Bivariate Poisson Distribution: Covariance Parameter

Bivariate Poisson Distribution: Covariance Parameter

I've been having a look at the probability distribution function of the
Bivariate Poisson with rates lambda1, lambda2 and lambda3 with lambda3
being the covariance between lambda1 and lambda2. As far as I know all
three have to be positive- why is this the case? I know by definition of
Poisson rates the rates have to be positive, but just by looking at this
equation it seems plugging in negative numbers for lambda3 still produces
solutions (link, Page 2 Equation 1):
http://isc.temple.edu/economics/wkpapers/Airports/MVPoisson/Karlis_Ntzoufras_Statistician.pdf
Can someone enlighten me? I have no access to academic papers so finding
out the answer is a bit difficult...