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# Math for Quantitative Finance

Take a guided tour through the powerful mathematics and statistics used to model the chaos of the financial markets.

Trading used to take place primarily at physical stock exchanges, with traders shouting prices and quantities into a sea of bodies.

As the trading world - like the rest of the world - has moved digital, the game has changed. While financial “experts” can still provide insights and make key decisions, the new heroes are math, statistics, and computer science.

The massive amount of trading data - and the frequency at which trading occurs - is a major reason why quantitative methods and automated algorithms have become a bedrock of Wall Street.

The New York Stock Exchange (NYSE) sees 2-3 million separate trades on a standard day. Given that trading hours are 9:30am to 4:00pm (23,400 seconds), about how many trades (on average) are occurring per second on the NYSE?

Under “normal” conditions (e.g., not around earnings reports), it is often reasonable to model a stock price as a random variable. With no information about stock X, which of the following is a better model?

**A:**Stock X increases by 0.1% or decreases by 0.1% each minute with equal probability.**B:**Stock X increases by $1 or decreases by $1 each minute with equal probability.

*no one* defaults, assuming that default is independent across the homeowners?

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