Alpha Quanta
First Concepts in Financial Engineering
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Numerical Methods
Asset Prices – Analytically
European Call Option – Analytically
Taylor Series
Ito’s Lemma & Stochastic Differential Equations
Multivariate Taylor Series
The Binomial Model
Discrete Ordinary Differential Equations
Finite Difference Methods for PDEs
Heat Equation (Diffusion Equation)
Explicit Euler FDM
Implicit Euler FDM
Neutron Flux Example
Wave Propagation Equation
Stability and Instability of Numerical Methods
Stability Problems of Explicit Euler
Spectrally Stable But Bad
Stability Properties of Implicit Euler
Crank–Nicolson FDM
Origins of the Fourier Transform
Heat Equation – Fourier Series
Fourier Transforms
Monte Carlo
Econometrics
❖ Short Notes ❖
Time Series
Markov Regime Switching
Recursive substitution
AR(1). Infinite MA
OLS Properties & Assumptions
OLS: Distributional Assumption
OLS: Sampling Properties
OLS Consistency. Asymptotic Regressors
Least Squares Coefficient Vector
Finding vector b
Finding vector b orthogonally
Covariance Matrix Estimation
How well does the data fit?
Estimator without error normality
GLS: Sampling properties
Gauss Markov Theorem & Proof
Gauss Markov Proof
Stochastic Convergence
Law of Large Numbers. Central Limit Theorem
Market Risk
Interest Rates, Yield and Duration
Value at Risk, VaR. A Point Measure of Risk
Expected Shortfall. A Spectral Measure of Risk.
VaR Calculation by Historical Simulation
Stressed Value at Risk, SVaR Calculation by Historical Simulation
Finite Difference Approximation of a Historical Empirical Distribution
VaR Under The Normal Distribution
Expected Shortfall Under The Normal Distribution
Two Portfolio VaR, Assuming The Normal Distribution
Variance & GARCH Models
Modelling Portfolio Losses Using Multivariate Models with Fat Tails
Extreme Value Theory
Pricing
Black Scholes and the Risk-Neutral Derivative Price
Q Measure. Stochastic Rates. Spot Forward.
American Options
Perpetual American Option
Trading Strategies
Advancements in Stochastic Volatility Model Development
Feynman Kac
European Call
European Put
First Theorem (FFTAP)
Contingent Claims, Replication, Complete Market
Second Theorem (SFTAP)
Self-financing Portfolio
Girsanov’s Theorem & the Forward Neutral Measure
Martingale Pricing Model
Q Exists Uniquely and Completes M
Martingales
Radon-Nikodym Theorem
Measure & Probability
Bond Pricing, Stochastic Interest Rates
Credit Risk
Bonds
Credit Derivatives: Credit Default Swaps
Models of Credit Risk
Ratings & Migration in Bond Valuation
Reduced Form Models
Credit Rating & Migration
Merton Model
Strategic Default
Default Correlation
Credit Derivatives
Model Fitting
Portfolio Theory
Two Fund Theorem
The Market Portfolio
The Case for Diversification
The Capital Asset Pricing Model
Risk Components of the CAPM Model
Optimal Portfolios in CAPM
Why CAPM? A General Factor Model
Numerical Methods
Asset Prices – Analytically
European Call Option – Analytically
Taylor Series
Ito’s Lemma & Stochastic Differential Equations
Multivariate Taylor Series
The Binomial Model
Discrete Ordinary Differential Equations
Finite Difference Methods for PDEs
Heat Equation (Diffusion Equation)
Explicit Euler FDM
Implicit Euler FDM
Neutron Flux Example
Wave Propagation Equation
Stability and Instability of Numerical Methods
Stability Problems of Explicit Euler
Spectrally Stable But Bad
Stability Properties of Implicit Euler
Crank–Nicolson FDM
Origins of the Fourier Transform
Heat Equation – Fourier Series
Fourier Transforms
Monte Carlo
Econometrics
❖ Short Notes ❖
Time Series
Markov Regime Switching
Recursive substitution
AR(1). Infinite MA
OLS Properties & Assumptions
OLS: Distributional Assumption
OLS: Sampling Properties
OLS Consistency. Asymptotic Regressors
Least Squares Coefficient Vector
Finding vector b
Finding vector b orthogonally
Covariance Matrix Estimation
How well does the data fit?
Estimator without error normality
GLS: Sampling properties
Gauss Markov Theorem & Proof
Gauss Markov Proof
Stochastic Convergence
Law of Large Numbers. Central Limit Theorem
Market Risk
Interest Rates, Yield and Duration
Value at Risk, VaR. A Point Measure of Risk
Expected Shortfall. A Spectral Measure of Risk.
VaR Calculation by Historical Simulation
Stressed Value at Risk, SVaR Calculation by Historical Simulation
Finite Difference Approximation of a Historical Empirical Distribution
VaR Under The Normal Distribution
Expected Shortfall Under The Normal Distribution
Two Portfolio VaR, Assuming The Normal Distribution
Variance & GARCH Models
Modelling Portfolio Losses Using Multivariate Models with Fat Tails
Extreme Value Theory
Pricing
Black Scholes and the Risk-Neutral Derivative Price
Q Measure. Stochastic Rates. Spot Forward.
American Options
Perpetual American Option
Trading Strategies
Advancements in Stochastic Volatility Model Development
Feynman Kac
European Call
European Put
First Theorem (FFTAP)
Contingent Claims, Replication, Complete Market
Second Theorem (SFTAP)
Self-financing Portfolio
Girsanov’s Theorem & the Forward Neutral Measure
Martingale Pricing Model
Q Exists Uniquely and Completes M
Martingales
Radon-Nikodym Theorem
Measure & Probability
Bond Pricing, Stochastic Interest Rates
Credit Risk
Bonds
Credit Derivatives: Credit Default Swaps
Models of Credit Risk
Ratings & Migration in Bond Valuation
Reduced Form Models
Credit Rating & Migration
Merton Model
Strategic Default
Default Correlation
Credit Derivatives
Model Fitting
Portfolio Theory
Two Fund Theorem
The Market Portfolio
The Case for Diversification
The Capital Asset Pricing Model
Risk Components of the CAPM Model
Optimal Portfolios in CAPM
Why CAPM? A General Factor Model
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Default Correlation
Copulas