# Questions tagged [geometric-brownian]

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### What is the meaning that Geometric Brownian motion is leptokurtic? [closed]

Does this have any relation to the symmetry of the normal distribution?
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### What are some alternatives to Geometric Brownian motion that can be used in the Black-Scholes? [closed]

I hear that there are many extensions to the black scholes model to make it more realistic, however, GBM does not account for volatile swings. Is there any sort of alternative approach to use instead?
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### Normality or Log-Normality of Regular Returns

Another old question on this site (How to simulate stock prices with a Geometric Brownian Motion?) inspired me to ask the following question: if we assume that regular returns could be normally ...
83 views

### Correctly simulating BEKK series to model asset returns

I am trying to create financial data as close as possible to that of asset returns. Using the R code I can collect some stock data and compute the return: ...
206 views

### From VG and NIG processes to GBM

I would like to find out if it is possible to reduce: the Madan-Seneta Variance Gamma (VG) model; the Barndorff-Nielsen Normal Inverse Gaussian (NIG) model to the standard Black-Scholes through a ...
94 views

### Sampling from SDE

In the case of the classic Geometric Brownian motion $$dS_t = \mu S_t dt + \sigma S_tdW_t$$ we solve it as $$S_t = S_0 \exp\left[ \left(\mu - \frac{\sigma^2}{2}\right)t + \sigma dW_t\right]$$ and ...
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### Geometric brownian motion and probabilities

A stock's price movement is described by the equations $dS_t=0.02S_tdt+0.25S_tdW_t$ and $S_0=100$. An investor buys a call option on said stock with a strike price $K=95$ which expires in $T=2$ years. ...
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### true or false: the risk-neutral measure is useless in this situation

Example 2 of this Wiki article on the risk-measure describes how a stock price $S_t$ that is modeled with Geometric Brownian motion with drift $\mu$ $$dS_t = \mu S_t dt + \sigma S_t dW_t$$ can be ...