# Tag Info

## Hot answers tagged random-walk

2

The first the solution to: $$dS_t = S_t\left[\mu dt +\sigma dW_t\right]$$ The second is the solution to: $$dS_t = S_t\left[\left(\mu -\frac{\sigma^2}{2}\right)dt + \sigma dW_t\right]$$ The difference is that the first one is a martingale when $\mu$ is equal to zero while the second one is not:  \mathbb{E}[S_0 exp(\sigma W_t)]= ...

2

I think the main difference even in this little example is the gain-loss asymmetry which is a known stylized fact: When you look at the big bump both time series posses your artificial one is perfectly symmetric whereas the real one takes longer for going up and then crashes in a relatively shorter time frame. This is a known phenomenon in real financial ...

1

I would confirm it. For time series forecasting, one can use 3 versions of random walk: RW model 1 (basic geometric random walk): stock returns in different periods are statistically independent (uncorrelated) and identically distributed (constant volatility) RW model 2: stock returns in different periods are statistically independent bot not identically ...

Only top voted, non community-wiki answers of a minimum length are eligible