Machine Learning in Finance

L01 Introduction to Financial Machine Learning

Machine Learning in Finance
Finance and ...

关于金融与金融工程

“金融”的意义

金融活动

金融研究

什么是金融？

与金融相关的诺贝尔经济学奖

什么是金融工程？

什么是工程？

兹维⋅\cdot博迪的定义

国际数量金融协会(iaqf)对金融工程的介绍

金融工程的研究领域

金融工程的核心问题

合成与复制

无套利动态过程

风险中性

金融工程发展的历史逻辑

关于金融工程教育

Research Methods

Finance and ...

关于金融与金融工程

“金融”的意义

金融活动

金融研究

期刊 创刊年份
The Journal of Finance 1946
Journal of Financial and Quantitative Analysis 1966
Journal of Financial Economics 1974
金融研究 1980
The Review of Financial Studies 1988
协会 创办年份
The American Finance Association 1939
中国金融学会 1950
Western Finance Association 1965
European Finance Association 1974
Society for Financial Studies 1987

什么是金融？

与金融相关的诺贝尔经济学奖

什么是金融工程？

金融工程(Financial Engineering)=金融(Finance)+工程(Engineering)\text{金融工程(Financial Engineering)}=\text{金融(Finance)}+\text{工程(Engineering)}

什么是工程？

兹维⋅\cdot博迪的定义

Financial engineering is the application of science-based mathematical models to decisions about saving, investing, borrowing, lending, and managing risk. -- by Zvi Bodie

国际数量金融协会(iaqf)对金融工程的介绍

金融工程的研究领域

金融工程的核心问题

合成与复制

无套利动态过程

风险中性

金融工程发展的历史逻辑

关于金融工程教育

Research Methods

Quantitative Methods in Finance

1827 Brown

The Scottish botanist, Robert Brown, gave his name to the random motion of small particles in a liquid. This idea of the random walk has permeated many scientific fields and is commonly used as the model mechanism behind a variety of unpredictable continuous-time processes. The lognormal random walk based on Brownian motion is the classical paradigm for the stock market. See Brown (1827).

1900 Bachelier

the concept of Brownian motion.} He developed a mathematical theory for random walks, a theory rediscovered later by Einstein. He proposed a model for equity prices, a simple normal distribution, and built on it a model for pricing the almost unheard of options. His model contained many of the seeds for later work, but lay `dormant' for many, many years. It is told that his thesis was not a great success and, naturally, Bachelier's work was not appreciated in his lifetime. See Bachelier (1995).

1911 Richardson

Most option models result in diffusion-type equations. And often these have to be solved numerically. The two main ways of doing this are Monte Carlo and finite differences (a sophisticated version of the binomial model). The very first use of the finite difference method, in which a differential equation is discretized into a difference equation, was by Lewis Fry Richardson in 1911, and used to solve the diffusion equation associated with weather forecasting. See Richardson (1922). Richardson later worked on the mathematics for the causes of war.

1923 Wiener

Norbert Wiener developed a rigorous theory for Brownian motion, the mathematics of which was to become a necessary modelling device for quantitative finance decades later. The starting point for almost all financial models, the first equation written down in most technical papers, includes the Wiener process as the representation for randomness in asset prices. See Wiener (1923).

1950s Samuelson

The 1970 Nobel Laureate in Economics, Paul Samuelson, was responsible for setting the tone for subsequent generations of economists. Samuelson 'mathematized' both macro and micro economics. He rediscovered Bachelier's thesis and laid the foundations for later option pricing theories. His approach to derivative pricing was via expectations, real as opposed to the much later risk-neutral ones. See Samuelson (1995)

1951 Itoˆ\^{o}

Where would we be without stochastic or Itoˆ\^{o} calculus? (Some people even think finance is only about Itoˆ\^{o} calculus.) Kiyosi Itoˆ\^{o} showed the relationship between a stochastic differential equation for some independent variable and the stochastic differential equation for a function of that variable. One of the starting points for classical derivatives theory is the lognormal stochastic differential equation for the evolution of an asset. Itoˆ\^{o}'s lemma tells us the stochastic differential equation for the value of an option on that asset.

In mathematical terms, if we have a Wiener process XX with increments dXdX that are normally distributed with mean zero and variance dt then the increment of a function F(X)F(X) is given by

dF=dFdXdX+12d2FdX2dtdF=\frac{dF}{dX}dX+\frac{1}{2}\frac{d^2F}{dX^2}dt\nonumber

This is a very loose definition of Itoˆ\^{o}'s lemma but will suffice. See Itoˆ\^{o} (1951).

1952 Markowitz

Harry Markowitz was the first to propose a modern quantitative methodology for portfolio selection. This required knowledge of assets' volatilities and the correlation between assets. The idea was extremely elegant, resulting in novel ideas such as 'efficiency' and 'market portfolios'. In this Modern Portfolio Theory, Markowitz showed that combinations of assets could have better properties than any individual assets. What did 'better' mean? Markowitz quantified a portfolio's possible future performance in terms of its expected return and its standard deviation. The latter was to be interpreted as its risk. He showed how to optimize a portfolio to give the maximum expected return for a given level of risk. Such a portfolio was said to be `efficient'. The work later won Markowitz a Nobel Prize for Economics but is rarely used in practice because of the difficulty in measuring the parameters volatility, and especially correlation, and their instability.

1963 Sharpe, Lintner and Mossin

William Sharpe of Stanford, John Lintner of Harvard and Norwegian economist Jan Mossin independently developed a simple model for pricing risky assets. This Capital Asset Pricing Model (CAPM) also reduced the number of parameters needed for portfolio selection from those needed by Markowitz's Modern Portfolio Theory,

1966 Fama

Eugene Fama concluded that stock prices were unpredictable and coined the phrase 'market efficiency'. Although there are various forms of market efficiency, in a nutshell the idea is that stock market prices reflect all publicly available information, that no person can gain an edge over another by fair means. See Fama (1966).

1960s Sobol, Faure, Hammersley, Haselgrove, Halton . . .

Many people were associated with the definition and development of quasi random number theory or low-discrepancy sequence theory. The subject concerns the distribution of points in an arbitrary number of dimensions so as to cover the space as efficiently as possible, with as few points as possible. The methodology is used in the evaluation of multiple integrals among other things. These ideas would find a use in finance almost three decades later. See Sobol (1967), Faure (1969), Hammersley and Handscomb (1964), Haselgrove (1961) and Halton (1960).

1968 Thorp

Ed Thorp's first claim to fame was that he figured out how to win at casino Blackjack, ideas that were put into practice by Thorp himself and written about in his best-selling Beat the Dealer, the 'book that made Las Vegas change its rules'. His second claim to fame is that he invented and built, with Claude Shannon, the information theorist, the world's first wearable computer. His third claim to fame is that he was the first to use the 'correct' formula for pricing options, formula that were rediscovered and originally published several years later by the next three people on our list. Thorp used these formula to make a fortune for himself and his clients in the first ever quantitative finance-based hedge fund. See Thorp (2002) for the story behind the discovery of the Black-Scholes formula.

1973 Black, Scholes and Merton

Fischer Black, Myron Scholes and Robert Merton derived the Black-Scholes equation for options in the early seventies, publishing it in two separate papers in 1973 (Black & Scholes, 1973, and Merton, 1973). The date corresponded almost exactly with the trading of call options on the Chicago Board Options Exchange. Scholes and Merton won the Nobel Prize for Economics in 1997. Black had died in 1995.

1974 Merton, again

In 1974 Robert Merton (Merton, 1974) introduced the idea of modelling the value of a company as a call option on its assets, with the company's debt being related to the strike price and the maturity of the debt being the option's expiration. Thus was born the structural approach to modelling risk of default, for if the option expired out of the money (i.e. assets had less value than the debt at maturity) then the firm would have to go bankrupt.

Credit risk became big, huge, in the 1990s. Theory and practice progressed at rapid speed during this period, urged on by some significant credit-led events, such as the Long Term Capital Management mess. One of the principals of LTCM was Merton who had worked on credit risk two decades earlier. Now the subject really took off, not just along the lines proposed by Merton but also using the Poisson process as the model for the random arrival of an event, such as bankruptcy or default. For a list of key research in this area see Schönbucher (2003).

1977 Boyle

Phelim Boyle related the pricing of options to the simulation of random asset paths. He showed how to find the fair value of an option by generating lots of possible future paths for an asset and then looking at the average that the option had paid off. The future important role of Monte Carlo simulations in finance was assured. See Boyle (1977).

1977 Vasicek

So far quantitative finance hadn't had much to say about pricing interest rate products. Some people were using equity option formula for pricing interest rate options, but a consistent framework for interest rates had not been developed. This was addressed by Vasicek. He started by modelling a short-term interest rate as a random walk and concluded that interest rate derivatives could be valued using equations similar to the Black-Scholes partial differential equation.

1979–81 Harrison, Kreps, Pliska

1979-81 Harrison, Kreps, Pliska Until these three came onto the scene quantitative finance was the domain of either economists or applied mathematicians. Mike Harrison and David Kreps, in 1979, showed the relationship between option prices and advanced probability theory, originally in discrete time. Harrison and Stan Pliska in 1981 used the same ideas but in continuous time. From that moment until the mid 1990s applied mathematicians hardly got a look in. Theorem, proof everywhere you looked. See Harrison and Kreps (1979) and Harrison and Pliska (1981).

1986 Ho and Lee

One of the problems with the Vasicek framework for interest rate derivative products was that
it didn't give very good prices for bonds, the simplest of fixed income products. If the model couldn't even get bond prices right, how could it hope to correctly value bond options? Thomas Ho and Sang-Bin Lee found a way around this, introducing the idea of yield curve fitting or calibration. See Ho and Lee (1986).

1992 Heath, Jarrow and Morton

Although Ho and Lee showed how to match theoretical and market prices for simple bonds, the methodology was rather cumbersome and not easily generalized. David Heath, Robert Jarrow and Andrew Morton took a different approach. Instead of modelling just a short rate and deducing the whole yield curve, they modelled the random evolution of the whole yield curve. The initial yield curve, and hence the value of simple interest rate instruments, was an input
to the model. The model cannot easily be expressed in differential equation terms and so relies on either Monte Carlo simulation or tree building. The work was well known via a working paper, but was finally published, and therefore made respectable in Heath, Jarrow and Morton (1992).

Finance & Fintech

Fintech

Financial Stability Board (FSB) "Monitoring of FinTech"
The FSB understands FinTech as technologically enabled innovation in financial services that could result in new business models, applications, processes or products with an associated material effect on financial markets and institutions and the provision of financial services.

中国人民银行《金融科技（FinTech）发展规划（2019-2021年）》

金融科技是技术驱动的金融创新（该定义由金融稳定理事会（FSB）于2016年提出，目前已成为全球共识），旨在运用现代科技成果改造或创新金融产品、经营模式、业务流程等，推动金融发展提质增效。

Investopedia
Financial technology (Fintech) is used to describe new tech that seeks to improve and automate the delivery and use of financial services.

CFA ® Program Curriculum
In its broadest sense, the term “fintech” generally refers to technology-driven innovation occurring in the financial services industry. For the purposes of this reading, fintech refers to technological innovation in the design and delivery of financial services and products.

CCB
Fintech=A(rtificial Intelligence)+B(igData)+C(loud Computing)+D(LT)+M(obile Internet)+I(oT)+X

Fintech应用领域：CFA ® Program Curriculum

Big Data & Data Science

Big Data （4v）





Data Science

Data Science Venn Diagram


Financial Forcasting with Big Data