I have a 25-year American put option on a portfolio that is composed of a few equities and money market. I model interest rates by CIR. I am thinking about modeling equities by lognormal model; but instead of using deterministic risk free rates, I will use the stochastic short rates from CIR. ie. St-St-1=(Rt-sigma^2)*St-1+St-1*sigma*(1-rho^2)^.5*Zt, where Rt is the output from CIR model and rho is the correlation. Is my method practically doable? Will it cause any problems such as increasing the number of scenarios for a reasonable result?

i think this is a very reasonable approach. couple questions: 1-how will you determine the vol term structure in the log-normal model? if you're using quotes from equity derivatives desks (most desks will quote you out to 10-15 years in maturity on the S&P500), then be sure to adjust that term structure down (stochastic rates contribute vol to the equity process) before inputting it into your simulation. 2-how will you determine the correlation between equity and rates, the rho in your equation. this is unstable over time, going from -50% to +50%. Recently (I'm posting in April 2009), the rate/equity correlation has been very high because of the flight to quality scenario (equities falling and bonds rallying).