Description: In this paper, we illustrate how to value American-style options using the Least-Squares Monte Carlo LSM approach proposed by Longstaff and Schwartz 2001 and investigate whether there exists an optimal regression complexity in the LSM framework for options pricing. In particular, we use the smoothing spline in the regression step, which allows us to control the regression complexity on a continuous scale with just one tuning parameter. Numerical results on American put options indicate that we need to use more than a linear regression, but as the regression becomes more complex, the accuracy of the LSM method quickly deteriorates. From 39th Actuarial Research Conference.

Description: This paper discusses the martingale approach for pricing American-type options without an expiry date. These options include the perpetual American put option and the perpetual maximum option in one stock case. The word “perpetual” means that the option has no expiry date. A main tool in this approach is the principle of smooth pasting.