FINANCIAL ASSET DYNAMICS

Advanced Quantitative Finance Library for Institutional-Grade Analytics

INSTITUTIONAL QUALITY
PORTFOLIO OPTIMIZATION
OPTIONS PRICING
RISK MANAGEMENT
VIEW CODE EXPLORE FEATURES

STOCHASTIC DIFFERENTIAL EQUATION MODELS

GEOMETRIC BROWNIAN MOTION (GBM)
dS(t) = μS(t)dt + σS(t)dW(t) Where: - S(t) = asset price at time t - μ = drift coefficient (expected return) - σ = volatility parameter - dW(t) = Wiener process increment
HESTON STOCHASTIC VOLATILITY MODEL
dS(t) = rS(t)dt + √V(t)S(t)dW₁(t) dV(t) = κ(θ - V(t))dt + σᵥ√V(t)dW₂(t) Where: - V(t) = variance process - κ = mean reversion speed - θ = long-term variance - σᵥ = volatility of volatility
ORNSTEIN-UHLENBECK PROCESS
dX(t) = θ(μ - X(t))dt + σdW(t) Mean-reverting process for: - Interest rates - Commodity prices - Volatility modeling
JUMP-DIFFUSION MODEL
dS(t) = μS(t)dt + σS(t)dW(t) + S(t⁻)dJ(t) Where: - dJ(t) = jump process - λ = jump intensity - Captures sudden price movements

MODEL IMPLEMENTATIONS

GBM SIMULATION

Classical Black-Scholes framework with geometric Brownian motion. Euler-Maruyama and Milstein schemes for numerical integration.

Use Cases:

- Equity price modeling

- Options pricing

- Risk neutral simulation

HESTON MODEL

Stochastic volatility with mean reversion and correlation structure. Full truncation scheme for variance process positivity.

Use Cases:

- Volatility smile modeling

- Exotic option pricing

- Risk management

ORNSTEIN-UHLENBECK

Mean-reverting process with analytical solutions and parameter estimation via maximum likelihood and method of moments.

Use Cases:

- Interest rate modeling

- Pairs trading

- Commodity prices

JUMP-DIFFUSION

Merton jump-diffusion with Poisson jump arrivals and log-normal jump sizes for crisis modeling.

Use Cases:

- Crisis risk modeling

- Option pricing

- Tail risk analysis

SABR MODEL

Stochastic Alpha, Beta, Rho model for interest rate derivatives with volatility smile dynamics.

Use Cases:

- Swaption pricing

- Interest rate options

- Volatility surface

CORRELATED ASSETS

Multi-dimensional SDE systems with Cholesky decomposition for correlation structure preservation.

Use Cases:

- Portfolio simulation

- Basket options

- Risk aggregation

QUANTITATIVE FINANCE CAPABILITIES

PORTFOLIO OPTIMIZATION

Advanced portfolio construction using Modern Portfolio Theory, Black-Litterman, and risk parity approaches. Mean-variance optimization with transaction costs, constraints, and robust estimation techniques for institutional applications.

RISK MANAGEMENT SUITE

Comprehensive risk metrics including Value-at-Risk (VaR), Conditional VaR, Maximum Drawdown, and stress testing. Monte Carlo simulation with variance reduction techniques for accurate tail risk estimation.

DERIVATIVES PRICING

Black-Scholes framework with extensions for American options, barrier options, and exotic derivatives. Finite difference methods, binomial trees, and Monte Carlo pricing with Greeks calculation for risk management.

MARKET REGIME DETECTION

Hidden Markov Models and regime-switching frameworks for identifying bull/bear markets, volatility regimes, and structural breaks. Automatic model selection and regime probability estimation.

REAL-TIME DATA INTEGRATION

Professional market data feeds with real-time processing, data cleaning, and transformation pipelines. Support for multiple data vendors and asset classes with institutional-grade data quality controls.

BACKTESTING FRAMEWORK

Robust backtesting engine with realistic transaction costs, market impact, and slippage modeling. Performance attribution, risk decomposition, and statistical significance testing for strategy validation.

TECHNICAL SPECIFICATIONS

SDE MODELS
6+ Stochastic Processes
OPTIMIZATION METHODS
5 Portfolio Strategies
RISK METRICS
20+ Risk Measures
MARKET DATA
Real-time Integration
PRICING MODELS
Black-Scholes + Extensions
NUMERICAL METHODS
Monte Carlo + FDM
FRAMEWORK
Python + NumPy + SciPy
VISUALIZATION
Interactive Dashboards