An Analysis of Dynamic Applications of Black-Scholes

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					           An Analysis of Dynamic Applications of
                       Black-Scholes
                                   Aileen Wang
                       Period 5 Computer Systems Research
           For decades people have invested in
           the stock market in with stocks,                 The purpose of this project is to
Abstract




                                                  Purpose
           options, and bonds. Various groups               investigate the Black-Scholes model,
           of people have worked towards                    a popular tool in helping European
           modeling the stock market with                   investors determine the calls and
           mathematics. Black-Scholes, which                puts of European options. The goal
           remains one of the most prevalent                however, is to adapt the European
           tools used by European investors                 model into an American model.
           today. However, the Black-Scholes                Conforming the model to American
           model is catered toward European                 parameters can be a helpful
           options, which have a definite time              investment tool to traders and
           for maturity. American stocks do not             investors alike.
           have such constraints and can be
           bought and sold at any time




                                                            The program will be coded in Java
                                                            consisting of two main components.
           Most of the work revolves around the             One is the stock class. The other,
                                                  Method

           Black-Scholes model and the input of
Scope




                                                            perhaps the most important part of
           its required variables. Because the              the project, is the Black-Scholes
           B-S model revolves around a constant             class containing the B-S formula and
           time period, it will first be                    model. Outputs will be a series of
           evaluated as such. Then, the B-S                 numerical data. This data will then
           model will be revised to output the              be outputted into a spreadsheet and
           inputs of the next time period,                  graphed as a time-series plot.
           making the model dynamic.                        Inputs will be price, volatility,
                                                            and interest rates. Historical data
                                                            on stocks and options can be used as
                                                            inputs.




           The results obtained should give                 [insert sample graph here]
           insight into future option pricing,
Results




           as well as underline the main
                                                  Sample




           differences in American and European
           option trading. The results will be
           presented in both table and
           graphical format (using spreadsheets
           and time-series plots). Although
           this is only one dynamic application
           of Black-Scholes, it may provide
           ideas for other investing tools that
           branch from models of markets of
           different nationalities.