Problem statement: Over centuries traders have seek ways to avoid risks, to take opportunity in market discrepancies, or just to guest the market direction in order to gain profit. It is in this state of mind that various types of financial securities have been conceived since then and over the last decades we have attended at a large spread and development of Options and Options markets with a considerable creation of many variants. This recent interest of investor in Options and an increasing wide volume of its trade over years lead nowadays to customized design types of Options called exotic Option which enable every investor to tail a security which best suits its need and aspirations. Obviously this is not without consequences as there are many aspects to take into consideration as the time value of money, the underlying asset, the trends or volatility, the predominant interest rate. When variables and conditions changes, the overall cost of Options might be affected thus led us to posit the problem of understanding of the functioning of options and the best existing models of pricing.
Purpose: All over our thesis we tackle the tenet principle of Options, how options works in general, give a deep description of one of its variety which is plain vanilla Option with stocks as the underlying asset. Option markets are described and their functioning as well as it has an influence in the price that is charged for Options. We expose the different elements which affect an option price and how an option can be created by the technique of Options replication. We then develop Option pricing models precisely the Binomial model and black and Scholes model and then we analyze the limit of the latter and try to propose way by which this shortcoming can be overcome. Research Approach: We have adopted in our work a descriptive approach where use mainly qualitative type of information. First we relate the theoretical background on options as written in many financial textbooks and then, through examples of application extracted from the book written mainly by JC Hull, we show the materiality of the use of options in everyday live and how they can be used for hedging, speculation and for arbitrage. Third, after exposing the pricing models we run a critical view on the assumptions of the black and Scholes model which somehow constitute one of its major shortcomings. This in turn gives us room to relax these conditions that lead us the result of the research and to some suggestions at the conclusion part. Result of the study: there are a wide range of options which are traded nowadays on Exchange Options markets and over the counter markets. Options have basic properties which are valid for every type of option but also some particular features depending to the custom need of investors. The most interesting aspect in the world of option is how best to determine their price and their value and since 1973 with the devise of the black and scholes model, lot of other techniques of valuation have been conceived trying to overcome the limitations observed in the black and Scholes model. Not to neglect is the binomial models which work pretty well in valuing American type of options and also is well implemented in computer systems to work out the price of exotic options. With the speed which Option variants are created every day, this subject still have a long way to go and still there is lot of work to be done by financial engineers to devise a model of pricing that can anticipate every possible situation that can be taken by investors through the way of Options.