Financial Engineering
This diploma covers arbitrage-free pricing, Ito calculus, and numerical implementation for derivatives and fixed income. Students work with Black-Scholes-Merton, binomial/trinomial trees, finite difference and Monte Carlo methods in Python/QuantLib, then extend to term structure models such as Hull-White and the LIBOR market model, local volatility via Dupire, and SABR smile calibration. The second half applies these tools to credit and counterparty risk: CDS curve bootstrapping, copula-based portfolio loss distributions, CVA/DVA/FVA, and model validation. Assessment is built around pricing, hedging, calibration, and writing model-risk documentation rather than reading surveys of finance.
What You'll Learn
Curriculum
Covers forward contracts, futures, interest rate parity, cost-of-carry, and the fundamental theorem of asset pricing. Students build zero-coupon bond and forward curve bootstrapping tools.
- Arbitrage, Law of One Price, and the Foundations of Linear Derivative Replication 2.5h
- Forward Pricing, Cost-of-Carry, and Interest Rate Parity 3.0h
- Futures Pricing, Daily Settlement, and Interest Rate Futures 3.0h
- Bootstrapping Zero-Coupon and Forward Curves from Money Market Instruments 3.5h
Introduces Brownian motion, Ito processes, Ito's lemma, martingales, the Girsanov theorem, and risk-neutral measure construction. Students derive stochastic differential equations for equity, FX, and short-rate processes.
- Brownian Motion, Filtrations, and Martingales: The Building Blocks of Asset Dynamics 2.5h
- Ito Processes, Ito's Lemma, and SDEs for Equity and FX 3.0h
- Girsanov Theorem, Risk-Neutral Measure Construction, and Short-Rate SDEs 3.0h
Implements binomial and trinomial trees, explicit/implicit and Crank-Nicolson finite difference schemes, and Monte Carlo simulation with variance reduction. Uses Python/NumPy or QuantLib to price path-dependent and early-exercise options.
- Binomial and Trinomial Trees: Calibration, Implementation, and American Exercise 2.5h
- Finite Difference Schemes for the Black-Scholes PDE: Explicit, Implicit, and Crank-Nicolson 3.0h
- Monte Carlo Simulation for Path-Dependent Options: GBM, Asian, and Barrier Pricing 2.5h
- Variance Reduction, Quasi-Monte Carlo, and Least-Squares Monte Carlo for Early Exercise 3.0h
Covers the Black-Scholes-Merton formula, option Greeks, delta-gamma-vega hedging, and implied volatility calculation. Students analyze P&L attribution and hedging error under discrete rebalancing.
- Lesson 1: The Black-Scholes-Merton Framework and Formula 2.5h
- Lesson 2: The Greeks: Delta, Gamma, Theta, Vega, and Rho 2.5h
- Lesson 3: Delta-Gamma-Vega Hedging and Rebalancing 3.0h
- Lesson 4: Implied Volatility, Volatility Smile, and Discrete Hedging Error Attribution 3.0h
Models zero-coupon yields using Vasicek, CIR, Hull-White, and HJM/LIBOR market model frameworks; covers caps, floors, swaptions, and bond options. Students calibrate short-rate models to market discount and volatility data.
- Zero-Coupon Yield Curves, Forward Rates, and Short-Rate Model Framework 3.0h
- Vasicek and CIR in Depth: Closed-Form Pricing, Calibration, and Volatility Fitting 3.5h
- No-Arbitrage Term Structure Models: Hull-White, HJM, and LIBOR Market Model 4.0h
- Pricing Interest Rate Derivatives: Caps, Floors, Swaptions, and Bond Options 4.0h
Extracts implied volatility surfaces from listed option quotes and models them with local volatility (Dupire) and SABR. Students fit and arbitrage-check surfaces for pricing exotics.
- Cleaning and Extracting Implied Volatilities from Listed Option Quotes 2.5h
- Arbitrage-Free Volatility Surface Construction and Interpolation 3.0h
- Local Volatility via the Dupire Equation 3.0h
- SABR Model Calibration and Exotic Pricing 3.5h
Covers default probability curves, credit default swaps, copula-based portfolio credit models, and valuation adjustments CVA/DVA/FVA. Students structure and risk-manage credit-linked notes and asset-backed cash flows.
- Default Probability Curves and Credit Default Swaps 3.0h
- Portfolio Credit Risk and Copula Models 3.5h
- CVA, DVA, and FVA Valuation Adjustments 4.0h
- Credit-Linked Notes and Asset-Backed Cash Flow Structuring 4.0h
Focuses on model risk governance, backtesting, benchmarking, stress testing, and turning prototypes into robust Python/QuantLib tools. Students review a pricing or risk model for assumptions, numerical stability, and regulatory-style documentation.
- Model Risk Governance and Regulatory-Style Validation Documentation 2.5h
- Backtesting, Benchmarking, and P&L Attribution for Trading and Risk Models 2.5h
- Stress Testing, Scenario Design, and Production Implementation Patterns in Python/QuantLib 2.5h
Career Relevance
Graduates can build derivatives pricing and risk tools in Python/QuantLib, calibrate SABR or Dupire volatility surfaces to market quotes, and compute XVA and expected shortfall for trading or risk books. This supports roles such as quantitative analyst, model validation analyst, or risk quant on derivatives desks, treasury risk teams, and counterparty credit teams.
Recommended Background
Working experience in finance operations, risk, or investment analysis and the ability to write Python/NumPy scripts; solid undergraduate-level probability, linear algebra, and calculus. Familiarity with options, swaps, and bond pricing is assumed.
Program Details
| Award | Diploma |
| Duration | 6 months |
| Level | Intermediate |
| Courses | 8 |
| Language | English (UI in 4 languages) |
Caden Academy is a private, fully online professional training provider operated by Replatform (a company registered in Hong Kong). We are not a university, college, or accredited institution.
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