Options Pricing¶
Under development
This optional advanced module is part of the course scaffold.
This module covers the pricing and risk of options: the Black–Scholes model and its assumptions, the Greeks as the language of options risk, and the implied volatility surface — where the model's failures are catalogued and where volatility trading actually happens — through local and stochastic volatility models. It is for learners who have worked through the stochastic calculus module and are targeting derivatives or volatility roles.
Topics¶
- No-arbitrage foundations: put–call parity and static bounds, before any model is assumed
- Black–Scholes: the hedging derivation, the formula, and an honest list of its assumptions
- The Greeks: delta, gamma, vega, theta, and managing an options book as a portfolio of sensitivities
- Implied volatility: definition, the smile and skew, term structure, and what the surface says about the model
- Local volatility and the Dupire construction: fitting the surface exactly, at a cost
- Stochastic volatility: the Heston model, its dynamics, and calibration in practice
- Practical calibration issues: noisy quotes, arbitrage-free interpolation, and surface stability day over day