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Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black- Scholes

Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

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Page 1: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

Aileen WangPeriod 5

Computer Systems Lab 2010TJSTAR June 3, 2010

An Analysis of Dynamic Applications of Black-

Scholes

Page 2: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 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

Page 3: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

Option trading is a variation of market trading

• Calls and puts

• More controlled

• Not necessarily at market price

What is option trading?

Page 4: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

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

Page 5: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

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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?

Page 6: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

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

Page 7: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

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

Page 8: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

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

Page 9: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

Black-Scholes

Page 10: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

Volatility

Page 11: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

AAPL – Sample Case

•At a given time t, the stock price for AAPL was 239.94. •APPL options used are ranged from 90.00 to 190.00 in increasing increments of 5.00.• Three days until maturity, volatility of 20%, and a risk free rate of 0.35%

Page 12: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

AAPL – Sample Case

•Graphs comparing call and put values of expected versus actual.

Page 13: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

AAPL – Sample Case

•Model is a good estimator for call, but put values tend to deviate as strike price increases

Page 14: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

Why doesn’t B-S always work?• Out of the money

• Strike price is above stock price, option has no value

• Disregards risk such as

• Stock market crashes

• Unexpected outside influences (terrorist attacks, mergers and acquisitions)

• Typos?

1/22/10

Limitations

Page 15: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

B-S has many assumptions that are far from valid in real life:• Disregard of extreme moves

• Assumes instant, cost-free trading

• Continuous time and continuous trading

• Standard trading (volatility risk of currency adjustments)

1/22/10

Limitations

Page 16: Aileen Wang Period 5 Computer Systems Lab 2010 TJSTAR June 3, 2010 An Analysis of Dynamic Applications of Black-Scholes

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