Mathematical finance
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Mathematical finance is the branch of applied mathematics concerned with the financial markets. It overlaps heavily with the fields of financial engineering and computational finance. Arguably, all three terms are synonymous.The subject naturally has a close relationship with the discipline of financial economics, but mathematical finance is narrower in scope and more abstract. A central difference is that while a financial economist might study the structural reasons why a company may have a certain share price, a mathematician or financial engineer may take the share price as a given, and attempt to use stochastic calculus to obtain the fair value of derivatives of the stock.
Mathematical finance articles
Mathematical tools
- Probability
- Probability distribution
- *Binomial distribution
- *Log-normal distribution
- Expected value
- Value at risk
- Risk-neutral measure
- Stochastic calculus
- Brownian motion
- Itô's lemma
- Girsanov's theorem
- Radon-Nikodym derivative
- Monte Carlo method
- Partial differential equations
- *Heat equation
- Martingale representation theorem
- Feynman Kac Formula
- Dynkin formula
- Stochastic differential equations
- Volatility
- *ARCH model
- *GARCH model
- Stochastic volatility
- Mathematical model
- Numerical method
- *Numerical partial differential equations
- **Crank-Nicolson method
- **Finite difference method
Derivatives pricing
- Rational pricing assumptions
- *Risk neutral valuation
- *Arbitrage-free pricing
- Futures
- *Futures contract pricing
- Options
- *Put-call parity (Arbitrage relationships for options)
- *Moneyness
- *Option time value
- *Pricing models
- **Black-Scholes
- **Black model
- **Binomial options model
- **Monte Carlo option model
- **Implied volatility
- ***Volatility smile
- **The Greeks
- Interest rate derivatives
- *Short rate model
- **Hull-White model
- *LIBOR Market Model
- *Heath-Jarrow-Morton framework
See also
- Computational finance
- Financial Engineering
- Derivative (finance), list of derivatives topics
- Fundamental financial concepts - topics
- Model (economics)
- Systematic Trading
- List of finance topics, List of finance topics (alphabetical)
- List of economics topics, List of economists
- List of accounting topics
- List of marketing topics
- List of management topics
External links
- [Prof. Don M. Chance] - technical notes covering derivatives and related material
- [Prof. Peter Carr] (PDF) - FAQs in Option Pricing Theory
- [Mathematics of Financial Markets], Prof. Mark Davis, Imperial College
- [finmath.com] - Mathematical finance Reading List
- [Global Derivatives] Quantitative Mathematics Glossary
- [Option Valuation], Prof. Campbell R. Harvey
- [ISDA.org] - The International Swaps and Derivatives Association
- [Option Tutor] - a visual presentation of modern option pricing theory
- [Quantnotes.com] - articles covering mathematical finance
- [Riskglossary.com] - online glossary, encyclopedia, and resource locator
- [Riskworx.com] - discussion of the application and theory of derivatives
- [rmetrics.org] - R based environment for teaching financial engineering and computational finance
- [Moneyscience.org] - open-access, multi disciplinary resource for academics and practitioners.
- [TheQUANTsterBlog] - informational resource with links, events and jobs.
- [QuantFinanceJob.com] - A community with quantitative finance guides, interview tips, book reviews and interview questions for Ph.Ds in physics,math and engineering to land a successful financial engineering job.
- [QuantFinanceJobs.com] - Specialist job board for quantitative finance, financial engineering and risk management.
- [Econophysics Blog]
- [Financial Maths articles and lecture notes] - Some articles as introduction to financial mathematics and lecture notes from great teachers, Simon Leger's website
- [QUANTster.com] - The Quantitative Finance Job Market Daily. THE source for Quants in North America.
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