Simulations of a Financial System Featuring Zipf-Mandelbrot Power Laws, Leverage Effects, Fat Tails, Covariance Structure and Long Memory: The Merton Model, Benchmark Asset Pricing Model or Hybrid Stochastic Pricing Model - Which Is Better?

This paper features a 1000 simulations of a set of 100 levered companies equity returns in a financial market. The goal was to generate a realistic distribution of company values that follow a Zipf-Mandelbrot power law. The returns should exhibit leverage effects, negative skewness, and feature Black Swan events of correlated down-turns. Realistic positive covariance structures of returns, systematic risk, plus evidence of long-memory properties. The Merton Model and two versions of the Platen Benchmark Asset Pricing Model (BAPM), the original model and the Stochastic Benchmark Process (SBP). The required market attributes were successfuly captured but the models proved to be highly sensitive to the chosen parameters. The BAPM model proved to be more flexible than the Merton Model and the SBP version more readily generated the stipulated financial market characteristics.