Mathematical Techniques in Finance. Amir Sadr

Mathematical Techniques in Finance - Amir Sadr


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Mortgage‐related 11.2 22% Corporate debt 9.8 8% Municipal 4 8% Federal agency securities 1.7 3% Asset‐backed 1.5 3% Money markets 1 2% Total 50.1

      Source: SIFMA.

Market Gross market value
Interest rate contracts 11.4
Foreign exchange contracts 3.2
Equity‐linked contracts 0.8

      Source: BIS.

Participant Usage Product
Households Custody, banking, borrowing Checking and interest bearing accounts, credit cards
Home mortgage, auto, student loan Level pay loans
Investments Cash, options brokerage accounts, financial or robo‐advisor advice for asset allocation
Insurance, estate planning Auto, home, life insurance; annuities
Corporations Financing Bonds, stock issuance
Cash flow management Commercial paper, lines of credit, swaps
Asset liability management, interest rate risk management Derivatives, interest rate futures, swaps, options
Insurers, mortgage servicers Rate risk Swaps, caps, swaptions
Pension plans Asset allocation and insurance Derivatives
Hedge funds Investment, speculation Leveraged products, derivatives, statistical methods
Banks, financial institutions Financial services All products
States and local government Financing Bullet bonds, callable bonds
Fannie Mae, Freddie Mac Financing, risk management Swaps, swaptions, swapped issuance
U.S. government Financing Bills, notes, bonds
Federal Reserve Monetary policy Repo and reverse, quantitative easing

      Banks and other financial institutions provide home mortgage, auto, and student loans in the form of level pay loans. These loans and receivables are in turn bought and securitized as mortgage‐backed and asset‐backed securities by companies originally set up by the U.S. government to promote home ownership and student loans, prominent among them are Fannie Mae (Federal National Mortgage Association), Freddie Mac (Federal Home Loan Mortgage Corporation), and Sallie Mae (Student Loan Marketing Association).

      Corporations raise capital by issuing stock (equity), which is publicly traded. Households participate in the stock market directly via brokerage accounts or retirement plans primarily investing in mutual funds and ETFs (Exchange Traded Funds). The allocation of investments between different assets or funds is the subject of portfolio selection.

      Firms and households use insurance and derivatives markets to mitigate and manage financial risk. Consumers buy home and auto insurance to protect against loss. Corporations raise money from the capital markets and manage their interest rate exposure through interest rate swaps and derivatives. Producers use commodity futures and derivatives to manage price risk, and pension plans and investors use equity derivatives for risk management and speculation.


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