Quantitative finance models and algorithms

v0.3

Collection of models with optimization algorithms for Time series analysis, algorithmic forecasting, quantitative research and risk-management.

Assets pricing and Optimization models

European Option Pricing

• European option pricing via Monte-Carlo simulation, Black-Scholes model
• discretization error estimate
• sensitivity analysis of option price to strike and volatility
• sensitivity of discretization error to number of simulations

Linear Asset Pricing

• linear asset pricing: FX income, capital budgeting, floating-rate notes
• univariate concave nonlinear optimization of IRR-YTM using Brent method and binary grid search on subintervals
• available as mixed integer programming problem, ready-to-use on NISQ devices

Time series analysis models

• Glosten-Jagannathan-Runkle GARCH(p, o, q)
• unsupervised optimization of parameters
• captures asymmetric shocks (leverage effect)

Seasonal ARIMA

• ARIMA(p, d, q)x(P, D, Q, s)
• unsupervised optimization of AR, MA and Seasonal parameters
• provides one-step-ahead predictions and out-of-sample forecast

Holt-Winters model

• triple exponential smoothing
• cross-validation via Conjugate gradient, TNC
• in-sample prediction and extrapolation

Smoothing methods

• Moving average
• Exponential smoothing
• Double exponential smoothing

License and Copyright

Licensed under the MIT License.