Heteroscedasticity: Only downside being "Hard to spell"

As mentioned in my last post, volatility of stock returns vary over time (Heteroscedasticity) and they happen in a systematic way so as to ensure mean reversion. The concept is appealing well beyond the regular homoscedastic models which assume constant volatility. And so the best book I had that provided hands on model calibration experience was the elementary “Time Series Analysis by Cryer and Chan”.

Wiki says on the subject:

“The possible existence of heteroscedasticity is a major concern in the application of regression analysis, including the analysis of variance, because the presence of heteroscedasticity can invalidate statistical tests of significance that assume that the modeling errors are uncorrelated and normally distributed and that their variances do not vary with the effects being modeled.”

Financial Time Series Characteristics: Crucial knowledge as always

Recently while studying for my Life Risk Management Exam coming fall I went off syllabus to studying market risks. I have always felt that financial models tend to have too many subtle assumptions that should always be borne in mind while working with them and the no-arbitrage principle tops that list.

The section on “Characteristics of financial time series” in the “Financial Enterprise Risk Management” Book (Chapter 14) had some interesting information that I felt would serve as rule of thumb in financial modeling. My regular perceptions on the subject did change dramatically.

Firstly;

“In spite of the assumptions in many models to the contrary, market returns are rarely independent and identically distributed.”

I have always felt the same as markets tend to be driven by common perceptions and copy cats a lot. Also there are many instances where markets go over kill with an idea and then subsequent corrections start to take place gradually. Also, mean reversion is always there very much observable. So does this mean models assuming a random walk process as in the Log-normal model is wrong?

MONTE CARLO APPROXIMATIONS: AS EXOTIC AS THE NAME GOES???

I get easily carried away by all things European; the architecture, the art, the culture, the accents, the visage (of women strictly). No surprise that out of assortments of quantification and approximation techniques, the Monte Carlo method catches my attention more. It's soooo Italian.

Monte Carlo in general is the name of the administrative area under the Principality of Monaco. Of course I know that because of Wikipedia and because I saw Selena Gomez strutting around it in a sunshine dress and certainly because Monaco rings of one of the finest racing circuits and records some of the most celebrated Formula 1 races ever.

However, the Monte Carlo Simulation seemed like too much unnecessary work for estimating Option prices. Most of you would remember it from your Financial Economics Exam (MFE) of SOA and I suppose its applications in Finance are just as many as the only two pages dedicated for it in the ASM Manual.

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.