Essays on American Options

This thesis deals with the pricing of American equity options exposed to correlated interest rate and equity risks. The first article, American options on high dividend securities: a numerical investigation by F. Rotondi, investigates the Monte Carlo-based algorithm proposed by Longstaff and Schwartz (2001) to price American options. I show how this algorithm might deliver biased results when valuing American options that start out of the money, especially if the dividend yield of the underlying is high. I propose two workarounds to correct for this bias and I numerically show their strength. The second article, American options and stochastic interest rates by A. Battauz and F. Rotondi introduces a novel lattice-based approach to evaluate American option within the Vasicek model, namely a market model with mean-reverting stochastic interest rates. Interestingly, interest rates are not assumed to be necessarily positive and non standard optimal exercise policy of American call and put options arise when interest rates are just mildly negative. The third article, Barrier options under correlated equity and interest rate risks by F. Rotondi deals with derivatives with barrier features within a market model with both equity and interest rate risk. Exploiting latticebased algorithm, I price European and American knock-in and knock-out contracts with both a discrete and a continuous monitoring. Then, I calibrate the model to current European data and I document how models that assume either a constant interest rate, or strictly positive stochastic interest rates or uncorrelated interest rates deliver sizeable pricing errors.