Methods in valuing American options

Abstract

The majority of mathematical finance problems are computed through an analytical approach, mainly through numerical methods such as the use of partial differential equations. For many years, the formula which dictates option prices described by Black-Scholes has earned its reputation as an exceptional solution in option pricing. Nonetheless, the complexity of these problems increases with the number of variables incorporated in the model. As instigated by Moore’s law, the advancements made in the integrated circuit (IC) industry has opened new doors to the use of more complex and rigorous algorithms which required time in the past. As a consequence, computer programs can now be used to simulate several scenarios in the majority of scientific fields. More specifically, the use of Monte Carlo Simulations is extensively used in financial modelling due to the randomness exhibited in financial instruments. These techniques are suitable when dealing with multiple variables since solving these might not be possible through analytic methods. In addition to this, generating a substantial amount of simulations will give a risk-neutral valuation. This study will investigate the use of Monte Carlo Simulations as an alternative to the conventional numerical approach in Actuarial pricing. Both quantitative and qualitative methodologies will be applied. The use of computer programs written in Python was recommended for the provision of the necessary simulations.