# Tag Info

### Self study references for a Mathematician

In general, quantitative finance requires mathematics, finance, and numerical programming. The mix of the three and the areas of focus within the three will depend on the particular area you intend ...

### Tick Imbalance Bars - Advances in Financial Machine Learning

Question 1. Actually, the assumption of trade data format is that you have timestamp, size and price (not bid/ask) of trade. Sometimes, trades(ticks) are included to Level 1 data (also called BBO) ...

### Measure of a Brownian motion = normal distribution?

It is correct that $$\mathbf{P}(t^{-1/2}W(t) \in[a,b])=Φ(b)−Φ(a), \forall t\in(0,\infty)$$ due to the stationary increments property of the Wiener process and the fact that you normalized the ...
Accepted

### Is this a poorly written example, or could volatility in fact be negative?

You seem to use the term "volatility" to describe two very different quantities: (1) the diffusion coefficient of your SDE and (2) the standard deviation of the log-returns under your modelling ...
Accepted

### Why are the greeks for the underlying stock 0 with the exception of delta?

In the black scholes model, today's stock price, risk free rate and stock volatility are considered independent variables. They are inputs to the model. Hence the cross partial derivatives are zero. ...

### Show a process is Martingale

Assuming standard BS dynamics for $S_t$, you have $\frac{Z_t}{Z_0}\equiv(\frac{S_t}{S_0})^p = \exp{((rt-\frac{\sigma^2}{2}t+\sigma W_t)(1-\frac{2r}{\sigma^2}))}$ Now, this is a lognormally ...
Accepted