A study of the Hobson and Rogers volatility model

We firstly examine the model of Hobson and Rogers for the volatility of a financial asset such as a stock or share. The main feature of this model is the specification of volatility in terms of past price returns. The volatility process and the underlying price process share the same source of randomness and so the model is said to be complete. Complete models are advantageous as they allow a unique, preference independent price for options on the underlying price process. One of the main objectives of the model is to reproduce the `smiles' and `skews' seen in the market implied volatilities and this model produces the desired effect. In the first main piece of work we numerically calibrate the model of Hobson and Rogers for comparison with existing literature. We also develop parameter estimation methods based on the calibration of a GARCH model. We examine alternative specifications of the volatility and show an improvement of model fit to market data based on these specifications. We also show how to process market data in order to take account of inter-day movements in the volatility surface. In the second piece of work, we extend the Hobson and Rogers model in a way that better reflects market structure. We extend the model to take into account both first and second order effects. We derive and numerically solve the pde which describes the price of options under this extended model. We show that this extension allows for a better fit to the market data. Finally, we analyse the parameters of this extended model in order to understand intuitively the role of these parameters in the volatility surface.

Uncle Tom's Cabin and the Irish National Tale

Accepted Version

A bookish history of Irish Romanticism

This chapter argues that authors of Irish Romantic novels and national tales, such as Maria Edgeworth and John and Michael Banim, are not only concerned with the extent to which their novels sought to copy from Irish culture but are also worried about the slightness of the novel form in relation to the copiousness of that culture. Such concerns led to attempts by Thomas Crofton Croker and others to add texture and tactility to their depictions of the Irish past, through antiquarian methodologies but also facsimiles, lithography, and other developments in print culture. The chapter demonstrates the ways in which Irish literary texts were concerned not only to accurately and minutely detail the past, but also to adduce evidence of such historical and cultural authenticity, working against teleological accounts of the birth of the modern historical method, which see Romantic history as unconcerned with the evidentiary foundations of the past.