Valuing American Derivatives by Least Squares Methods

Least Squares estimators are notoriously known to generate sub-optimal exercise decisions when determining the optimal stopping time. The consequence is that the price of the option is underestimated. We show how variance reduction methods can be implemented to obtain more accurate option prices. We also extend the Longsta¤ and Schwartz (2001) method to price American options under stochastic volatility. These are two important contributions that are particularly relevant for practitioners. Finally, we extend the Glasserman and Yu (2004b) methodology to price Asian options and basket options.

When to Quit Under Uncertainty? A real options approach to smoking cessation

This paper models the decision to quit smoking like an investment decision where the quitter incurs a sunk withdrawal cost today and forgoes their consumer surplus from cigarettes (invests) and hopes to reap an uncertain reward of better health and therefore higher utility in the future (return). We show that a risk-averse mature smoker who expects to benefit from quitting may still rationally choose to delay quitting until they are more confident that quitting is the right decision for them. Such a decision by the smoker is due to the value associated with keeping their option of whether or not to quit open as they learn more about the damage that smoking will have on their future utility. Policies which reduce a smoker’s uncertainty about the damage that smoking with have on their future utility is likely to make them quit earlier.