AMS Seminar: Helyette Geman (JHU) @ Whitehead 304
Title: Transaction Clock, Stochastic Time Changes and Stochastic Volatility
Abstract: The first part of the talk will establish that, by No Arbitrage, the log – price process of a stock has to be a time-changed Brownian motion under the physical probability measure. Aggregate volume and number of trades are empirically tested as possible drivers of the stochastic clock allowing one to recover normality of stock returns.
The second part of the talk will show how stochastic volatility can be represented through a stochastic time change, outside the stochastic differential equations classically used for volatility in a number of founding models in Finance. This representation is particularly useful if one wishes to choose a Levy process (outside Brownian motion) for the stock log- price, as independent increments are contradicted by volatility clustering observed in financial markets. The CGMY process with stochastic volatility will be provided as an example.