Aileen Wang

Period 5

An Analysis of Dynamic Applications of Black-

Scholes

Purpose

Investigate Black-Scholes model

Apply the B-S model to an American market

Dynamic trading vs. fixed-time trading

Questions

To what kind of stock options is the Black-Scholes model most applicable to?

Validity: How does Black-Scholes generated call and put values

compare with the actual historical values?

Variable factors: Stocks of a different industry (finance sector stocks vs.

agriculture vs. technology) Different volatilities, different price levels

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Scope of Study

Analysis of input variables

What are they? How will they be

obtained? What formulas are

necessary to calculate them?

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

Background Information

Black-Scholes: Two parts 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

Procedure and Method

Main language: Java Outputs:

Series of calls and puts Spreadsheet, time-series plot

Inputs Price Volatility Interest rate Test data and historical data

Black-Scholes

Volatility

Results

Explore Option pricing with mathematics Validity of the model Comparing stocks of different volatility, industry, and

nature

Further research Comparison with other mathematical models Application into markets in other countries