Δίκαιη αξία δικαιωμάτων προαίρεσης με φράγματα
Interest rate derivatives pricing models

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Abstract
During the year 1973, three researchers who worked independently from different starting points, proposed one of the most fundamental models in modern Economic theory. The impact from this discovery was enormous, while these researchers were awarded the Nobel prize of Economics in 1997. The celebrated Black, Scholes and Merton’s risk neutral pricing formula altered the way in which one of the most important and traded class of financial instruments is priced. In addition, it shaped the way market practitioners and researchers perceive the stochastic behavior of traded risky assets. This new and vibrant field of Mathematical Finance is developing until now, attracting more and more researchers every year. The revolution that happens in the field of Computer Science paired with the growth of Financial Markets, has led to the development of new theoretical and numerical methods for the study of various financial derivatives including Barrier Options which are the main theme of this MSc thesis. The theoretical results and formulas concerning the fair price of barrier options that are reviewed in this thesis were also numerically verified using Monte Carlo simulation techniques. These techniques can easily be modified to estimate the price of more complex financial derivatives that may have intricate or intractable pricing formula.