# Tag Info

• 1,866

• 7,458
Accepted

### What is the difference between standard deviation, volatility and quadratic variation?

Using only words and no equations: Knowing the Variance (or standard deviation) of a Brownian Motion we can calculate the uncertainty in the future position of a particle. Knowing $\sigma^2$ and ...
• 9,935

### Are two stochastic processes independent if the Wiener processes inside are uncorrelated

 My "answer" below is not a really an answer for I have completely misinterpreted your original question. I thought you asked about the covariance of 2 processes over a given time horizon (i.e. ...
• 14.3k
Accepted

### What are the units of the variables appearing in a standard stochastic differential equation for a Wiener process?

$\sigma S$ is in units of dollars per square root of a unit of time. $\sigma$ is usually quoted as an annual or daily percentage. $dX ^2$ is in units of time, as $E[(dX)^2] = dt$. Here ...
• 1,335

### Bounded Stochastic discrete process

I believe that the process you postulate has a Beta conditional distribution. If my memory serves me well, I have encountered it in the book by Liptser and Shiryayev "Statistics of Random Processes" ...
• 4,247

• 5,503
1 vote
Accepted

### Regression of stochastic integral on Wiener process

By definition, $${\mathbb Cov}(M_t,W_T) = {\mathbb E}[M_t W_T] - {\mathbb E}[M_t] {\mathbb E}[W_T] = {\mathbb E}[M_t W_T]$$ since ${\mathbb E}[M_t] = {\mathbb E}[W_T] = 0$. We now consider the ...
1 vote

### Differentiability of solutions of a stochastic differential equation

Rather non rigorously, $\frac{W(t)}{t} \sim N(0,\frac{1}{t})$ if $t \to 0$ , we can see the variance goes to infinity. Hence Ito process is not differentiable.
• 351
1 vote

### How to Evaluate Expected Value powered 4 of a Wiener Process?

You state $X(t_j) - X(t_{j-1}) \backsim \mathcal{N}(0, \frac{t}{n})$. Thus: \begin{equation} X(t_j) - X(t_{j-1}) = \sqrt{\frac{t}{n}} Z , \end{equation} where $Z \backsim \mathcal{N}(0, 1)$. Note that:...
1 vote

### Can anyone explain to how Hull get from stock returns to continuously compounded stock returns?

The key is on the left hand side. Recall that the differential of log of x is: $d \ln x =\frac{1}{x}dx$ So you get: $\ln x_t-\ln x_0=at$ Which you will need to exponentiate to get rid of the log: ...
1 vote
Accepted

### Interpretation of IV and its use in stock movement prediction

The Bachelier model which assumes that price follows a normal distribution is a correct approximation for the Black-Scholes one for short times t. When time is short it's fine to ignore drift because ...
• 2,137

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