One such approach showing promising results is the Gauss-Hermite expansion, based on the set of "physicist" Hermite polynomials. The Gauss-Hermite expansion also allows for obtaining closed form option pricing formulas. Interesting themes for a thesis are: a conducting an empirical analysis of the pricing and hedging performance of existing expansion-based methods; b investigating the properties of expansion methods based on other sets of orthogonal polynomials; c extending the Gauss-Hermite expansion method to price derivatives on multiple underlying; d using expansion-based methods to obtain closed form option pricing methods for non-affine stochastic volatility models.
Mathematics and Statistics Master's thesis topics
Corrado, C. Journal of Futures Markets , 16, Journal of Derivatives , 4, Jurczenko, E.
Maillet, and B. Necula, C. Microfoundations of stochastic volatility models A popular approach for modeling volatility consists in using exogenous stochastic volatility models.
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In this respect, one departs from the central hypothesis of the Black-Scholes-Merton model, concerning a constant level of volatility, by specifying exogenously a dynamics in general, affine of the underlying and its instantaneous variance. However, there are, at micro level, various sources, such as the heterogeneity of traders in beliefs, in preferences or in behavior and their interaction generating herding phenomena that could influence the dynamics of volatility. It is, therefore, much more appealing to investigate the implications of such micro-foundations that could lead, in a partial or general equilibrium framework, to an endogenously determined in general, non-affine dynamics of the underlying-volatility system.
Interesting themes for a thesis are: a conducting an empirical analysis of the option pricing performance of existing non-affine stochastic volatility models; b modeling heterogeneity and interaction in financial markets; c modeling the dynamics of heterogeneity in beliefs; d analyzing the implications of the heterogeneity and interaction of traders on the dynamics of volatility. Alfarano, S. Lux, and F. Wagner Time-variation of higher moments in a financial market with heterogeneous agents: An analytical approach.
Journal of Economic Dynamics and Control , 32 1 Follmer, H. Schweizer A microeconomic approach to diffusion models for stock prices. Mathematical Finance , 3, Horst, U. Financial price fluctuation in a stock market model with many interacting agents. Economic Theory , 25, Kaeck, A.
Risk Measures We are interested in studying measures to quantify the amount of capital that a financial institution should be required to raise and use for regulatory purposes. The theory of risk measures has been having a considerable influence on the debate about regulatory capital as witnessed by the current solvency regimes, such as the Basel regimes for banks and Solvency II and the Swiss Solvency Test for insurance companies.
Program of Study
Risk measures can be fruitfully used for valuation and pricing purposes, from the single instrument level to the company level. Examples of possible topics are mergers and acquisitions, distribution policy, financing policy, investment policy, restructuring activity, real options valuation, derivatives pricing, hedging, fixed-income valuation, interest rate contingent claims valuation, credit-sensitive contingent claims valuation, operational risk modelling, model risk issues, securitization, numerical methods for option valuation, time series modelling, capital allocation, performance measurement, risk measurement, and many more.
Students can also choose subjects for their Master's thesis in the list published by the Department of Banking and Finance of the University of Zurich. Since we encourage a strong cooperation with the financial industry, consider also the following thoughts:. Your thesis is officially supervised by a local professor, but a practitioner comes up with the precise topic and gives you the needed guidance. You already have contacts to the financial industry because you received a tuition fee grant, for example and you use these contacts to negotiate for an interesting project and guidance.
You are eager to work on a practical project, but you currently lack the industry contacts. You might want to combine the Master's thesis with a part-time internship in the financial industry. In any case, make sure your thesis supervisor is really interested in the topic you plan to work on. The supervisor has an important, but limited role.
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Once this is done, you are essentially on your own until you hand in the Master's thesis for grading. The thesis supervisor is not expected to read a first draft of the report.
The Master's thesis should be about pages long, but it is quality and not quantity that matters. In essence, you should tell us as much as - and no more than - we need to understand what the problem is and what we can learn from it or how you have solved it. You should familiarize yourself with the necessary text processing or typesetting software you plan to use before you start to work on your Master's thesis. If you plan on writing a mathematically-orientated thesis i.
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The thesis has to be written in English and be typed and printed in reasonable quality. Exact proofreading is required and use of a spelling checker recommended. The period allowed for completion of the Master's thesis is 6 months and starts with the formal issuance of the topic. The oral presentation of the Master's thesis has to be done within 4 weeks after the submission of the thesis. If your Master's thesis is the last module before the completion of your studies please look at the Dean's Office information on graduation.
The Master's thesis is graded.