Mathemtical Methods

• Asymptotic analysis
• Copulas
• Differential equations
• Expected value
• Ergodic theory
• Feynman–Kac formula
• Fourier transform
• Gaussian copulas
• Girsanov's theorem
• Itô's lemma
• Martingale representation theorem
• Mathematical models
• Monte Carlo method
• Numerical analysis
• Real analysis
• Partial differential equations
• Probability
• Probability distributions
  • Binomial distribution
  • Log-normal distribution
• Quantile functions
  • Heat equation
• Radon–Nikodym derivative
• Risk-neutral measure
• Stochastic calculus
  • Brownian motion
  • Lévy process
• Stochastic differential equations
• Stochastic volatility
  • Numerical partial differential equations
    • Crank–Nicolson method
    • Finite difference method
• Value at risk
• Volatility
  • ARCH model
  • GARCH model

• The Brownian Motion Model of Financial Markets
• Rational pricing assumptions
  • Risk neutral valuation
  • Arbitrage-free pricing
• Futures contract pricing
• Options
  • Put–call parity (Arbitrage relationships for options)
  • Intrinsic value, Time value
  • Moneyness
  • Pricing models
    • Black–Scholes model
    • Black model
    • Binomial options model
    • Monte Carlo option model
    • Implied volatility, Volatility smile
    • SABR Volatility Model
    • Markov Switching Multifractal
    • The Greeks
    • Finite difference methods for option pricing
    • Vanna Volga method
    • Trinomial tree
  • Optimal stopping (Pricing of American options)
• Interest rate derivatives
  • Short rate model
    • Hull–White model
    • Cox–Ingersoll–Ross model
    • Chen model
  • LIBOR Market Model
  • Heath–Jarrow–Morton framework

Other Sections

• Computer Programming Paradigms
• Financial Risk Management