Market microstructure and option pricing: probabilistic and pathwise approaches
File(s)
Author(s)
Bellani, Claudio
Type
Thesis
Abstract
In Chapter I, I will give an introduction to order-driven markets and Hawkes processes. The
description of order-driven markets is enhanced by the implementation of a simulator of limit
order books.
In Chapter II, I will present my investigation on price impact in order-driven markets. I will
describe a non-average detection of the distorsion of prices during large trade executions. Such a
detection will hinge on a granular model of limit order books based on state-dependent Hawkes
processes. The measurement of price impact will be a function of the stochastic processes that
govern the arrival of orders. Demonstrations will be given on empirical data from NASDAQ.
In Chapter III, I will present my investigation on mathematical models of optimal trading execution
strategies. I will define the concept of good trade execution, and I will construct explicit adapted
good trade execution strategies in the framework of linear temporary price impact. I will describe
how good trade execution strategies minimise trading costs in a pathwise sense, a point of view
not yet considered in the literature, and the consequent model robustness.
In Chapter IV, I will present my investigation on the classical models of option pricing through
the lenses of a Rough Path-inspired analysis. I will describe the pricing and hedging of financial
derivatives refraining from the use of probability, and I will give pathwise presentations of the
fundamental equations of Mathematical Finance.
description of order-driven markets is enhanced by the implementation of a simulator of limit
order books.
In Chapter II, I will present my investigation on price impact in order-driven markets. I will
describe a non-average detection of the distorsion of prices during large trade executions. Such a
detection will hinge on a granular model of limit order books based on state-dependent Hawkes
processes. The measurement of price impact will be a function of the stochastic processes that
govern the arrival of orders. Demonstrations will be given on empirical data from NASDAQ.
In Chapter III, I will present my investigation on mathematical models of optimal trading execution
strategies. I will define the concept of good trade execution, and I will construct explicit adapted
good trade execution strategies in the framework of linear temporary price impact. I will describe
how good trade execution strategies minimise trading costs in a pathwise sense, a point of view
not yet considered in the literature, and the consequent model robustness.
In Chapter IV, I will present my investigation on the classical models of option pricing through
the lenses of a Rough Path-inspired analysis. I will describe the pricing and hedging of financial
derivatives refraining from the use of probability, and I will give pathwise presentations of the
fundamental equations of Mathematical Finance.
Version
Open Access
Date Issued
2021-08
Date Awarded
2021-10
Copyright Statement
Creative Commons Attribution-Non Commercial 4.0 International Licence
License URL
Advisor
Brigo, Damiano
Cass, Thomas
Armstrong, John
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)