Singular points binomial method for pricing American fixed lookback options

Abstract

An option is the opportunity to buy or sell an underlying asset with a fixed price at a given time in the future. One of the biggest difficulties in option theory is determining the correct value of an option. In this thesis, we discuss what European and American options are, we further move on to price American lookback options using the singular point method. We use singular points which are formed on the nodes of the tree and apply the binomial method to find price of the option which are represented as continuous piecewise linear functions. The reflection principle and combinatorics are used in pricing European lookback options. Under the reflection principle the emphasis is on finding the appropriate probability convenient to use in pricing the option under the method suggested by John Hull.