Abstract
This thesis contributes to three measures of variability: covariance, correlation and implied variance in the context of highfrequency data, assets trading and implied variance parametrization model, respectively. For the spot covariance estimation we establish asymptotic normality of the kernel covariance estimator for both fixed and shrinking bandwidth. We propose the threshold kernel for the case with jumps and derive its asymptotic distribution for a fixed bandwidth. We establish the performance of the kernel and threshold kernel covariance estimators with simulated data for asset prices. We apply the estimator to forecast the covariance matrix using Vector Heterogeneous Autoregressive (VHAR) model.We then consider a portfolio optimisation problem in a market with pairs of assets whose prices follow the cointelation model recently introduced. Optimization is performed with respect to traditional Financial Mathematics criteria: meanvariance and power utility maximization, as well as P&L maximization with a dynamic switching algorithm between the two resulting optimal strategies. In Machine Learning approach we find the P&L maximizing strategies for various admissible sets using a clustering methodology. We do it for simulated data from the same cointelation model used with Financial Mathematics criteria and compare the results. Note that the Machine Learning methodology applies more generally to any pairs of mean reverting assets.
Finally, the IVP model for parametrization of implied variance surface is more general than the popular in industry SVI model because of extra parameters that allow better fit in the tails. The functional form of these parameters can be chosen arbitrarily with varying degrees of success. We want to find a functional form that gives the best possible fit in the tails with the least possible numbers of parameters. We propose a convergence result of implied variance CEVtype stochastic volatility model as maturity increases to IVP. We outline the proof and show that it is key in identifying this functional form.
Date of Award  1 Jun 2020 

Original language  English 
Awarding Institution 

Supervisor  Cristin Buescu (Supervisor) & Weining Wang (Supervisor) 