Tinkering with RSLN-2

I have decided to dedicate a fraction of my time to “Stochastic Modeling:  Theory and Reality from an Actuarial Perspective” book. Even after six years into the profession my shallow perspective tells me that this should be our primary skill set.

As a first step I jumped straight to the section on “Regime Switching Models” to study the RSLN (Regime Switching Log-normal) model. The Actuarial Literature elsewhere tends to be inundated with this model whenever it comes to Stock models. Actuaries seem to be rebels against normal statisticians who would prefer regressive models over probability models.

Although the Brownian-motion assumption seems too convenient to believe, I do believe a certain level of auto-correlation may exist between successive stock returns. A lognormal model would be a classic Brownian-motion example with each interval being completely independent of the other. However, with all that has been written the RSLN-2 should be different.

The RSLN-2 cleverly switches between two lognormal models of different parameters by way of a simple markov process. One regime represents a more stable (less volatility) and positive average return region while other a less stable (high volatility) region with average negative return. The simplicity of the concept being attractive made parameter estimation fun while easily contemplating each step. Starting with the same dataset as in the book to confirm (1956 – 1999 TSE 300) my parameters:

The parameter estimates by way of Maximum Likelihood Estimation were spot on and so I went on to simulate accumulation rates over a 5 year investment in TSE-300. Due to computing power I limited the simulations to only 100. Results indicated a less than 15% chance of losing money. The following graphic illustrates the accumulation at 5 percentile levels:

Extremely proud of my work I attempted to model the KSE-100 data from Nov 1991 to Feb 2012 (an odd selection I agree but Nov 1991 is when KSE-100 started). The parameter estimates were amusing:

	KSE-100	TSE-300
µ1	0.017876	0.012358
µ2	(0.010740)	(0.015718)
σ1	0.062040	0.034691
σ2	0.142099	0.077721
р12	21.12%	3.75%
р21	47.39%	21.08%

Apparently the KSE-100 showed much more volatility than TSE-300 clear signs of an unstable economy over various periods, rampant inflation and high interest rates. The probability of losing money were over 30% on a 5 year accumulation with too much fluctuation:

The 5% percentile level depicts above shows a anti-selection opportunity while approaching time 60 for participants to pull out with their fund at a peak level near time 55. The observations were enlightening somewhat; the return distribution observed in KSE-100 may not be symmetrical like TSE-300, but then again this could be because of non-sufficient data (biased selection).

CONCLUSION

The RSLN-2 is conceptually simple and easy to model. While one may think that it does not incorporate mean reversion and auto-correlation, I believe the markov process behind the regime switch compensates well for that.