In mathematics, Brownian motion is described by the Wiener process; a continuous-time stochastic process named in honor of Norbert Wiener.

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Distribution of Geometric Brownian Motion

Please let me know where I have been mistaken! Let the SDE satisfied by the GBM $S(t)$ be $$ \frac{dS(t)}{S(t)} = \mu dt + \sigma dW(t). $$ Then, the underlying BM $X(t)$ will satisfy $$ dX(t) = ...
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Modelling EUR/USD with Ornstein-Uhlenbeck + jumps?

I'm trying to simulate a process as close as possible to EUR/USD of the ten past years. I've used a Ornstein-Uhlenbeck process: $$d X_t = -\theta (X_t - \mu) d t + \sigma d B_t$$ with the ...
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Ito calculus problem

given $S^1$ satifying the SDE $\quad dS_{t}^{1}=S_{t}^{1}((r+\mu)dt + \sigma dW_t), \quad S_{0}^{1}=1 $ and the safe asset $S_{t}^{0}$ $\quad S_{t}^{0}:=e^{rt} \quad for \quad r\geq 0$ Q1. how ...
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Geometric Brownian Motion: d(S) vs. d(ln(S))

I am quoting from "Tools for Computational Finance, 5th Edition" [Seydel]. I wonder whether the histogram of simulations of the first (yellow) SDE makes sense... especially given that Seydel ...
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How do I artificially generate intraday ticks data from a given input (Open,High,Low,Close,Volume) using Brownian Bridge method?

How do I artificially generate intraday ticks data from a given input (Open,High,Low,Close,Volume) using Brownian Bridge method? https://en.wikipedia.org/wiki/Brownian_bridge P.S: Brownian Bridge ...
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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 ...
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Particular Conditional Expectation of Geometric Brownian Motion

If we have the density function $$f_{Y}(y,t)=\frac{1}{y \sqrt {2\pi\sigma^2t}}exp(-\frac{(ln \ y - \mu t)^2}{2\sigma^2t})$$ Then the mean of $Y(t)=e^{X(t)}$ conditional on $Y(0)=y_0$ is found to be ...
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Is Geometric Brownian Model suitable for long term price forecast?

I was thinking of using Geometric Brownian Motion to forecast future prices of timber (say one variable, the stumpage price of sawtimber). I tested the time series with Augmented Dickey-Fuller test ...
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Soft: Interpretation Fractional BM in finance

Suppose we are in the BS framework. If we replace the Brownian Motion with a more general fractional Brownian motion therein, how can it be interpreted? That is what is a financial interpretation of ...
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Monte Carlo simulation of Multifractional Brownian Motion in MATLAB

Code under is taken from http://en.literateprograms.org/Monte_Carlo_simulation_(Matlab) ...
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Monte Carlo, convexity and Risk-Neutral ZCB Pricing

I've built a simplistic Excel monte carlo model to price a zero-coupon bond, but it came up with a slightly unepxected result so I wanted to confirm whether my maths is just a little rusty or my model ...
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Convolution of inverse gaussian and power law distributions

I am trying to understand how the first passage time density of Brownian motion with drift is modified by the presence of waiting times that are distributed as a power law In other words, what is the ...
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Distribution of Brownian Bridge

I know from Karatzas & Shreve (1991) that a Brownian Bridge $B(t)$ from $a$ to $b$ on time interval $[0,T]$ satisfies: $B(t)=a(1-t/T) + b*t/T + [W(t) - W(T)*t/T]$, where $W(t)$ is a standard ...
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SAS code for Brownian Motion

I want to simulate call options using monte carlo algorithm. I am a noob SAS user but i know that i need to: -simulate random stock prices with no dividend in respect to different ...
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38 views

Modelling commodity price uncertainty with brownian motion - time period impacts

background I have two separate models of a metals resources company. Each model produces a series of accounting and cashflows forecast for different assets, and consolidates these to a overall ...
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25 views

Simulated Price Data via Harmonic Logarithmic Walks?

Hi I came up with this equation last week and was wondering if: 1) There was already a name for this mathematical process. If so, where I might find more information. 2) Also, I am not adept at ...