Option Pricing Model
Financial math came unexpectedly into my life. I can say that while I enjoyed probability to a great deal since high school, statistics didn’t come that natural to me. When a topic didn’t come natural to me, I usually relied on the teacher to give me inspiration and that initially wasn’t the case in with statistics.
But the topic of financial math emerged out of nowhere. I simply took the financial math course since it was being taught by one of my favorite professors: Dr. Marasigan. I then had a tendency to respect and prefer elder professors in the math department, and he was without a doubt, one of the most dear to me.
The topics in the financial math course started with moments, then evolved to martingales, then to Ito’s Lemma and geometric Brownian motions, and to the Black-Scholes option pricing model. The topics made me to rethink about statistics, and financial math became a serious contender as my favorite topics when I was deeply submerged to algebra and number theory. At that time I had no idea that it would be a large part of my life.
Especially when we were done with discussing Ito’s Lemma, Dr. Marasigan assigned each student group to discuss the following topics in the class, and my group was assigned to discuss on the derivations and interpretation of the Black-Scholes equation, and solving the PDE. I still remember utilizing two books in detail, to determine what theorems were worth proving in the class, and what theorems were out of scope other than their interpretations. I still remember him coming up to me, and tapping my shoulder to tell me that I did a wonderful job after the presentation. That was one of the best moments not just in college, but in my entire schooling days.
When I came to the US, I spent some serious time with econometrics. It was such an engrossing topic especially when the data set was large, and when it was also a panel data set (a set of cross section data over some time). Meanwhile, because I wanted to stay in touch with some more “fun”, I have been reading my friends’ notes on higher level math that were applied in economics from Dr. Lau. In my last semester at the graduate school, I was planning to take one of the math courses, but because of my continued focus on the thesis and econometrics, I could not. But I had a chance to take the other class of Dr. Lau, Options and Futures.
This one was less about all the details of theories behind financial math development through the Black-Scholes, but more of their applications and “derivatives” of the Black-Scholes option pricing models for exotic options and all. So without my intentions, I covered a great deal of financial math related to the Black-Scholes option pricing model and other derivatives from two my favorite professors.
And after graduation, I got into the financial services industry in 2008, doing business valuations. The BV industry uses what is simply called “Option Pricing Method” to value each breakpoints based on a company’s capital structure, and utilizes the Black-Scholes option pricing model for that. Then there came more applications, such as computations for asset volatilities, when the industry paid more attention to the value of invested capital (instead of simply the value of equity). There also came various lookback option valuations (for quantifying the discount for lack of marketability) and Monte Carlo simulations, which I think made the lives of many accountants more difficult. But all the changes have been welcome additions for me.
None of those were new to me when they came out, and even after 10 years since I first encountered the Black Scholes model, I only have to review only a few elements to recall what most of things are.
I see that the accounting and the financial reporting world is yet to see some of the valuation techniques that are often used in the investment banking world (such as the econometric models), but it’s getting there and a lot has already changed since I first got into this field in 2008.
I still miss playing with data at times — so much that I play with some random data set from time to time on STATA. But overall, I am pretty excited with where the business valuation industry is at — or, to be more precisely, where the financial reporting world is at.
And in retrospect, it’s all very funny — where I am and what I had gone through to be where I am at. I really thank my professor, Dr. Marasigan, for this. May you rest in peace, “Doc Mara”. It’s not a coincidence that you left us on the Pi Day.