From Physics to Finance Piotr Karasinski Global Head of Quantitative Development, HSBC Email: firstname.lastname@example.org
Physics versus Finance Physics: • We believe in the existence of universal eternal fundamental laws, written in the language of mathematics, that can explain the physical world. Finance: • Past performance is not a guarantee of future performance • Models create markets and shape the way market participants think and act. Their use influences market behaviour. • According to George Soros’s reflexivity theory people’s biases and actions can affect the direction of the underlying economy.
How I Got into Finance • In late May 1984, while in my last year of physics PhD studies at Yale, I ran into a Yale physics friend, wearing the traditional graduation gown and accompanied by his whole family. He worked somewhere in New York and came to Yale to attend his PhD graduation. • I said “Tom, could you help me find a job in New York”. “Would you like to trade gold options?” he replied. I knew what gold was, had no idea what the word option meant but was desperate to get a job, any job! Having nothing to lose I immediately exclaimed “I would love to”. • Tom called me a week later saying that his boss, head of trading at commodity trading firm Mocatta Metals, was looking to hire somebody like me. I went to NY a couple of days later for an interview and got hired. Tom’s boss had an applied math PhD from Courant Institute. Mocatta Metals was run by its founder Yale psychiatry professor Henry Jarecki. • I knew nothing about finance, let alone about option pricing (the term derivatives did not exist in 1984). I learned the whole field on the job by working on projects and through my own readings. What made a big difference was that in April 1987 I moved to Goldman Sachs where I was hired by Fischer Black. I got the interview through a Mocatta Metals friend who knew a member of Fischer’s quant team.
Why Physics? • Reading “Biography of Physics” by George Gamov was the tipping point. I was particularly taken by the human drama behind the process of discovery. I found this book on the for-sale shelf, selling for something like 10 cents, in a scientific book store in Warsaw. • Fascination with the idea that you can discover the ultimate laws of nature doing table-top experiments and capture the results through mathematics lead me to study physics at Warsaw University followed by doctoral studies at Yale.
Why Finance? • I found in finance what I was looking for in physics: the ability to combine intellectual thought and practical action. I enjoy the interdisciplinary nature of the practice of finance in a global bank. • The desire for commercial success might be in my DNA. My father ran his own small manufacturing business in Warsaw so I grew up with, and was fascinated by, the commercial side of life.
What You Need for Business Success Quote from Kenneth D. Brody, co-founder of Taconic Capital Advisors, former Goldman Sachs partner. Ken received a BS in EE from the University of Maryland and a MBA from the Harvard Business School. “Good judgment regarding human behaviour is more important than intelligence in achieving business success"
Good Sense in Seeking Truth in the Sciences Quote from "Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences” by Rene Descartes Good sense is, of all things among men, the most equally distributed; for every one thinks himself so abundantly provided with it, that those even who are the most difficult to satisfy in everything else, do not usually desire a larger measure of this quality than they already possess. And in this it is not likely that all are mistaken the conviction is rather to be held as testifying that the power of judging aright and of distinguishing truth from error, which is properly what is called good sense or reason, is by nature equal in all men; and that the diversity of our opinions, consequently, does not arise from some being endowed with a larger share of reason than others, but solely from this, that we conduct our thoughts along different ways, and do not fix our attention on the same objects. For to be possessed of a vigorous mind is not enough; the prime requisite is rightly to apply it. The greatest minds, as they are capable of the highest excellences, are open likewise to the greatest aberrations; and those who travel very slowly may yet make far greater progress, provided they keep always to the straight road, than those who, while they run, forsake it.
Advice from Freeman Dyson The following piece of wisdom from Freeman Dyson is highly relevant when moving from maths/physics into finance. “I gazed at the stars as a young boy,” he once wrote. “That’s what science means to me. It’s not theories about stars; it’s the actual stars that count.”
Jobs in Finance • Business: • Trader • Structurer/Marketer • Strategist • Quant/IT: • Quant in a front-office group • Quant developer • Quant in a control function: model validation, product control, market/credit risk management • Software developer
Types of Derivative Financial Products • Underlying asset: equity, interest rate, foreign currency, commodity, credit, cross-asset (hybrid) • Linear products: futures, forwards, swaps (interest rate, equity, …) • Nonlinear products: vanilla/plain options, exotic options • Market place: exchange traded, OTC (over-the-counter)
What Do Quants Do? • Implement derivatives pricing models • Develop tools for calibrating model parameters • Analyse model performance • Provide day-to-day trading desk support
What We Are Looking For? • People who enjoy solving problems that involve finance, maths, computation and software development in an interdisciplinary dynamic environment. • People with keen interest in finance demonstrated through own reading, specialized coursework, etc. • Skills/Qualities: • Common sense • High level of energy and enthusiasm • Communication/interpersonal • Ability to work in a team environment • Maths (with special emphasis on probability and stochastics) • Computing • Programming: C++, C#, Java, VBA/EXCEL, Matlab, Splus/R
Computational Techniques • Direct numerical integration, linear algebra (eigensystems) • Root-finding, linear and non-linear least-square fitting, function minimization • Monte-Carlo: quasi-random (Sobol points), pseudo-random (Marsenne Twister) • PDEs • Crank-Nicholson in one dimension • ADI in two and three dimensions (Crank-Nicholson for each dimension) • Up/Down winding • Various techniques for dealing with discontinuities (Rannacher time-stepping, etc.) • Smoothing boundary conditions • Fast Fourier and Laplace transforms • Numerical libraries: NAG, IMSL, GSL (Gnu Scientific Library), etc.
Probability/Statistics and Stochastics • Probability/Statistics: • One and multi dimensional normal distribution: need to know inside-out • Poisson distribution • Concepts: mean/median value, variance/covariance, skew, kurtosis, leptokurtic (fat-tailed), biased/unbiased estimator, sampling distribution for an estimator, Fisher transformation applied to correlation estimation • Stochastics: • Markov chains • Poisson processes • Wiener process, arithmetic and geometric Brownian motions • Gaussian mean-reverting, Ornstein-Uhlenbeck, process and its properties • Kolmogorov forward (Fokker-Planck)/backward equation • Stochastic calculus: Ito’s lemma, Girsanov’s theorem • Monte-Carlo simulation of stochastic processes (start with Ornstein-Uhlenbeck) • Concepts: mean-reversion, auto/cross-correlation, drift, volatility, stochastic volatility, estimation of volatilities/correlations
Basic Finance Knowledge • Basic facts about stocks, bonds, call/put options, interest rates, inflation: • Stocks: dividend yield, price volatilities, P/E ratios • Bonds: coupon rate, yield-to-maturity • Forwards and futures • Call/put options: strike, expiry, implied volatility, option delta/gamma/vega • Interest rates: • time value of money • compounding of interest • short-rate (continuously compounded instantaneous interest rate) • interbank rate (LIBOR), yields on government and corporate bonds with standard maturities (typically 5 and 10 years), interest rate swap rates • real and nominal rate, inflation
Models to Read About • CAPM: Capital Asset Pricing Model as it led Black and Scholes to their option pricing model • Black-Scholes model • Derive the Black-Scholes PDE using Ito lemma and riskless hedge argument • Gaussian Mean-Reverting Short-Rate model (also known under Vasicek and Hull-White names)
Books General Interest • Emanuel Derman, “My Life as a Quant: Reflections on Physics and Finance” • Perry Mehrling, “Fischer Black and the Revolutionary Idea of Finance” • Robert E. Rubin “In an Uncertain World: Tough Choices from Wall Street to Washington” • Barry Schachter and Richard R. Lindsey “How I Became a Quant” • Lisa Endlich “Goldman Sachs: The Culture of Success” Preparing for a quant job interview • Paul Wilmott “Frequently Asked Questions in Quantitative Finance” • Timothy Crack “Heard on the Street: Quantitative Questions from Wall Street Job Interviews” Technical Quant Books • Paul Miron and Philip Swannell “Pricing and Hedging Swaps” • John C. Hull “Options, Futures and Other Derivatives” • Paul Glasserman “Monte-Carlo Methods in Financial Engineering” • Steven E. Shreve “Stochastic Calculus for Finance”
Books (continued) Economics & Financial Markets Books • Robert Shiller “Irrational Exuberance” • William Silber “Principles of Money, Banking, and Financial Markets” Other • Freeman Dyson “The Scientist as Rebel” • Robert Solomon, Kathleen Higgins, “A Short History of Philosophy” • Daniel Goleman “Emotional Intelligence” • Roger Fisher “Getting to Yes: Negotiating Agreement Without Giving In” • Eric Berne “Games People Play: The Psychology of Human Relationships” • Robert Greene “The 48 Laws of Power”, “The 33 Strategies of War” • Elizabeth Kuhnke “Body Language for Dummies” • William Zinsser “On Writing Well”, “Writing to Learn”
Articles and Magazines Articles • RISK Books, www.riskbooks.com, publishes collections of articles • March 9, 2006, The Wall Street Journal “Proving Ground: Why Students of Prof. El Karoui Are in Demand” (see www.ermii.org/News/Article_NEK_WSJ1.pdf) • www.ssrnc.com has lots of interesting quant papers • www.defaultrisk.com is the web’s biggest credit risk modelling resource Magazines • Risk www.risk.net • Financial Analyst Journal www.cfapubs.org/loi/faj?cookieSet=1 • Wilmott www.wilmott.com