put under volatility risk. We represent the price of the option, in terms of the moneyness ($S_0/K$), for different values of $\lambda$. We analyse here the consequences of a sudden increment in the volatility of the stock. We have used the following values for the parameters: $r=4\%$, $\delta_a=\delta_b=1.75\%$, $\sigma_a=10\%$ and $\sigma_b=25\%$. The pay-off function is depicted in a solid (black) line.[]{data-label="figVPM"}](figure2.eps "fig:"){width="60.00000%"} ]{}

The following two examples deal with the effect of a change in the volatility on put prices. In figure \[figVPM\] we can see how the price of the put steadily increases with the likelihood of a sudden growth in the volatility level. The behaviour reverses in figure \[figVPMX\], where a possible change of volatility would imply a reduction in the put value. Note that we are assuming in this figure a market set-up which lead to the presence of a maximum admissible value for $\lambda$, $\bar{\lambda}\approx 0.509$, with no clear reason —see \[SB\].

[![Option prices for a perpetual vanilla put under volatility risk. We represent the price of the option, in terms of the moneyness ($S_0/K$), for different values of $\lambda$. We analyse here the consequences of a severe reduction in the volatility of the stock. We 