A Brief Introduction of FE

What is FE? Financial engineering (quantitative finance, computational finance, or mathematical finance): –A cross-disciplinary field which uses quantitative methods developed in math or engineering to solve financial problems.

Time and Risk A typical financial problem concerns how to allocate and deploy economic resources, both spatially and across time, in an uncertain environment. Example: Investment for retirement Time and risk

A Brief Review of the History of FE (EMH) 1930’s: Statistical tools were introduced to analyze financial data ’s: Efficient market hypothesis (EMH) : (Maurice Kendall (1953), Harry Roberts (1959), Eugene Fama (1965)) –Market information, such as the information reflected in the past record or the information published in financial press, must be absorbed and reflected quickly in the stock price.

More about EMH: a Thought Experiment Let us start with a thought experiment: Assume that Prof. Chen had invented an formula which we can use to predict market movements very accurately. What would happen if this formula was unveiled to the public?

More about EMH: a Thought Experiment Suppose that it predicted that stock XYZ would rise dramatically in three days to $110 from $100. The prediction must induce a great wave of immediate buy orders. Huge demands on stock XYZ will push its price to jump to $110 immediately. The formula fails!

EMH: From Random Walk to Stochastic Calculus EMH points out the riskiness is an intrinsic attribute to financial markets. EMH is a starting point where more advanced mathematics steps in: –Random walk –Robert Merton in 1969 introduced stochastic calculus to understand how prices are set in financial markets through “equilibriums”.

A Brief Review of the History of FE (Portfolio Theory) Then, the problem is how to manage financial risk: –Diversification: “Do not put all the eggs in one basket”. 1952: Harry Markowitz and portfolio theory 1962: William Sharpe and Capital Asset Pricing Model (CAPM) 1970’s: Index funds appeared.

Building More Complex Financial Instruments: Black and Scholes The work of Markowitz and Sharpe gave a birth to the area of quantitative finance. People can utilize the theory they invented to construct new financial instruments fine-tuned to their risk appetites. Starting from 1970’s, the development in the theory of quantitative finance stimulates the prosperity of derivative markets.

Building More Complex Financial Instruments: Black and Scholes A derivative is a financial instrument that has a value determined by the price of something else. Example: –A gallon of gasoline is not a derivative. –However, the following agreement is a derivative: You enter into an agreement with a friend that says: when the price of a gallon of gasoline in 1 year is greater than $20, you will pay him $1; when the price is less than $20, he will pay you $1.

A Brief Review of the History of FE (Black Scholes Theory) 1973: Black and Scholes developed their celebrated option pricing formula. –One price (no arbitrage) principle : Harrison, Kreps, and Pliska used a general theory of continuous-time martingales to extend the Black-Scholes work to price numerous other “derivative” securities.

Political Impetus: Regan and Thatcher A serious stagflation fatigued the entire capitalism world during the period of 1970s and early 1980s. That stimulated several major western countries, led by Regan in US and Thatcher in UK, to switch away from the Keynesian economics to the New Classical Doctrine. The new classical economics emphasizes less government intervention and free market principle.

The Rise and Decline of FE A friendly political environment and the corresponding academic preparation prompted a rapid growth in the derivative markets and in turn the demand for more sophisticated mathematical tools. However, the credit crisis in casts doubt on the philosophy behind financial engineering. What is the next step? –My interest: liquidity-caused market inefficiency