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Mathematical Methods for Quantitative Finance Course

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Mathematical Methods for Quantitative Finance Course

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Mathematical Methods for Quantitative Finance Course

Name: Mathematical Methods for Quantitative Finance Course
Price: 2994 PHP

Master the rigorous mathematical foundations that drive modern quantitative finance, from stochastic calculus and derivatives pricing to portfolio optimization and risk measurement. This course equips analysts, researchers, and finance professionals with the theoretical depth and computational tools demanded by top-tier institutions. Build the expertise to model markets, price complex instruments, and manage risk with precision.

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What you will learn:

Build probability spaces, sigma-algebras, and stochastic processes for financial modeling.
Derive the Black-Scholes-Merton PDE and price exotic options using analytical and numerical methods.
Construct yield curves, duration measures, and interest rate derivative pricing models from first principles.
Apply Monte Carlo simulation, finite difference schemes, and FFT methods to real pricing problems.
Implement mean-variance optimization and factor models to design and evaluate institutional-grade portfolios.
Quantify tail risk using Extreme Value Theory, copulas, and coherent risk measures for regulatory compliance.

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Course content

8 Chapters • 39 LessonsDuration between 4 and 360 hours (you decide)

Chapter 1See details

Foundations of Quantitative Finance Mathematics

Lesson 1 • Linear Algebra Essentials
Introduces vectors, matrices, and linear transformations used throughout portfolio and factor models. Provides tools for solving systems of financial equations.
Lesson 2 • Calculus Review for Finance
Reviews differentiation and integration with emphasis on financial applications such as sensitivity analysis. Bridges undergraduate calculus to advanced financial mathematics.
Lesson 3 • Real Analysis and Number Systems
Covers real numbers, limits, and continuity as the backbone of financial modeling. Connects rigorous analysis to pricing and risk measurement.
Lesson 4 • Probability Theory Fundamentals
Establishes probability spaces, random variables, and expectation as the language of uncertainty in finance. Underpins all stochastic modeling in later chapters.

Chapter 2See details

Statistical Methods for Financial Data

Lesson 1 • Multivariate Statistical Techniques
Extends analysis to covariance matrices, principal components, and factor structures. Directly supports portfolio construction and risk decomposition.
Lesson 2 • Hypothesis Testing in Finance
Applies classical and robust tests to financial data including normality and autocorrelation checks. Supports model validation and regulatory reporting.
Lesson 3 • Regression Analysis Fundamentals
Builds ordinary least squares regression for factor exposure and return attribution. Introduces diagnostics that ensure model validity.
Lesson 4 • Descriptive Statistics for Returns
Summarizes return distributions using moments, quantiles, and shape measures. Establishes baseline data characterization before inferential methods.
Lesson 5 • Estimation Theory and Methods
Covers maximum likelihood and method-of-moments estimation for financial models. Connects estimator properties to reliable parameter inference.

Chapter 3See details

Stochastic Processes and Brownian Motion

Lesson 1 • Martingale Representation and Girsanov
Covers the martingale representation theorem and Girsanov's change-of-measure technique. Enables risk-neutral pricing in continuous-time models.
Lesson 2 • Ito Calculus and Stochastic Integrals
Develops the Ito integral and Ito's lemma for transforming stochastic processes. Enables derivation of stochastic differential equations for asset prices.
Lesson 3 • Discrete-Time Stochastic Processes
Introduces random walks, Markov chains, and martingales in discrete time. Provides intuition before transitioning to continuous-time models.
Lesson 4 • Brownian Motion Construction
Defines standard Brownian motion and its key properties including continuity and quadratic variation. Forms the foundation for Ito calculus.
Lesson 5 • Diffusion Processes and SDEs
Analyzes solutions to stochastic differential equations including mean-reversion models. Connects process properties to financial model selection.

Chapter 4See details

Derivatives Pricing Theory

Lesson 1 • Black-Scholes-Merton Framework
Derives the Black-Scholes-Merton PDE and closed-form option pricing formula. Connects Ito calculus and risk-neutral measure to practical pricing.
Lesson 2 • Exotic and Path-Dependent Options
Prices barrier, Asian, and lookback options using analytical and simulation methods. Extends the BSM framework to non-standard payoff structures.
Lesson 3 • Volatility Modeling and Implied Volatility
Analyzes the volatility smile, skew, and term structure from market option prices. Introduces local and stochastic volatility model concepts.
Lesson 4 • Binomial and Lattice Models
Builds discrete-time binomial trees for option pricing and American exercise. Bridges intuition between discrete and continuous models.
Lesson 5 • No-Arbitrage Pricing Principles
Establishes the law of one price, replication, and no-arbitrage bounds for derivatives. Provides the economic logic underlying all pricing models.

Chapter 5See details

Fixed Income Mathematics

Lesson 1 • Term Structure of Interest Rates
Constructs zero-coupon yield curves and forward rate curves from market data. Connects curve shapes to economic theories of interest rates.
Lesson 2 • Heath-Jarrow-Morton Framework
Models the entire forward rate curve evolution using the HJM no-drift condition. Generalizes short-rate models to infinite-dimensional rate dynamics.
Lesson 3 • Bond Pricing and Yield Measures
Derives present value formulas for coupon bonds and defines yield, duration, and convexity. Establishes the quantitative toolkit for fixed income analysis.
Lesson 4 • Short-Rate and Affine Models
Develops Vasicek, CIR, and affine term structure models for interest rate dynamics. Enables analytical bond pricing under stochastic rates.
Lesson 5 • Interest Rate Derivatives Pricing
Prices caps, floors, swaptions, and bond options using market and model-based methods. Applies term structure models to real fixed income derivatives.

Chapter 6See details

Portfolio Theory and Optimization

Lesson 1 • Multifactor Models
Extends CAPM to Fama-French and arbitrage pricing theory factor models. Enables return attribution and risk decomposition across multiple factors.
Lesson 2 • Performance Measurement and Attribution
Quantifies portfolio performance using Sharpe, Sortino, and information ratios. Decomposes returns into allocation and selection effects.
Lesson 3 • Capital Asset Pricing Model
Derives the CAPM equilibrium pricing equation and beta as a systematic risk measure. Connects portfolio theory to asset pricing and cost of capital.
Lesson 4 • Constrained Portfolio Optimization
Solves portfolio problems with long-only, budget, and factor constraints using Lagrangian and quadratic programming. Bridges theory to practical implementation.
Lesson 5 • Mean-Variance Framework
Formalizes Markowitz mean-variance optimization for portfolio selection. Derives the efficient frontier and minimum-variance portfolio analytically.

Chapter 7See details

Risk Measurement and Management

Lesson 1 • Copulas and Dependence Modeling
Models joint tail dependence using Gaussian, t, and Archimedean copulas. Addresses the limitations of linear correlation in risk aggregation.
Lesson 2 • Credit Risk Modeling
Quantifies default probability, loss given default, and credit exposure using structural and reduced-form models. Supports credit portfolio management.
Lesson 3 • Hedging Strategies and Greeks Management
Designs delta, gamma, and vega hedges for derivatives portfolios. Connects risk sensitivities to dynamic rebalancing and P&L explanation.
Lesson 4 • Value at Risk and Expected Shortfall
Defines VaR and Expected Shortfall as coherent risk measures and derives them analytically and via simulation. Connects measures to capital adequacy requirements.
Lesson 5 • Extreme Value Theory
Applies block maxima and peaks-over-threshold methods to model financial tail risk. Provides statistically rigorous estimates for rare loss events.

Chapter 8See details

Numerical Methods in Quantitative Finance

Lesson 1 • Model Calibration and Validation
Calibrates pricing models to market quotes and validates fit using statistical diagnostics. Ensures models are both mathematically consistent and market-consistent.
Lesson 2 • Optimization Algorithms for Finance
Implements gradient descent, Newton-Raphson, and evolutionary algorithms for model calibration and portfolio optimization. Addresses convergence and local minima issues.
Lesson 3 • Numerical Integration and Fourier Methods
Applies Gaussian quadrature and fast Fourier transform to option pricing under characteristic functions. Enables efficient pricing for models without closed forms.
Lesson 4 • Monte Carlo Simulation Methods
Generates asset price paths and computes option prices and risk measures via simulation. Introduces variance reduction techniques to improve computational efficiency.
Lesson 5 • Finite Difference Methods for PDEs
Solves the Black-Scholes PDE using explicit, implicit, and Crank-Nicolson schemes. Analyzes stability and convergence of finite difference grids.

Certification

Your valid completion certificate

This course is for you:

Finance professional: seeking the mathematical depth to move into quantitative roles.
Graduate student: bridging coursework in economics or statistics toward financial modeling.
Data scientist: applying existing technical skills to structured financial problem-solving.
Risk analyst: building rigorous foundations to strengthen model validation and reporting work.
Career changer: transitioning from engineering or physics into quantitative finance systematically.
Self-taught investor: replacing intuition-based thinking with mathematically grounded analytical methods.

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