Browsing by Author "Makenge, Emmanuel Mgosi"

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    Pricing lookback options when stock prices are mean reverting
    (University of Dar es Salaam, 2013) Makenge, Emmanuel Mgosi
    This work is about pricing lookback options when stock prices are geometrically mean reverting. It is started with the assumption that B(i) is the Brownian motion with respect to the risk neutral measure Q. The basic model of this dissertation is derived which is also known as Black and Scholes partial differential equation for the given mean reversion geometric Brownian motion and solved indirectly to get solutions of this work. Equivalent expressions between standard geometric Brownian motion and mean reversion geometric Brownian motion are found by the help of their lognormal distributions comparison in order to get the relationship between these two geometric Brownian motions. Also, the explicit solutions for lookback options under standard geometric Brownian motion at time 0 and at time t were derived in order to use them in the process of transformation by means of equivalent expressions. The approximated solutions of lookback options at time t when stock prices are geometrically mean reverting were derived by the help of equivalent expressions and the explicit solutions for lookback options under standard geometric Brownian motion at time t so as to obtain the main results of this dissertation. Finally, each of the obtained results is evaluated by the help of MATLAB. From the analysis of the results it seems that the obtained results can be used in financial markets due to the fact that these options can be exercised in some situations, and cannot be exercised in other situations depending on variation of parameters (volatilities, mean reversion speeds and risk interest rates).