**2. Motivation**

In this section, we present results for a set of options similar to those used in Longstaff and Schwartz (2001), but to illustrate the effect of PCS, we consider pricing call options instead of put options. In all cases, we use a current value of the stock of 40 and an interest rate and dividend rate of 6%. A non-zero dividend is needed to make the American call option pricing non-trivial and to have positive early exercise premia. Options range between being 10% In The Money (ITM) and Out Of The Money (OTM), have maturities of *T* = 1 or *T* = 2 years and have *J* = 50 early exercise possibilities per year. We also consider two levels of the volatility and set *σ* = 20% or *σ* = 40%. The reported estimates are based on *I* = 100 independent simulations, each of

<sup>2</sup> The main parts of the paper present results for the simple Black–Scholes–Merton setup. The reason for this is obvious: we want to have fast and precise benchmark results available. Without these, it makes no sense to talk about one method being more efficient than another. Section 5, though, shows that these conclusions extend to other asset dynamics, like the stochastic volatility model of Heston (1993), and to options with other payoff functions, like options written on multivariate underlying assets.

which uses *N* = 100,000 paths and the first *L* = 3 weighted Laguerre polynomials and a constant term as regressors in the cross-sectional regressions. We assess model performance using *Bias* = *I*−<sup>1</sup> ∑*I i*=1 *P*ˆ *i* − *P* , *StDev* = *I*−<sup>1</sup> ∑*I i*=1 *P*ˆ *i* − *P*¯ *i* 2 and *RMSE* = *I*−<sup>1</sup> ∑*I i*=1 *P*ˆ *i* − *P* 2, respectively, where *P* is the true option price, *P*ˆ *i* is the *i*th simulated price and *P*¯ *i* the average model price.
