatar
3 votes
1 answer
652 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 + \...
tosik's user avatar
  • 476
2 votes
1 answer
226 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 $\...
develarist's user avatar
  • 3,040
2 votes
1 answer
506 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 {...
silgon's user avatar
  • 123
2 votes
2 answers
224 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 ...
Masher's user avatar
  • 491
1 vote
2 answers
303 views

Can I apply the Kelly criterion directly, without fitting any distributions?

Problem I want to apply the Kelly criterion to asset returns, so that I know how much to hold of each, ideally (and how much I should keep as a cash reserve). As far as I understand the Kelly ...
danuker's user avatar
  • 123
1 vote
0 answers
790 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 ...
simmy's user avatar
  • 585