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FİNANSAL MATEMATİK
Hedging, Arbitraging, Pricing
Eğitim Program Taslağı
Mart 2015
Doç. Dr. Kutlu MERİH
Bu sunum Finansal Matematik Analiz için gerekli ve temel olan konuları içeriyor.
Bunlara ek yapılabilir veya daraltılabilir.Her konu wikipedia ile bağlantılı hale
getirilmiştir.Böylece içerik ve kapsam hakkında fikir
edinilebilir.
Temel Matematik
Calculus Power / Taylor SeriesDifferential Equations Real AnalysisMathematical models
Olasılık ve Dağılımlar
Probability Probability Distributions Quantile FunctionsValue At Risk Expected Value İntegral Dönüşümler
Moment Üreten Fonksiyon Laplace Transformation Karakteristik Fonksiyon
Stokastik Prosesler
Binomial Distribution/ProcessNormal Distribution/ProcessLog-normal Distribution/ProcessPoisson Distribution/Process
Korelasyon - Kointegrasyon
KorelasyonKointegrasyonCopulasGaussian CopulasDiğer Copulas
Volatilite/Heteroscedasticity
Volatility ARCH model GARCH model
Stochastic volatility SABR Volatility Model Markov Switching Multifractal
Stokastik Analiz
Risk-neutral Measure Stochastic IntegralsChapman-Kolmogorov KDDPartial Differential Equations
Heat Equation
Stochastic Differential Equations Itô's LemmaStochastic Calculus
Brownian Motion Lévy Process
Bu kısma ben talibim: K. M.
Türev Ürün Fiyatlama
The Brownian Motion Model of Financial Markets
Rational pricing assumptions Risk neutral valuation Arbitrage-free pricing
Futures Futures contract pricing
Options Put–call parity (Arbitrage relationships for options) Intrinsic value, Time value Moneyness
Black-Scholes Fiyatlama Black–scholes Model Black Model Binomial Options Model Monte Carlo Option Model Implied Volatility, Volatility Smile Optimal Stopping (Pricing Of American Options
)
Türev Ürün Duyarlılığı: Grekler
Gamma Lambda Rho Speed Theta Ultima Vanna Vega Vomma Zomma
The table shows the relationship of the more common sensitivities to the four primary inputs into the Black-Scholes model (spot price of the underlying security, time remaining until option expiration, volatility and the rate of return of a risk-free investment)
and to the option's value, delta, gamma, vega and vomma. Greeks which are a
first-order derivative are in blue, second-order derivatives are in green, and third-order derivatives are in yellow.
Note that vanna is used, intentionally, in two places as the two sensitivities are mathematically equivalent.
SpotPrice (S)
Volatility(σ)
Time toExpiry
(τ)
Risk-FreeRate
(r)
Value (V) Δ Delta ν Vega Θ Theta ρ Rho
Delta (Δ) Γ Gamma Vanna Charm
Gamma (Γ) Speed Zomma Color
Vega (ν) Vanna VommaDvegaDtime
Vomma Ultima
speed
zomma
color
Olasılık Metrik Değişimleri
Girsanov's Theorem Radon–Nikodym Derivative Martingale Representation Theorem
Feynman–Kac Formula Statistical Finance
Alternatif Teknikler
Asymptotic AnalysisErgodic TheorySaddlepoint Approximation
Nümerik Teknikler
Numerical AnalysisMonte Carlo Method Numerical Methods
Laplace TransformsFourier Transforms
Numerical Partial Differential Equations Crank–Nicolson Method Finite Difference Method Finite Elements Method
Faiz Türevleri
Interest rate derivatives Short rate model
Hull-White model Cox-Ingersoll-Ross model Chen model
LIBOR Market Model Heath-Jarrow-Morton framework
Diğer Destek Konular
Chaos Theory and FractalsComputational Finance Quantitative Behavioral Finance Derivative (Finance), List Of Derivatives
Topics Modeling And Analysis Of Financial
Markets International Swaps And Derivatives
Association Fundamental Financial Concepts - Topics Model (Economics) List Of Finance Topics
