Questions tagged [normal-distribution]
The normal-distribution tag has no usage guidance.
9 questions
2
votes
3
answers
709
views
Simulating covariance matrices with nonzero correlation
How would you simulate a covariance matrix of 1,000 stocks where each pair has nonzero correlation?
I have literally no idea how to start with this.
Any suggestions?
- 2,662
8
votes
3
answers
7k
views
Why does the Markowitz mean-variance model require the assumption of normality?
Given $N$ assets, the Markowitz mean-variance model requires expected returns, expected variances and a $N \times N$ covariance matrix. The joint distribution is fully defined by these measures.
...
- 233
7
votes
4
answers
2k
views
In Black-Scholes, why is $\log{\frac{S_{t+\triangle t}}{S_t}} \sim \phi{((\mu - \frac{1}{2}\sigma^2)\triangle t, \sigma^2 \triangle t)}$?
I don't understand why in the formula
$$\log{\frac{S_{t+\triangle t}}{S_t}} \sim \phi{\left((\mu - \frac{1}{2}\sigma^2)\triangle t, \sigma^2 \triangle t\right)}$$
the mean is $(\mu - \frac{1}{2}\sigma^...
- 73
4
votes
3
answers
775
views
Why is it so rare for finance theory to depart from the normal distribution?
I understand almost all of the theory that has been built upon in quantitative finance is based on the normal distribution, and obviously you wouldn't want to throw all of it out the window on a whim ...
- 912
4
votes
1
answer
7k
views
How to use the Feymann-Kac formula to solve the Black-Scholes equation
I have the Black-Scholes equation for European option with maturity $T$ and strike $K$
$$\begin{cases}\frac{\partial u}{\partial t} = ru - \frac{1}{2} \sigma^2 x^2 \frac{\partial^2 u}{\partial x^2}-r ...
- 43
2
votes
1
answer
542
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 {...
- 123
2
votes
2
answers
232
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 ...
- 491
1
vote
2
answers
4k
views
Confidence Intervals of Stock Following a Geometric Brownian Motion
In preparation for my Options, Future's and Risk Management examination next week, I have been presented with a series of questions and their answers. Unfortunately, my lecturer, one of the less ...
0
votes
1
answer
1k
views
Why should we use log returns? Log normality
According to this link, there are some reasons we have to use log returns.
But I can not understand the first reason provided in the link:
First, log-normality: if we assume that prices are ...
- 127