Financial Mathematics

In this GitHub repository, you'll discover a collection of projects reflecting my expertise in quantitative finance and time series modeling. These projects encompass a range of endeavors, including portfolio optimization, risk management, and options pricing. I've implemented various quantitative techniques such as the Calibrated Markowitz model to derive optimal portfolios and efficient frontiers based on market data. Additionally, I've tackled multi-period portfolio optimization problems, employing discrete-time investment strategies to maximize returns while managing risk effectively. Moreover, I've delved into derivative pricing and risk assessment by building options pricing models, including the Black-Scholes model, and implementing methodologies such as Monte Carlo simulation and finite difference methods. In parallel, I've explored time series modeling techniques, developing models for forecasting and analyzing financial data. Through these projects, I've honed my skills in quantitative analysis, financial modeling, and time series forecasting, showcasing my proficiency in addressing complex financial challenges.
Here are some of the files listed below with clickable links. For all the files visit

Content

• mathfinance.py
  • Library of all the functions created.
• Portfolio Optimization | Risk Management
  • Calibrated Markowitz model to Market data and find the Optimal Portfolio and The Efficient Frontier.
  • Computed Optimal investment strategy for a Multi-period Portfolio Optimisation problem in discrete time.
  • Implemented Wiener Construction of Brownian Motion.
  • Simulated SDE’s.
  • Simulated Delta hedging strategy in discrete time.
  • Retrieved Options data from financial APIs and performed analysis.
  • Implied volatility calculations using various methods.
  • VaR and Expected Shortfall (CVaR) using Historical, Parametric & Monte Carlo methods for Risk Assessment.
• Options Pricing Model
  • Built a Black-Scholes Options pricing model in C++ and Python.
  • Developed a Monte Carlo Pricer for options to simulate pricing scenarios and wrote unit tests in C++ and Python.
  • Implemented Finite Difference Method to price an Option by solving Black-Scholes PDE.
  • Implemented Binomial Option pricing Model to price various options including European Call and American put Options.
  • Simulated Stochastic Volatility model for Stock prices.
  • Calibrated Jump-Diffusion model to Options Market prices.
• Miscellaneous
  • Black Scholes PDE and Formula.
  • Brownian Motion.
  • Call Option.
  • Candlestick Data Visualisation.
  • Gaussian Copula.
  • Gaussian Copula Exponential.
  • Geometric Brownian Motion.
  • Various Interest Rates.
  • Investigating Investment Advice.
  • Ito's Lemma.
  • Maths Examples.
  • Monte Carlo Method for Integration.
  • Multi-Dimensional SDE's.
  • Multivariate Sampler.
  • Multivariate Gaussian Distribution.
  • Normal Distribution, Central Limit Theorem and Simulating Random variables.
  • Portfolio Visualisation.
  • Realised Volatility Cones.
  • Simulating Multivariate Gaussian using Cholesky Decomposition.
  • Two-Mutual-Fund theorem.
  • Utility Functions.
  • Unit Test.