Stochastic Volatility (2019-2020)

2019-2020
Lecturer(s): 
Dr Matteo Burzoni
Course Term: 
Hilary
Course Overview: 

This course provides an introduction to models of randomly fluctuating asset price volatility. In particular extensions of the Black-Scholes (BS) model to continuous-time local and stochastic volatility models. We also discuss volatility derivatives such as variance swaps, and the relationships between, local, implied, stochastic and realised volatility.

Course Syllabus: 

Different notions of volatility: spot, realised and implied volatility; stylised facts of asset returns; deterministic volatility model; local volatility (LV) models and the Dupire equation; stochastic volatility (SV) models; incompleteness and multiplicity of martingale measures; market completion; delta and vega hedging; robustness of the BS hedging paradigm; realised variance and volatility derivatives; relations between implied and spot volatility.

Reading List: 

1) J P Fouque, G Papanicolaou and K R Sircar: Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press 2000
2) J Gatheral: The Volatility Surface: A Practitioner's Guide, Wiley 2006
3) S E Shreve: Stochastic Calculus for Finance II: Continuous-Time Models, Springer 2004

Please note that e-book versions of many books in the reading lists can be found on SOLO and ORLO.