Naive method to test the convergence of simulation and its applications in the computation of bankruptcy probability

Abstract

We analyse a naive method using sample mean and sample variance to test the convergence of simulation. We find this method is valid for identically, independently distributed samples, as well as correlated samples with correlation disappearing in long period. Our simulation results on the approximation to bankruptcy probability (BP) show the naive method compares well with the Half-Width, Geweke and CUSUM methods in terms of accuracy and time cost. There are clear evidences of variance reduction from tail-distribution sampling for all convergence test methods when the true BP is very low.

Keywords:

• naive method
• simulation convergence
• bankruptcy probability

JEL:

• C63
• G17

Acknowledgements

We acknowledge helpful suggestions from referees. The views expressed in this paper are those of the authors, and do not reflect those of any others. All remaining errors are our own.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

Jiang thanks Bin Liu and Jia Yan for comments, and National Science Foundation of China [No. 71071027, 71173233]for financial supports.

Notes

1. Another popular methods is the variance ratio method,[7–9] which concerns multi-chains simulation. Since this paper is confined to single-chain simulation, we do not cover that method.

2. The simulation result with $\alpha 1=0.01$ for the junk-grade firm is not given here, but is available from the authors on request.

3. The simulation result with $\alpha 1=0$ for the investment-grade firm is not given here, but available after request to the authors