SVI 302 · Tier 300 — Advanced — Stochastic & Volatility · 3 credits
Volatility & the Surface
Implied volatility, the surface, and the parametric fits — SABR, SVI, Heston, Dupire — that smooth and complete it.
Prerequisites
Learning Objectives
- Define implied volatility as the volatility that equates a Black-Scholes price to an observed market price, and explain why it must be solved for numerically.
- Read an implied-volatility surface along its two axes — moneyness (skew) and expiry (term structure) — and say what each slice is pricing.
- State the SABR stochastic-volatility dynamics and name what each of its four parameters — alpha, beta, rho, nu — controls on the smile.
- Write the raw SVI total-variance slice and explain what each of its five parameters controls geometrically.
- State the Heston model's two coupled SDEs and explain what each of its five parameters controls.
- Explain the difference between implied volatility and local volatility, and state what 'local' means as a function of spot and time.