have used the following values for the parameters: $r=4\%$, $\delta_a=\delta_b=1.75\%$, $\sigma_a=40\%$ and $\sigma_b=25\%$. The previous market conditions lead to the existence of threshold $\bar{\lambda}\approx 0.509$. We also plot the theoretical limiting case $\lambda \rightarrow \infty$ for which $H_a$ should equal $H_b$.[]{data-label="figVPMX"}](figure3.eps "fig:"){width="60.00000%"} ]{}

Another interesting property of option put prices (not related to $\bar{\lambda}$) is the following: If we observe the insets of figures \[figVPM\] and \[figVPMX\] we will see that in the former case all prices, apart from the undisturbed one, decay with the same power law whereas the in the latter case the exponent changes with $\lambda$. In fact the first exponent is fully determined by the parameter values [*after*]{} the change. The reason lies in the fact that in this case we have $|\beta^{-}_b|<|\beta^{-}_a|$, and since $|\beta^{-}_a|<|\gamma^{-}_a|$ for any value of $\lambda$, the $\beta^{-}_b$ exponent dominates the extreme behaviour. Note that this feature was subtly present in figure \[figVCM\] as well.

We finally show how we can use the result in (\[moment-generating\]) to obtain the moments of the exercise time thanks to (\[moments\]). In particular, we present the mean value of this first-passage time when the location of the boundary does not depend on $r$, as in 