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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

European option pricing

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

GJR-GARCH

  • 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

SARIMAX

Holt-Winters model

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

Holt-Winter model

Smoothing methods

  • Moving average
  • Exponential smoothing
  • Double exponential smoothing

Smoothing methods

License and Copyright

Copyright (c) 2019 Oleksii Lialka

Licensed under the MIT License.