| Περίληψη : | The aim of this dissertation is the modeling of the algorithm that Longstaff & Schwartz proposed in 2001 as an alternative method for pricing American-style options. The algorithm, known as the Least-Squares Monte Carlo method, is named after the innovative techniques its instigators combined as the tool of their valuation. The key of their innovation is the usage of a simple Least-Squares regression in order to approximate the continuation value, while the path/s of the stochastic variable/s is/are simulated under the desired stochastic process using the Monte Carlo simulation method. The application of the method here expands in two different models; one containing one stochastic variable, the underlying asset’s price, and a second one containing two stochastic variables, the underlying asset’s price and the interest rate. Due to the nature of the algorithm, it is easy applicable under various conditions and, furthermore, under various types of options. In cases that traditional methods cannot produce a valid, regarding computational time and accuracy, result or even cannot produce a result at all , such as path-dependent options with multiple stochastic factors, the algorithm of Longstaff & Schwartz (2001) makes the pricing possible. Reaching a conclusion, it was quite impressive to end up having exactly the same price for different type and number of basis functions, proving that the algorithm is pretty robust yielding fully consistent results in all possible cases. In addition, in general context and in most cases, when the underlying asset’s price follows a Geometric Brownian Motion, the option found out worthing more than that under any other stochastic process. MatLab was the tool used in this application of the LSM algorithm in a programming environment.
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