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Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio ...
Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. [1] This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or portfolio of a business, project , or any other investment.
Historical simulation in finance's value at risk (VaR) analysis is a procedure for predicting the value at risk by 'simulating' or constructing the cumulative distribution function (CDF) of assets returns over time assuming that future returns will be directly sampled from past returns.
Financial risk modeling is the use of formal mathematical and econometric techniques to measure, monitor and control the market risk, credit risk, and operational risk on a firm's balance sheet, on a bank's accounting ledger of tradeable financial assets, or of a fund manager's portfolio value; see Financial risk management.
Monte Carlo methods are used in corporate finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining the distribution of their value over the range of resultant outcomes.
Binomial Lattice for equity, with CRR formulae Tree for an bond option returning the OAS (black vs red): the short rate is the top value; the development of the bond value shows pull-to-par clearly . In quantitative finance, a lattice model [1] is a numeric approach to the valuation of derivatives in situations requiring a discrete time model.
The valuation itself combines (1) a model of the behavior of the underlying price with (2) a mathematical method which returns the premium as a function of the assumed behavior. The models in (1) range from the (prototypical) Black–Scholes model for equities, to the Heath–Jarrow–Morton framework for interest rates, to the Heston model ...
John Hull and Alan White, "One factor interest rate models and the valuation of interest rate derivative securities," Journal of Financial and Quantitative Analysis, Vol 28, No 2, (June 1993) pp. 235–254. John Hull and Alan White, "Pricing interest-rate derivative securities", The Review of Financial Studies, Vol 3, No. 4 (1990) pp. 573–592.