Course info

This course describes some continuous-time generalisations of the Black-Scholes (BS) model to account for time-varying and, in particular, stochastic volatility (SV). A brief summary of the
observed stylised features of asset returns and of the implied volatility (IV) of traded options is followed by a description of deterministic volatility models, local volatility (LV) models (where
we derive the so-called Dupire formula) and SV models, where we describe how traded options can be used to complete the SV market, which is incomplete if only the stock and cash are traded. We
describe a robustness feature of BS-style hedging in the face of model error, and a model-independent method for valuation and hedging of a class of volatility derivatives called variance swaps. The relation
between some different notions of volatility is also explored.