Spring Term 2024

April 18 - May 17, 2024
Stochastic volatility modeling and fractional Brownian motion
Elisa Alòs Alcade (Universitat Pompeu Fabra, Barcelona)

1. The option pricing problem: Derivatives: forwards and futures. Non-arbitrage prices. 2. The Black-Scholes formula: The Black-Scholes price and the Black-Scholes model. Spot and implied volatilities: the implied volatility surface. 3. The volatility process: Spot volatilities. Local volatilities and Dupire formula. Stochastic volatilities Stochastic volatility models: The Heston and the SABR models. 4. The fractional Brownian motion: Long-memory and short-memory Gaussian processes. The fractional Brownian motion and its main properties. 5. Models based on the fractional Brownian motion: Rough volatilities and the implied volatility surface. Volatility derivatives under rough models.

April 9 - 18, 2024
A crash course in Economic History
James Fenske (University of Warwick)

Lectures covering the Great Divergence, the Industrial Revolution, and the Great Depression. Discussion of Delong’s "Slouching Towards Utopia: An Economic History of the Twentieth Century”.