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.

1. FİNANSAL
MATEMATİK
Hedging, Arbitraging, Pricing
Eğitim Program Taslağı
Mart 2015
Doç. Dr. Kutlu MERİH

2.  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.

3. Temel Matematik
 Calculus
 Power / Taylor Series
 Differential Equations
 Real Analysis
 Mathematical models

4. Olasılık ve Dağılımlar
 Probability
 Probability Distributions
 Quantile Functions
 Value At Risk
 Expected Value
 İntegral Dönüşümler
 Moment Üreten Fonksiyon
 Laplace Transformation
 Karakteristik Fonksiyon

5. Stokastik Prosesler
 Binomial Distribution/Process
 Normal Distribution/Process
 Log-normal Distribution/Process
 Poisson Distribution/Process

6. Korelasyon - Kointegrasyon
 Korelasyon
 Kointegrasyon
 Copulas
 Gaussian Copulas
 Diğer Copulas

7. Volatilite/Heteroscedasticity
 Volatility
 ARCH model
 GARCH model
 Stochastic volatility
 SABR Volatility Model
 Markov Switching Multifractal

8. Stokastik Analiz
 Risk-neutral Measure
 Stochastic Integrals
 Chapman-Kolmogorov KDD
 Partial Differential Equations
 Heat Equation
 Stochastic Differential Equations
 Itô's Lemma
 Stochastic Calculus
 Brownian Motion
 Lévy Process
Bu kısma ben talibim: K. M.

9. 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 option
 Intrinsic value, Time value
 Moneyness

10. Black-Scholes Fiyatlama
 Black–scholes Model
 Black Model
 Binomial Options Model
 Monte Carlo Option Model
 Implied Volatility, Volatility Smile
 Optimal Stopping (Pricing Of American Optio
)

11. Türev Ürün Duyarlılığı: Grekler
 Gamma
 Lambda
 Rho
 Speed
 Theta
 Ultima
 Vanna
 Vega
 Vomma
 Zomma

12.  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.

13. Spot
Price (S)
Volatility
(σ)
Time to
Expiry
(τ)
Risk-
Free
Rate
(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 Vomma
Dvega
Dtime
Vomma Ultima

14. speed
zomma
color

15. Olasılık Metrik Değişimleri
Girsanov's Theorem
Radon–Nikodym Derivative
Martingale Representation Theorem
Feynman–Kac Formula
Statistical Finance

16. Alternatif Teknikler
 Asymptotic Analysis
 Ergodic Theory
 Saddlepoint Approximation

17. Nümerik Teknikler
 Numerical Analysis
 Monte Carlo Method
 Numerical Methods
Laplace Transforms
Fourier Transforms
 Numerical Partial Differential Equations
Crank–Nicolson Method
Finite Difference Method
Finite Elements Method

18. Faiz Türevleri
Interest rate derivatives
Short rate model
 Hull-White model
 Cox-Ingersoll-Ross model
 Chen model
LIBOR Market Model
Heath-Jarrow-Morton framework

19. Diğer Destek Konular
 Chaos Theory and Fractals
 Computational 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