Simulation

Overview

Monte Carlo and agent-based simulation let a hypothesis, or an estimator, be tested against a model whose true parameters are known by construction — before it is tested against real market history, which offers only one, limited, realized path.

Core questions

• Does an estimator recover the correct parameter when applied to data simulated from a model where the true parameter is known?
• How sensitive is a result to the simulation's distributional assumptions?

Mathematical formulation

Monte Carlo standard error

For an estimator computed from N independent simulated paths with per-path standard deviation σ, the standard error of the simulated estimate shrinks as 1/√N. This is the basic convergence rate that governs how many paths a simulation study needs, and it is markedly slower for tail-risk estimates than for a mean.

Methods we use

• Monte Carlo methods in financial engineering

  Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering. Springer.

• Zero-intelligence order book simulation

  Farmer, J. D., Patelli, P., & Zovko, I. I. (2005). The predictive power of zero intelligence in financial markets. PNAS, 102(6), 2254–2259.

• Self-exciting point-process simulation

  Hawkes, A. G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika, 58(1), 83–90; and Bacry, E., Mastromatteo, I., & Muzy, J.-F. (2015). Hawkes processes in finance. Market Microstructure and Liquidity, 1(1), 1550005.

Open problems

• How many simulated paths are needed before a tail-risk estimate, rather than a mean, stabilizes?
• How should a simulated model's calibration be validated against a market regime it was not calibrated on?