Still during the '90s, economist laughed at engineers who were claiming they can do jobs in finance better than economists. Over the time new job roles have emerged, such as quant developers, allowing engineers and mathematicians to take cruical roles within banking and finance. The prelude to rampaging employment of engineers and mathematicians in the finance sector is that some researchers, in year 1973, had figured out how to price European put and call options. These researchers were Fisher Black, Myron Scholes and Robert Merton. The mathematics behind the work of these researchers is rigorous and cannot be taught to professionals lacking high skills in mathematics, following an anecdote I heard, is that professors from Royal Institute of Technology (KTH, Sweden) earned fortunes from that time (in the 70s?) market mispricing of financial options. The KTH professors held skills and knowledge that professionals in finance at that time had not acquired. Pricing financial contracts and their hedging has been and still is rocket science in finance. The underlying mathematics used for pricing and hedging financial assets is difficult enough to require engineers or mathematicians to have Ph. D. degree with skills in stochastic calculus to fully understand the mathematical theory and works in pricing and hedging financial assets. Myself, I have a Master of Science degree in Engineering Physics with major in Applied Mathematics and Computations Science and can only motivate above mentioned concepts for pricing and hedging financial assets. However, even thought I do not hold some Ph.D. degree in engineering or mathematics, there still are few things that are to my advantage, the advantage is that reality is more complex than theory making some theories in some sense less useful in modern application. If the model is too realistic then in worst case there is only brute force computing to resort to. Financial computations and simulations can be compute intensive. Even today with modern computers we lack compute resources to perform different advanced computations in finance, which contributes to my interest in computational finance.
The Nobel Prize winning research by Black-Scholes and Merton for pricing and hedging European put and call options have flaws forcing one to take other complex approaches in pricing and hedging these assets. Instead of the term volatility I will here use the term noise. Most financial models, equations and formulas are derived by use of the normal distribution to approximate noise. Think of noise as the spiky random behavior of an underlying relative stock returns, these returns are usually modeled from a normal distribution. Fortunately the normal distribution has many very pleasant properties making it easy to handle and work with. Because of the pleasant properties of the normal distribution, the normal distribution is the favorite distribution among many mathematicians, engineers and economists. The Nobel Prize (1997) winning research by Black-Scholes and Merton for pricing and hedging European call options has itself the normal distribution as noise. Unfortunately, there are many cases where modeling noise with the normal distribution is not good enough, especially when it comes to anomalous behavior in noise. Scholes and Merton worked in a company, Long-Term Capital Management, which got liquidated in 1998 since they did not pay enough attention to risk in their investments. For a following whole decade after the liquiditation of Long-Term Capital Management, the banking and finance world continued to ignore risk by applying the faulty normal distributed noise. Then there came the global financial crisis in 2008 proving the banking and finance world the danger in modeling by normal distributed noise. So in 2008 it became very evident that risk should be modeled by use of heavy tailed distributions, i.e. in other words it got evident risk anomalities could not follow the tails of a normal distribution. Unfortunately there is a huge set-back with improving the stock model with non-Normal distributed noise: To change distribution, to model with another distribution than the normal distribution, makes many of the derived and used models in finance dysfunctional and invalid. This due to the pleasant properties of the normal distribution are lost when changing to noise of another distribution. So modeling noise without the normal distribution moves us back closer to square one. The work (in year 1973) by Black, Scholes and Merton gave new roles to engineers and mathematicians. A new role emerged again after the financial crisis in 2008 and that time it was - the Risk Analyst.
In my thesis I studied the recovery of volatility smiles from given set of a few data points. Within finance this recovery is called impled volatility estimation. The volatility smile is a "fix" to justify and allow noise to have normal distributed behavior in manner to allow one to use certain formulas and equations which are correct in local sense but more or less faulty in global sense. So this fix or cheat does give rise to at least mimicing fatter tails. To use a volatility smile as a fix is not specific to my thesis, it is actually generally used in finance. The recovery of missing volatility smile is done by iteration of updates volatility smiles till a cost function of sum of known errors is minimzed. This type of inverse problem has multiple solutions whereby exploiting degrees of freedom I used different clever techniques to find a solution of my choice. By use of big data and estimation of returns, correlations and volatilities I can see myself derive new money making models in banking and finance. The underlying data does not only need to be financial, it may as well be Machine Learning processed data of human behavior scraped from posts, tweets and news. Any tiny improvement in predicting returns, correlations and volatilities may yield tremendous profits. By combining my skills in data science, numerical analysis, computational engineering and finanace I see myself to have an interesting and valuable asset.