American options and stochastic interest rates

Abstract We study finite-maturity American equity options in a stochastic mean-reverting diffusive interest rate framework. allow for non-zero correlation between the innovations driving price and rate. Importantly, we also to assume negative values, which is case some investment grade government bonds Europe recent years. In this setting focus on call put characterize analytically their two-dimensional free boundary, i.e. underlying values that trigger optimal exercise of option before maturity. show non-standard double continuation regions may appear, extending findings documented literature constant Moreover, contribute by developing bivariate discretization processes converges distribution as time step shrinks. This discretization, described recombining quadrinomial tree, allows us compute options’ prices analyze boundaries with respect current Finally, document existence policies non-dividend-paying equity.