Poisson process $N(t)$ with density $\lambda$, could generate a compensated Poisson Process $$M(t) = N(t) - \lambda t,$$ $M(t)$ is a martingale with mean of $0$.
Now, how could I calculate the volatility of this compensated Poisson process $M(t)$?
ps. volatility = standard deviation, or, let mean $$\mu := E\{f(t)\}$$, then volatility
$$\sigma := E\{(f(t)-\mu)^2\} $$.