Burning Rubber: Failure Story for the most part

I have been trying to get in roots with the “SCIENCE” part of Actuarial Science. Actuarial Exams are absolutely loaded with material on “probability” and entailing Loss Models but the world has now moved on to bigger things like Big Data and GLMs, Extreme Value Theory and Solvency II (it’s probably all they can tweet about).

It’s all the more important to get the amassed knowledge accounted for and get our facts straight but I think it’s equally important to develop our tool kit and use technology at our aid. This is the part that excites me the most and while for the past few months I have been trying to get hands on practice at probability models, model fitting, and some quantitative finance related mathematics, everything while using MAPLE 18 at my aid.

However, usually in my ambition I don’t get much done but rather lose track and go off on a tangent.

The Beginning

Primarily, MAPLE appeals to the ease of writing mathematical functions and notations; it skips the long codes and lets mathematicians do what they are good at. Writing a call option function was as easy as:

Hence, a call value was easily computable by substituting values for respective parameters in the function. Further, Greeks for the call were easily computable by writing differentials with respect to the parameter of choice.

And so it progressed….

What followed was me getting carried away, trying to do everything on MAPLE. The madness was in check while I studied “Linear Algebra” with the aid of MAPLE, however it did start to get unhealthy after a while when I decided to solve the Loss Models book on it.

As a life actuary although exposed to a wide array of Loss Models in exams, I never get to apply them although some of them I believe would soon be coming in handy for say modeling claim reporting lags, short term group contracts and definitely catastrophe modeling.

Fiddling with the CIR

Interest Rate models are my biggest bother and I haven’t yet quiet wrapped my head around how any model let alone single factor models can emulate interest rate movements. It’s because interest rates don’t have a code or a system; they don’t even exhibit the Brownian motion characteristics of stock prices. I have seen Least Square calibrations of Cox-Ingersoll many times but have never quite agreed with the results.

Of course users would argue that such models are essentially for short durations and hence any systematic change in the economy can damage the results.

Through Wiki, I learned that the Cox-Ingersoll essentially has a “Non-central Chi-squared distribution” for future rates and had this ambitious idea to calibrate the model using Maximum Likelihood. What followed was me trying to calibrate daily US treasury rates for a period of a year and a half having approximately 350 instances.

Suffice to say that the calibration failed and I realized I was basically asking MAPLE to do too much iteration. So that was more than 2 hours of my life I won’t get back but I live to fight another day.

And then the Loss Models madness

I must have been in desperate need for some intellectual stimulation if I decided to solve the Klugman book (which I was rather scared of during the Exam C days).

It was good discovering the wide array of built-in probability distributions and the ease with which PDFs, CDF, MGFs, etc can be used. Also impressive are the built in Maximum Likelihood methods and Hypothesis testing.

What followed was me exploring distributions I have never quiet worked with before. A log-logistic distribution calibration on time to failure data of some submarine part was one of the successful calibrations and so detailed a utility for the model:

However, I ended up spending too much time learning to and then solving rather easy problems just for the pleasure of solving them by software. The following must have taken at least 10 minutes at first to learn to write and solve:

However, once I had the hang of it I was doing problems and plotting curves for the fun of it.

When I finally stopped

It was all an attempt again to seek mastery over the subject matter while learning new software but the more you work with probability models the harder it becomes to acknowledge them as interesting and worthwhile. This follows a feeling of frustration of yet again failing to acquire even a little sense of accomplishment and an inside echo reminding you of what your life has become.

This guy tells it best:

when your computer dies and you're forced to see the mess you've become pic.twitter.com/QtpFdYuUGc
— Tyler Oakley (@tyleroakley) October 25, 2014