1. AILEEN WANG PERIOD 5 An Analysis of Dynamic Applications of Black-Scholes

2. Purpose Investigate Black-Scholes model Apply the B-S model to an American market Dynamic trading vs. fixed-time trading

3. Scope of Study Analysis of input variables  What are they?  How will they be obtained?  What formulas are necessary to calculate them? Making the model dynamic

4. Related Studies 1973: Black-Scholes created 1977: Boyle’s Monte Carlo option model  Uses Monte Carlo applications of finance 1979: Cox, Ross, Rubenstien’s bionomial options pricing model  Uses the binomial tree and a discrete time-frame Roll, Geske, and Whaley formula  American call, analytic solution

5. Background Information Black-Scholes  Black-Scholes Model  Black-Scholes equation: partial differential equation Catered to the European market  Definite time to maturity American Market  Buy and sell at any time  More dynamic and violatile

6. Procedure and Method Coding classes: Stock class, B-S function Main language: Java Outputs:  Series of calls and puts  Spreadsheet, time-series plot Inputs  Price  Volatility  Interest rate  Test data and historical data Accuracy: the price can be compared to a calculator or historical data.

7. Results Explore  Option pricing with mathematics  Differences in the USA and Euro markets Further research  Comparison with other mathematical models  Application into markets in other countries