Pricing American Put Options and Determining Optimal Exercise Strategy

Abstract

This thesis examines three numerical methods for pricing American put options: the Least-Squares Monte Carlo method (LSM), the Binomial method (BM), and the Implicit Finite Difference method (FDM). Our study focuses on comparing the accuracy and efficiency of these models, assessing their prices against historical market prices, and analysing their behaviour under various market conditions to identify optimal early exercise times. Our findings suggest that BM is the most reliable and efficient model with less granular parameter settings, whereas LSM and FDM are highly sensitive to parameter changes, requiring a larger number of simulations and spatial steps for accurate pricing. Consequently, in environments requiring rapid computation of put options, BM is the superior model, whereas applications requiring high accuracy, LSM may be the preferable model due to its greater versatility. Compared to historical market prices, our models indicate that the market severely overvalues American put options, suggesting that market illiquidity prevents these options from reaching their “true” value. Optimal early exercise times occur when the pricing models converge to the same exact put value. This happens when the option moves deeply in-the-money and the put option price equals the "immediate exercise value," suggesting that exercising early is more beneficial than continuing to hold the option.