An Introduction to Quantitative Finance

A Three-Principle Approach

Christopher Hian Ann Ting

• Publisher: WSPC
• Year: 2015
• ISBN:
  9789814704328
• Topic: Negocios y empresa
• Subtopic: Ingeniería financiera

This concise textbook provides a unique framework to introduce Quantitative Finance to advanced undergraduate and beginning postgraduate students. Inspired by Newton's three laws of motion, three principles of Quantitative Finance are proposed to help practitioners also to understand the pricing of plain vanilla derivatives and fixed income securities.

The book provides a refreshing perspective on Box's thesis that "all models are wrong, but some are useful." Being practice- and market-oriented, the author focuses on financial derivatives that matter most to practitioners.

The three principles of Quantitative Finance serve as buoys for navigating the treacherous waters of hypotheses, models, and gaps between theory and practice. The author shows that a risk-based parsimonious model for modeling the shape of the yield curve, the arbitrage-free properties of options, the Black-Scholes and binomial pricing models, even the capital asset pricing model and the Modigliani-Miller propositions can be obtained systematically by applying the normative principles of Quantitative Finance.

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This concise textbook provides a unique framework to introduce Quantitative Finance to advanced undergraduate and beginning postgraduate students. Inspired by Newton's three laws of motion, three principles of Quantitative Finance are proposed to help practitioners also to understand the pricing of plain vanilla derivatives and fixed income securities.

The book provides a refreshing perspective on Box's thesis that "all models are wrong, but some are useful." Being practice- and market-oriented, the author focuses on financial derivatives that matter most to practitioners.

The three principles of Quantitative Finance serve as buoys for navigating the treacherous waters of hypotheses, models, and gaps between theory and practice. The author shows that a risk-based parsimonious model for modeling the shape of the yield curve, the arbitrage-free properties of options, the Black-Scholes and binomial pricing models, even the capital asset pricing model and the Modigliani-Miller propositions can be obtained systematically by applying the normative principles of Quantitative Finance.

Request Inspection Copy

Readership: Advanced undergraduates and graduate students in quantitative trading; practitioners who are interested to find out how models are derived ab initio.
Key Features:

• Physics-inspired three-principle approach to "unify" many important and useful models of Finance and Quantitative Finance
• Bridge over the gap between theory and practice
• Interesting quotes and real-life stories to keep the readers enthralled

Chapter 1

Introduction

1.1A Brief History of Quantitative Finance

Stories are usually a friendly way to start a conversation. Writing a book is perhaps no different. I start by telling the real story about how Quantitative Finance came to say “Hello World!”

It all happened in the 20th century.

When the American Association of Finance was founded in 1940, it was set up merely as a special organization of the American Association of Economics. The original goal was to focus on the major topics currently engaging the world of finance; and to develop the managerial and business aspects of finance (see Guthmann [Gut46]). Although the first issue of the Journal of Finance had already appeared in print by August 1946, Finance as an academic discipline did not quite exist until the 1950s, according to Miller [Mil99]. There was no framework, no paradigm, and no model with which to theorize the practice of finance.

A few years after the second World War, however, many researchers steeped in economics, better known as financial economists these days, made and continue to make inroad into Finance. Their thoughts, theories, hypotheses, models, and economic rationale permeate all Finance textbooks. Even to these days, Finance is still considered as a subfield of economics, but “distinguished by both its focus and its methodology” (see Ross [Ros08] and Summers [Sum85]). Therefore, it is not entirely unjustifiable to regard Finance as a new field that emerged from the well established discipline of economics.

Applied mathematicians can trace the origin of Financial Mathematics to 1900 when Bachelier published his highly original PhD thesis Théorie de la spéculation [Bac00]. But Quantitative Finance and Finance share the same defining moment when Markowitz’s article entitled “Portfolio Selection” [Mar52] was published in 1952. This 15-page article is an offshoot of his doctoral thesis. Similar to Bachelier’s experience during the defence of his thesis, the review committee did not know how to classify Markowitz’s highly original dissertation. “It’s not math, it’s not economics, it’s not even business administration” (see Bernstein [Ber92]). Despite this “isn’t” concern, Markowitz earned his PhD anyway. Since this watershed defence of a purely theoretical dissertation, slowly but steadily, Finance — a concoction spewing out from a cauldron of accounting, business, economics, and econometrics — gained recognition as an academic discipline by itself.

Much like Finance emerged from the broader field of economics, Quantitative Finance took off in 1973 when stochastic calculus was first applied by Black and Scholes [BS73], and independently by Robert Merton [Mer73]. They succeeded in solving the option pricing problem. The analytical solution called the Black–Scholes formula is widely used by many option traders. The Black–Scholes partial differential equation is regarded as one of the 17 world-changing equations by some quarters (see Stewart [Ste12]). Black and Scholes were inspired by the idea of delta-hedging in a book entitled “Beat the Market: A scientific Stock Market System” written by Thorp and Kassouf [TK67]. The simple yet brilliant stroke of genius is their realization that by dynamically hedging away the volatility, “in equilibrium, the expected return on such a hedged position must be equal to the return on a riskless asset” [BS73].

Since the 1980s, mathematicians, physicists, and computer scientists made their ways to Wall Street, which began to beckon to them as the financial industry — investment banking in particular — was on the cusp of a series of fundamental transformations, driven by relentless competition, technological advancements, and new requirements to deal with volatility. Fischer Black of the Black–Scholes formula was among the earliest to join a Wall Street bank in 1984. Looking back 11 years later before he passed away, he recalled finding the investment bank, where he was made a partner, better for continual learning than a university (see Mehrling [Meh05]). This is indeed a first-hand testimony of the fact that Quantitative Finance was in the formative phase. Transforming ever so rapidly during Black’s time in an investment bank, even he had to keep learning while developing new models to price and manage the risks of new financial products.

But what exactly is Quantitative Finance? Mathematical modeling, statistics, programming, a huge dose of clever ideas with which to examine the financial instruments in the financial markets, and all of these combined together, can be seen and illustrated in the life of a pioneering quant¹ on Wall Street: Emanuel Derman. His views on quants and Quantitative Finance are as follows [Der04]:

Quants and their cohorts practice “financial engineering” — an awkward neologism coined to describe the jumble of activities that would better be termed quantitative finance. The subject is an interdisciplinary mix of physics-inspired models, mathematical techniques, and computer science, all aimed at the valuation of financial securities. The best quantitative finance brings real insight into the relation between value and uncertainty, and it approaches the quality of real science; the worst is a pseudoscientific hodgepodge of complex mathematics used with obscure justification.

The models built by the pioneering quants started to gain traction in the financial industry. In 1992, the International Association of Financial Engineers (IAFE)² was founded, and the first issue of IAFE’s Journal of Derivatives appeared in fall 1993. Suddenly, Wall Street needed more quants to build pricing models. To cater to this growing need, specialized master programs in financial engineering, computational finance, and the likes, started to sprout in the early 1990s, and rapidly spread across the North America, Europe, and Asia.

A second generation of quants and their stories on Wall Street are lucidly captured in “The Quants” [Pat10]. Here, statistical arbitrage, i.e., money making, the inner circle business, which eluded Derman and his friends, takes center stage. This time round, quants are math whizzes or computer scientists who develop sophisticated systems to trade securities around the world, or price financial instruments such as securities related to mortgages. On the back of the huge amount of profit generated, quants emerged as a very powerful group on Wall Street before the 2008 financial crisis.³

During the few years leading to the bursting of the housing bubble in the U.S., having quants within the sell-side division and at the buy-side front desks became an in thing. It was suspected that financial institutions sometimes employed quants to attract business because other banks were doing so profitably. Amid the feverish housing market, the demand for quants was so overwhelming that PhDs in engineering and actuary science were also enlisted to price the mortgage-backed securities, collateral debt obligations, and complex credit derivatives.

1.2The 2008 Global Financial Crisis and Quantitative Finance

Not surprisingly, the blame for the near collapse of the global financial system fell on the quants. “The formula that felled Wall St” by Jones,⁴ “Recipe for Disaster: The Formula That Killed Wall Street” by Salmon,⁵ “Maths geniuses and meltdown” by Witzel,⁶ “Do Blame The Quants” by Portela,⁷ just to name a few, dramatize how the models completely failed to reflect the risks in complex credit derivatives. Obliquely, the arrows of blame were shot at the model builders, namely, the quants, who had not been professional in their work and ethical conduct. Two quant models, in particular, Gaussian copula and value-at-risk metric, ran the gauntlet of severe criticism by acrimonious antagonists and detractors.

Taleb, one of the most vocal critics, put himself in the shoes of a philosophical birder. He spotted the metaphorical Black Swans before the 2008 financial crisis [Tal07] and cried out as a lone voice in the wilderness:

Globalization creates interlocking fragility, while reducing volatility and giving the appearance of stability. In other words it creates devastating Black Swans. We have never lived before under the threat of a global collapse. Financial Institutions have been merging into a smaller number of very large banks. Almost all banks are interrelated. So the financial ecology is swelling into gigantic, incestuous, bureaucratic banks — when one fails, ...