Mathematical Techniques in Finance. Amir Sadr

Mathematical Techniques in Finance - Amir Sadr


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standard normal random variable,
BMBrownian motion
Brownian motion at time
along sample path
proportional, lognormal volatilityATM, ATMFat‐the‐money spot, at‐the‐money forward
Dirac's delta function,
absolute, normalized volatilityCMSconstant maturity swap rateAD,
Arrow‐Debreu price, today's price of unit payoff at state
on future date
i.i.d.independent and identically distributed

      While economics as a social science studies the behavior of economic agents in the generation, acquisition, and expenditure of goods and services, finance is focused on the acquisition and management of capital in financial markets.

      Focusing on the end user, finance can be divided into personal finance, corporate finance, and government finance. Savings, investments, and loans, such as credit card, student, automobile, and home mortgage, insurance products, and estate planning are examples of personal finance. The raising of capital by borrowing and debt or selling shares and equity by a company and the management of a company's funds are the focus of corporate finance. Monetary policy, central banking, tax systems, and the oversight of the banking sector and financial markets fall under government finance.

Sector Net Worth ($Trillions)
Households 123.35
Firms 33.9
Government −26.8
Total 130.46

      Source: U.S. Federal Reserve Z.1 Statistical Release.

Category $Trillions Percentage
Real estate 32.8 24%
Consumer durable goods 6.1 4%
Checking, savings, money market accounts 15.2 11%
Debt securities, bonds 5.1 4%
Equities, mutual funds, investments 79 57%
Misc 1.3 1%
Total assets 139.6 100%
Home mortgage loans 10.9 67%
Credit card, auto loans 4.2 26%
Other loans 1.1 7%
Total liabilities 16.2 100%
Net worth 123.35
U.S. World
Bonds 50.1 123.5
Stocks 40.7 93.6
Derivatives 15.8
Foreign Exchange 6.6/day

      Sources: World Bank, BIS, SIFMA.


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Librs.Net
Type Outstanding debt
Treasury 21.0 42%