A Comparison Between Different Numerical Schemes for the Valuation of Unit-Linked Contracts Embedding a Surrender Option

In this paper we describe and compare different numerical schemes for the valuation of unit-linked contracts with and without surrender option. We implement two different algorithms based on the Least Squares Monte Carlo method (LSMC), an algorithm based on the Partial Differential Equation Approach (PDE) and another based on Binomial Trees. We introduce a unifying way to define and solve the valuation problem in order to include the case of contracts with premiums paid continuously over time, along with that of single premium contracts, usually considered in the literature. Finally, we analyse the impact on the fair premiums of the main parameters of the model