binary call without drift risk. We represent the variance of the lifetime of the option, in terms of the moneyness (${S_0}/{K_0}$), for different values of $\lambda$. The values of the parameters were adjusted in order to keep the drift unchanged: $\tilde{\theta}_a=\tilde{\theta}_b=1.5\%$.[]{data-label="figVFPT"}](figure5.eps "fig:"){width="60.00000%"}]{}

In figure \[figVFPT\] we plot an example of the standard deviation of the exercise time which will illustrate the constant drift instance. Clearly this is only feasible if the value of the parameters are well tuned: $\mu_a=2\%$, $\mu_b=3.5\%$, $\sigma_a=10\%$ and $\sigma_b=20\%$. The outcome fits our anticipation, since the possibility of a larger volatility increases the uncertainty about the mean exercise time.

Conclusions and future work {#Last}
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In this article we have considered the implications that the presence in the market of volatility and dividend risk has for option prices. The proposed market model allows random changes in both the dividend-payment rate and the volatility level of stock shares, but in a very specific way: only one change is feasible, and the final market properties are foreseeable. The model, however, is rich and realistic enough to obtain valid financial results. We have focused our attention on the problem of pricing perpetual American options: derivatives with no expiration limit 