A Monte Carlo approach for the American put under stochastic interest rates

Abstract

This paper presents a new approach for the valuation of an American put option under stochastic interest rates. The paper combines a Monte Carlo simulation approach for the valuation of Bermudan options and the valuation technique for American options proposed by Geske and Johnson [1984. The American put option valued analytically. Journal of Finance, 39(5), 1511–1524]. Numerical results show that the price estimates are accurate with very low standard errors. The simulation algorithm used to generate the price estimates is fast and easy to implement. The effect of stochastic interest rates is clearly reflected in the option prices. Especially under regimes where interest rate volatility is high this effect can be important to incorporate. Also for long lived options this can be an important extension.