FIN 420 · Year 4 · Semester 1 · 3 credits · Mathematics & Statistics

Financial Engineering & Derivatives

Mastering no-arbitrage replication, dynamic hedging, and stochastic models to price modern market risk and embedded insurance guarantees.

Full practice exam · 30 Q · 120 min

Season 1 · 8 episodes

Dynamic Replication: The Aegis Life Guarantee

When market turbulence exposes a four-hundred-million-dollar hedging deficit in Aegis Life's variable annuity portfolio, lead ALM actuary Maya Lin must construct a mathematically unshakeable replication and risk engine before the state insurance commission audit shuts down their flagship annuity line.

Protagonist · Maya Lin, FSA, CFA, Lead Asset-Liability and Derivatives Actuary at Aegis Life & Annuity.

Setting · Aegis Life headquarters in Chicago, spanning trading floors, actuarial risk labs, and the executive boardroom overlooking Lake Michigan.

Stakes · If Aegis cannot rigorously price, dynamically hedge, and prove statutory solvency under VM-21 for its twelve-billion-dollar block of retirement guarantees, the company faces a catastrophic credit downgrade, forty million dollars in immediate unhedged trading losses, and mandatory regulatory seizure.

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Episodes

Season finale: Maya presents a multi-Greek, jump-resilient hedging architecture calibrated under ASOP Number 56, turning a four-hundred-million-dollar capital shortfall into a self-funding dynamic hedging program that passes regulatory scrutiny with zero statutory capital deficiency.

From the lecturer: Welcome to FIN 420. Financial engineering is not merely an abstract branch of applied probability; it is the mathematical spine of modern life insurance reserving, enterprise risk management, and quantitative asset-liability management. In this course film series, we bridge continuous-time stochastic calculus with practical actuarial balance sheets. When watching each film, keep a notebook open: never passively observe a derivation. Pause when prompted to set up the replicating portfolio, write down the partial differential equation, or sketch the risk-neutral probability tree before I unveil the solution. You will need a solid grasp of multivariable calculus, probability theory (STAT 230), and financial mathematics (ACT 201). By the conclusion of this course, you will not only be fully equipped to master the financial derivatives and embedded guarantee components of SOA Exam ALTAM and the Quantitative Finance and Investment (QFI) track, but you will also understand the deep mechanics of delta-gamma hedging, variable annuity guarantees (GMxB), short-rate calibration (Vasicek, CIR, Hull-White), and the operational reality of model risk in volatile markets.

Cold open

At 6:15 AM on a Monday, Maya's terminal flashes red. A four percent drop in the S&P 500 index over the weekend has created an immediate thirty-two million dollar cash shortfall in Aegis Life's flagship guaranteed annuity reserve, and the Chief Risk Officer demands an exact replication strategy before the morning trading desk opens.

preparing lecture…

Transcript

Define the Law of One Price and strict absence of arbitrage in discrete-time financial markets.
Construct a synthetic replicating portfolio using an underlying stock and a risk-free money market bond.
Derive the one-period delta-hedging ratio and risk-neutral valuation formula from first principles.
Link arbitrage-free pricing to actuarial reserving and embedded guarantee valuation under SOA ALTAM/QFI.