The public defense of Jean Paul Murara's doctoral thesis in Mathematics/Applied Mathematics

Doctoral thesis and Licentiate seminars

Datum: 2019-10-04
Tid: 13.15

The public defense of Jean Paul Murara´s doctoral thesis in Mathematics/Applied Mathematics will take place at Mälardalen University, room Lambda, at 13.15 on October 4, 2019.

Title: Market Models with Stochastic Volatillity

Serial number: 294

The faculty examiner is Professor Marieke Huisman, University of Twente.

The faculty examiner is Professor Guglielmo D’Amico, University G. D'Annunzio of Chieti-Pescara, and the examining committee consists of Professor Mahouton Norbert Hounkonnou, University of Abomey-Calavi, Professor Christos Skiadas, Technical University of Crete, Professor associado José Luis da Silva, University of Maderia

Reserve; Associate Professor Juma Kasozi, Makerere University

Abstract:

Financial Markets is an interesting wide range area of research in Financial Engineering. This thesis is concerned with Market Models with Stochastic Volatility in order to understand some financial derivatives, mainly European options, exchange rates and electricity prices. Stochastic volatility models appear as a response to the weakness of the constant volatility models. In the thesis, we deal with different models where the volatility is itself a random process and we present the techniques of pricing European Options. Comparing single factor stochastic volatility models to constant factor volatility models it seems evident that the stochastic volatility models represent nicely the movement of the asset price and its relations with changes in the risk. However, these models fail to explain the large independent fluctuations in the volatility levels and slope. We introduce a variation of ChiareHa and Ziveyi model and we use the first order asymptotic expansion methods to determine the price of European Options. Multiscale stochastic volatilities models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. We present an asymptotic expansion for the option price. We provide experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices are compared to the approximation obtained by Chiarella and Ziveyi. We also implement and analyze the Regime-Switching GARCH model using real NordPool Electricity spot data. We allow the model parameters to switch between a regular regime and a non-regular regime, which is justified by the so-called structural break behavior of electricity price series. In splitting the two regimes we consider three criteria, namely the intercountry price difference criterion, the capacity/flow difference criterion and the spikes-in­ Finland criterion. We study the correlation relationships among these criteria using the mean-square contingency coefficient and the co-occurrence measure. We also estimate our model parameters and present empirical validity of the model. We also consider a market model with four correlated factors and two stochastic volatilities. An advanced Monte Carlo method is used to find the no-arbitrage price of the European call option in the considered model. Furthermore, we forecast the stochastic volatility for exchange rates using EWMA and observe the effect of the out of sample period and the effect of the decay factor. We also compare the performances between the Crank-Nicolson scheme and the lognormality condition when pricing the European options in a two-dimensional Black-Scholes equation.