The brownian-motion tag has no wiki summary.
4
votes
1answer
116 views
Covariance of brownian motion and its time average
It's a question pertaining to the correlation of a log asset process (following BM) and its time average, to put it into form, if
$$X(t)=\mu t+\sigma W(t)$$
then
$$ ...
5
votes
1answer
205 views
How to simulate correlated Geometric brownian motion for n assets?
So I'm trying to simulate currency movements for several currencies with a given correlation matrix. I have the initial price, drift and volatility for each of the separate currencies, and I want to ...
1
vote
2answers
120 views
Statistics of difference between two GBMs
if I have two asset prices modeled separately as geometric brownian motions. How do i go about calculating the expected statistics of their difference? Like given the sigmas and mus of both processes, ...
5
votes
2answers
228 views
Correlation decay in lognormal distribution
I noticed that if you use two correlated geometric brownian motions, the correlation structure decays in time pretty fast even for really high correlation values.
I think that is not replicating ...
4
votes
1answer
200 views
Derivation of Ito's Lemma
My question is rather intuitive than formal and circles around the derivation of Ito's Lemma. I have seen in a variety of textbooks that by applying Ito's Lemma, one can derive the exact solution of a ...
5
votes
2answers
147 views
Simulation of GBM
I have a question regarding the simulation of a GBM. I have found similar questions here but nothing which takes reference to my specific problem:
Given a GBM of the form
$dS(t) = \mu S(t) dt + ...
2
votes
2answers
113 views
Comparison of Brownian Motion Expected Drawdown and simulated results
Can anyone tell me whether results as predicted by Brownian Motion for a given mean and std, match what you get by measuring actual drawdown from simulated results over a number of iterations?
3
votes
0answers
81 views
Estimating two normal random numbers with one equation
Subtitle: Estimating the correlation of the shocks driving two commodities in
two multi-factor models
I am fitting two 2-factor models to electricity and gas futures, respectively.
In order to ...
5
votes
2answers
353 views
What is the average stock price under the Bachelier model?
Let's say stock price follows following process:
$$dS(t) = \sigma dW(t)$$
where $W(t)$ is Standard Brownian motion. The initial level for the stock is $S(0)$. Define the average of stock price ...
7
votes
2answers
208 views
GBM 3d plot with R
I want to plot the density of the GBM in a 3d plot. So I have on one axis the stock price, on the other the time and on the z axis the density. At the end I want to produce this graph.
The formula I ...
4
votes
1answer
1k views
How to simulate stock prices with a Geometric Brownian Motion?
I want to simulate stock price paths with different stochastic processes. I started with the famous geometric brownian motion. I simulated the values with the following formula:
...
8
votes
1answer
1k views
Estimation of Geometric Brownian Motion drift
One can find many papers about estimators of the historical volatility of a geometric Brownian motion (GBM). I'm interested in the estimation of the drift of such a process. Any link on this topic ...
5
votes
3answers
388 views
What are the limitations of brownian motion in finance?
What are the limitations of brownian motion in its applications to finance?
4
votes
4answers
360 views
Expected Growth
The model assumption of the Black-Scholes formula has two parameters for the geometric Brownian motion, the volatility $\sigma$ and the expected growth $\mu$ (which disappears in the option formulae). ...
