  The telegraph process $X(t)$, $t>0$, (Goldstein, 1951) and the geometric
telegraph process $S(t) = s_0 \exp\{(\mu -\frac12\sigma^2)t + \sigma X(t)\}$
with $\mu$ a known constant and $\sigma>0$ a parameter are supposed to be
observed at $n+1$ equidistant time points $t_i=i\Delta_n,i=0,1,..., n$. For
both models $\lambda$, the underlying rate of the Poisson process, is a
parameter to be estimated. In the geometric case, also $\sigma>0$ has to be
estimated. We propose different estimators of the parameters and we investigate
their performance under the high frequency asymptotics, i.e. $\Delta_n \to 0$,
$n\Delta = T<\infty$ as $n \to \infty$, with $T>0$ fixed. The process $X(t)$ in
non markovian, non stationary and not ergodic thus we use approximation
arguments to derive estimators. Given the complexity of the equations involved
only estimators on the first model can be studied analytically. Therefore, we
run an extensive Monte Carlo analysis to study the performance of the proposed
estimators also for small sample size $n$.
