A Large Scale Comparison of Option Pricing Models with Historical Market Data

SUMMARY
We obtained market data from the Chicago Board of Option Exchange for the period 1988-1990, and used six-month records of option trades from January-June, 1988 for a set of 13 stocks.

Model accuracy is measured in mean relative error and root mean square relative error between model price and market price in dollar. The four models are :

  1. BS -- Black-Scholes model;
  2. AMC -- American Constant volatility binomial model;
  3. EUS -- European Stochastic volatility binomial model;
  4. AMS -- American Stochastic volatility binomial model.

8192-node CM2 and 8192-node DECmpp-12000 at NPAC are used to conduct runs for the two parallel models (EUS and AMS).

Model Performance Comparison Without Optimization of Parameters
In a preliminary comparison, we examined the performance of the four pricing models using a simple method of parameter estimation. The two graphs below summarize models comparison on total 13 stocks without opitimized model parameters.

Detailed comparsion of model bias between model result and market price for BS and AMS models on individual stocks WITHOUT opitimized model parameters can be shown graphically below: 
Company Stock              Number of Trades Conducted

    

  1. AT&T                                  5230

  2. Bristol Myers Squibb                 11390

  3. Chrysler Corp.                       11989

  4. Eastman Kodak(1)                      1695

  5. Eastman Kodak(2)                      7698

  6. Ford Motor Corp.                     11756

  7. General Electric                      9075

  8. Hewlett Packard                      11043

  9. IBM (1)                               3300

  10. IBM (2)                              19352

  11. Texas Instruments                    11291

  12. Walmart                               2867

  13. Xerox                                 1865


*TOTAL*                                108851

Model Performance Comparison With Optimization of Parameters
In a refinement of our evaluation of model accuracy, we used optimized techniques to estimate model parameters. pricing models using a simple method of parameter estimation. Key model parameters optimized are initial volatilities, variance of volatility and correlation between stock price and volatility. Detailed comparsion of model bias between model result and market price for BS and AMS models on individual stocks WITHOUT opitimized model parameters can be shown graphically below: 
Company Stock              Number of Trades Conducted

    

  1. AT&T                                  5230

  2. 

  3. 

  4. Eastman Kodak(1)                      1695

  5. 

  6. 

  7. General Electric                      9075

  8. Hewlett Packard                      11043

  9. IBM (1)                               3300

  10. IBM (2)                              19352

  11. Texas Instruments                    11291

  12. 

  13. Xerox                                 1865


*TOTAL*                                 62851

Northeast Parallel Architectures Center, Syracuse University, npac@npac.syr.edu
This page is maintained by Gang Cheng, gcheng@npac.syr.edu