Course 4: Financial Engineering

Financial Engineering covers the computation of the fair valuation and joint return distribution for the main asset classes of financial instruments.

In particular, this course covers the following topics:

Valuation across financial instruments, including linear pricing theory foundations, risk-neutral valuation for derivatives, capital asset pricing framework.
Identification, modeling and forecasting of key risk drivers for the returns of equities, fixed income, derivatives, credit, high frequency, foreign exchange
Repricing techniques: Monte Carlo full repricing, analytical Greeks approximations

After the course you will obtain a Statement of Completion. Furthermore, you can choose to complete an optional code-based project that will count as one of the two Practical Projects towards the ARPM Certification.

Step 0 - Valuation axioms

• About quantitative finance

• The Checklist: ten-steps for risk and portfolio management

• Valuation foundations

• Financial instruments background definition

• Linear pricing theory: core

• Fundamental axioms of linear pricing

• Fundamental theorem of asset pricing

• Risk neutral pricing

Step 0 - Valuation models

• Capital asset pricing model framework

• Linear pricing theory: further assumptions

• Completeness

• Equilibrium: pure capital asset pricing model

• Arbitrage pricing theory

Step 1 - Risk drivers identification

• Risk drivers identification

• Equities

• Currencies

• Fixed-income

• Derivatives

• Credit

Step 2+3 - Quest for invariance & Estimation

• Quest for invariance

• Simple tests

• Efficiency: random walk

• Mean reversion: continuous state

• Mean reversion: discrete state

• Volatility clustering

• Multivariate quest

• Cointegration

• Estimation

• Joint estimation via (dynamic) copulas

Step 4 - Projection

• Projection

• One-step historical projection

• Univariate analytical projection

• Multivariate analytical projection

• Monte Carlo

• Historical

• Application to credit risk

• Square-root rule and generalizations

Step 5 - Repricing

• Repricing

• Exact repricing

• Taylor approximations

• Joint P&L distribution