The history of Quantitative Finance is essentially a history of the conquest of "Volatility". The story is about how a few exceptionally talented men across both sides of the Atlantic grappled with the concept of volatility and ultimately tamed it. The story starts off in 1952 with volatility of financial assets being introduced a statistical measure of financial risk and ends in the present day with it becoming a financial asset itself. That’s pretty much all there is to quantitative finance. Rest is just details and an awful lot of very advanced mathematics. Then again, this could be a gross understatement. Talking of details and math, we should remember that it’s a huge body of content and very dense and sophisticated mathematics that underlie the development of modern quantitative finance in a short span of around 50 years.

It all started in Chicago in 1952 with Harry Markowitz and ended in Chicago sometime around 2003 when the new VIX was introduced. In that sense we may be living in the post-historical period. Of course, the post-historical era, which we call the post-Heston period below, could be a very long one with great many innovations in the field of quantitative finance coming our way.

The historical timeline that outlines how Volatility got transformed from being a measure of financial risk to financial asset can be divided into three broad periods. If we were to take a Jurassic Park style tour of Quant Finance then we can separate these periods as:

- Black-Scholes Era (1952 – 1987)
- Heston Era (1988 – 2007)
- Post Heston (2007 – Present)

** **

**Black-Scholes Era (1952 – 1987)**

Black Scholes era began when in 1952, Harry Markowtiz, during the course of completing his Ph.D. dissertation realized that volatility is a statistical concept and in fact, is the same as the concept of standard deviation. And, mathematically speaking, this is the proxy for financial “risk”. The Black-Scholes era can also be termed as the era of constant volatility.

It was in 1973, when Fischer Black and Myron Scholes presented their seminal – and perhaps, the most famous paper in all of quantitative finance – on option pricing. This could, in many ways, be considered a true formal beginning of the discipline of quantitative finance. .

**Heston Era (1988 – 2007)**

In my opinion the Heston era began around the time when John Hull and Alan White published their one factor stochastic volatility model in 1987. But this was still not a game changer. The real paradigm shift happened when, in 1993, Steven Heston, then at Yale University came up with his two factor stochastic volatility model. This was the first break with physics-like models that had dominated the quantitative finance up to then. Heston’s model of stochastic volatility was based on a far more complex process than the ordinary geometric Brownian motion type mathematical models – which were directly borrowed from statistical physics – that had characterized the dynamics of asset price models up to then. There is no parallel of such a process in physics. Imagine, Einstein thinking about a diffusion process of a molecule which follows a random walk in a “medium” which is itself vibrating in a random manner.

Ironically, even though Heston introduced a revolutionary way of visualizing volatility and the option pricing problem and, advertently or inadvertently, made a decisive break with physics-like models of quant finance, much of the Heston era was dominated by the other type of volatility models, i.e. the *volatility surface* and *local volatility*. It was only from 2003 onwards that banks started using Heston’s model extensively and quants and traders started recognizing the utility of this model. In fact, to be precise, both concepts of “volatility surface” and “local volatility” do not merit the addition of the word “model” after them. Volatility surface and Local Volatility are not really models. They are just another way of looking at stochastic volatility.

**Post Heston (2007 – Present)**

The post-Heston era started with the financial crisis of 2007-2008. During the ensuing market turmoil the stochastic volatility models more or less broke down. This is a period that witnessed big spikes in volatility in many FX options market, such as the Dollar-Yen market, it caused serious problems for traders. What was really troubling, and perhaps bewildering at the same time, was the observation that somehow volatility has acquired a life of its own independent of that of the underlying asset. Is such a thing possible? Is it possible for volatility to have the freedom to rise or fall on its own accord without any change in the underlying asset, say, the FX rate?

Enter a new class of models known as the Stochastic Local Volatility (SLV) models. The most important development came with the publication of a stochastic local volatility model by Ren, Madan, and Qian in 2007. As we shall see later on in these notes, this model incorporated an independent stochastic component in the volatility process that would change the dynamics of the process significantly. Grigore Tataru and Travis Fisher at Bloomberg also developed an SLV model in 2010 for pricing barrier options. Tataru and Fisher make a key observation in their paper, which perhaps explains the motivation for the development of SLV models and what we have argued in the above paragraph. The authors note that prices of barrier and path dependent options mostly depend on the dynamics of the market. Vanilla option prices don’t matter that much for their pricing. What is important is how the market behaves and, in particular, how volatility rises and falls with the arrival of information and passage of time. SLV models try to matching this extra market dimension to obtain good exotic option prices.

**Reference:**

*The above is an excerpt from the upcoming book, The Book of Greeks by Rahul Bhattacharya which will be published by CFE School Publishing.*

Any comments and queries can
be sent through our
web-based form.

__
More on History of Finance >>__

back to top