Questions tagged [brownian-motion]

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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How to compute covariance of brownian motion？

For example, how to compute the covariance of w3 and w2 if Wt means standard Brownian motion.
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Summary of Stochastic Derivatives, Integrals, Expectations, and Variances

I wanted to make a summary table of stochastic functions to improve my understanding. Maybe the following should be a wiki page on this site so others can add functions and examples? Does the ...
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Continuous option pricing: Brownian Bridge

I have a question on the proof of the formula of Sup(S) between 2 simulation points. Do you know how the prove the following formula? Thanks
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negative values in geometric brownian motion

A GBM (Geometric Brownian Motion) $\frac{dx}{x} = \mu dt + \sigma dW$ solves to $x_t = x_o e^{(\mu - \sigma^2)t + \sigma W_t}$ From the solution, it is clear that $x_t$ cannot become negative. ...
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How to fix my Ornstein-Uhlenbeck parameter MLE in Python?

I am trying to fit time-series data into an Ornstein-Uhlenbeck process. Here is my code so far: ...
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Predicting time series using Jump Diffusion model and Neural Networks

I am trying to understand the difference between using Jump diffusion model and Neural Networks or more precisely LSTM to predict time series data regardless what that data contains for example a ...
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Rate of return of a bond price

Assume $B(t, T)$ is a zero coupon bond price and assume that it has dynamics $dB(t, T) = B(t, T)[\mu(t, T)dt + \sigma(t, T)dW_t]$, where $W_t$ is a Brownian motion under $(\Omega ;F; P)$ and $P$ is an ...
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Let $W_t$ denote a standard Brownian motion. Evaluate this integral [closed]

$$\int_{0}^{t}d(W_{u}^2)$$ How can I deal with this kind of problem? If there is no function given to apply Itô's formula.
Find a formula for the price of a derivative paying $\max(S_T(S_T-K),0)$
Develop a formula for the price of a derivative paying $$\max(S_T(S_T-K))$$ in the Black Scholes model. Apparently the trick to this question is to compute the expectation under the stock measure. So,...