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Financial Engineering for Investment

Mathematics
Python
MATLAB

Quantitative Risk Management

Data Science for Finance

Quantitative Portfolio Management

This course prepares for the Financial Engineering for Investment module of the ARPM Certificate body of knowledge.

About ARPM (Lab, Courses, Certification)

ARPM Lab – how it works

ARPM Lab – contents

About Quantitative Finance: P vs Q

The “Checklist” executive summary

Financial engineering for investment

Background definitions

Valuation foundations

Points of interest

Linear pricing theory: core

Linear pricing: fundamental axioms

Stochastic discount factor

Fundamental theorem of asset pricing

Risk-neutral pricing

Summary

Capital asset pricing model framework

Covariance principle

Summary

Linear pricing theory: further assumptions

Completeness

Equilibrium: pure capital asset pricing model (CAPM)

Arbitrage pricing theory (APT)

Intertemporal consistency and martingales

Non-linear pricing theory

Non-linear pricing: fundamental axioms

Non-linear pricing: valuation as evaluation

Risk drivers identification – overview

Equities risk drivers

Fixed-income risk drivers

Currencies risk drivers

Strategies risk drivers

Summary

Derivatives risk drivers

Credit risk drivers

Insurance risk drivers

Operations risk drivers

Summary

Introduction

Projection – overview

One-step historical projection

Analytical univariate projection

Efficiency: Lévy processes

Univariate Ornstein-Uhlenbeck process

Mean reversion (continuous state)

Volatility clustering: stochastic volatility; time change

Long memory: fractional Brownian motion

Mean reversion (discrete state)

Introduction

VAR(1)/Multivariate Ornstein-Uhlenbeck

Analytical multivariate projection

Monte Carlo projection

Multivariate Markov chains

Historical bootstrapping

Square-root propagation of risk, generalizations, violations

Pricing at the horizon – overview

Exact repricing

Equities

Currencies

Fixed income

Derivatives

Credit

Introduction

Carry

Currencies

Fixed income

Derivatives

Taylor approximation

Equities

Fixed income: duration-convexity

Derivatives: delta-gamma-vega-…

Hybrid stress-matrix