I will soon distribute a form with, hopefully, a full list of projects and supervisors. You should list your top 6 preferences on this. It is likely that demand for some projects will outstrip supply, so not all students will get their first choices. Placements will be given careful consideration after the preliminary results of April/May exams are known to the examiners and will be restricted to those students who have performed well in exams to date.

Once projects have been allocated please contact your supervisor as soon as possible to discuss your timetable for the summer. In many cases lecturers will be taking their annual holiday during the period of your project. It is important that you discuss details with your supervisor to make sure that there are no prolonged periods without the possibility of a meeting. Some lecturers have already specified dates when they will be away and these are detailed below.

Some students may have organised projects/placements themselves in discussion with me. Please let me have final details as soon as possible so that this can be fitted into the overall scheme.

Anke Wiese

• Modeling financial market prices using the ARCH and GARCH models
  Supervisor: Janusz Brzeszczynski, HWU School of Management and Languages
  Number of students: 2
  Periods of absence:
  Summary: This project involves estimation of various types of ARCH models. Empirical applications can be based on the data set composed of the major international stock market indices or the data from the foreign exchange market. Different data frequency will be used. As the by-product, the obtained results may be useful for verifying the hypothesis about the financial markets efficiency.
  
  Computing component: over 75%.
  

• Effects of Microfinance on Firm Performance: Evidence from Romania
  Supervisor: David Brown, HWU School of Management and Languages
  Number of students: 1
  Periods of absence:
  Summary: USAID conducted a microfinance program in Romania in the late 1990’s and early 2000’s. Did the firms receiving the loans achieve performance benefits, or was the money wasted? The project will compare the performance of loan recipients before and after receiving the loan to that of otherwise similar firms not receiving loans.
  
  Computing component: Intensive computing component, working with a large dataset. The student needs to have access to the STATA statistical software package.

• Autocorrelated Conditional Duration (ACD) of Shares at the London Stock Exchange
  Supervisor: Boulis Ibrahim, HWU School of Management and Languages
  Number of students: 2
  Periods of absence: 5 weeks annual leave the starting date of which may vary but provisionally from 28 June to end of July.
  Summary: This project will deal with the modeling of time between trades on some shares that trade at the London Stock Exchange. The modeling will use ACD models which are time varying models of positive variables. They are related to statistical treatment of survival analysis.
  
  Computing component: The candidate(s) should expect extensive computing work on a substantial database of high frequency trade by trade data. This requires detailed knowledge of SQL (Standard Query Language) or Microsoft Access (In the case of Access, however, the candidate must be self equipped with a computer that has 3 or 4 GB RAM and 200GB or so of spare disk capacity).
  

• Modeling Consumption Asset Pricing Models in Developed and Emerging Stock Markets
  Supervisor: Moh Sherif, HWU School of Management and Languages
  Number of students: 2
  Periods of absence:
  Summary: To address the empirical failure of the CCAPM, considerable attention has been devoted to market frictions as well as alternative utility specifications. Both of these strands can claim some success, but they have until now been considered separately. The focus of this project is therefore to consider both in the same study.
  
  First considered is whether the value of relative risk aversion can be changed by using parametric and non parametric tests and different utility functions. Whereas the power utility model introduces a basic learning framework of the relation between consumption and asset returns, there is general consensus that there is evidence against the model as an asset pricing tool and for its ability to resolve the equity premium puzzle. Within the context of representation of agent models, various studies have attempted to introduce more general preferences. In this project, tests are made of the traditional CAPM, CCAPM, H-CCAPM, Epstein and Zin (1989, 1991) model, and external habit formation specification using GMM.
  
  Further we investigate the pricing errors of asset pricing models by estimating the vertical and minimum distances to the Hansen-Jagannathan bound (Hansen and Jagannathan (1991, 1997)).
  
  Different utility specifications are found to have considerably less impact than the introduction of market frictions, which in general has a significant impact, and the model is often accepted. Therefore, in the second part of this project we investigate the impact of a combination of utility specifications and market frictions on the performance of asset pricing models.
  
  Computing component: Empirical applications will be based on the data set composed of the major developed and emerging international stock market indices.
  
  

• Numerical Methods for SDEs
  Supervisor: Istvan Gyongy, UoE School of Mathematics
  Number of students: 1-2
  Periods of absence:
  Summary: Main Reference: The maximum rate of convergence of discrete approximations for stochastic differential equations" by J.M.C. Clark and R.J. Cameron, Stochastic Differential Systems. Lecture Notes in Control and Inform. Sci. 25 162--171. Springer, Berlin.
  
  Computing component: Knowledge of some programming language ( such as C++, Java, etc) or relevant mathematical package (MAPLE, Matlab, etc) is desirable (Monte Carlo simulations).

• Accelerated Numerical Schemes
  Supervisor: Istvan Gyongy, UoE School of Mathematics
  Number of students: 1- 2
  Periods of absence:
  Summary: Main Reference: "Expansion of the global error for numerical schemes solving stochastic differential equations" by D. Talay and L. Tubaro, Anal. Appl. 8 (4) (1990) 94-120.
  
  Computing component: Knowledge of some programming language ( such as C++, Java, etc) or relevant mathematical package (MAPLE, Matlab, etc) is desirable (Monte Carlo simulations).
   

• Mean-reverting stochastic volatility models and equivalent martingale measures
  Supervisor: Sotirios Sabanis, UoE School of Mathematics
  Number of students: 1-2
  Periods of absence:
  Summary: This project is an extension of the option offered under the same title. Recall that empirical evidence on underlying asset prices strongly suggest that asset price volatility is stochastic. Thus, alternative option pricing methods were considered in order to eliminate the biases in the Black-Scholes model. A popular class of models is known as stochastic volatility models, where volatility is assumed to be an Ito process. As a result, a contingent claim can not be duplicated by a self- financing portfolio consisting of a number of (underlying asset) shares and a (zero-coupon) bond due to the additional source of uncertainty (i.e., the Brownian motion that drives the volatility process). Therefore, the market is not complete (in the sense of Harrison and Pliska) and the existence of a unique equivalent martingale measure (EMM) does not hold. However, the no-arbitrage assumption insures that there exists a EMM, in fact there exist many equivalent martingale measures. As a consequence, different authors set different criteria in order to choose the "appropriate" EMM and price options in continuous-time.
  
  The aim of this project is to price European options using different EMMs.
  
  Reading:
  
  Hobson, D. (2004). Stochastic volatility models, correlation, and the q-optimal measure, Mathematical Finance, 14 (4),537-556.
  Delbaen, F. and W. Schachermayer (1996). The variance-optimal martingale measure for continuous processes, Bernoulli 2, 81-106.

• Local volatility function models
  Supervisor: Sotirios Sabanis, UoE School of Mathematics
  Number of students: 1-2 
  Periods of absence:
  Summary: The aim of this project is to price index derivatives using historical data from the International Financial Futures and Options Exchange (LIFFE) in London. Under the benchmark approach of Heath & Platen, the pricing and hedging of derivatives does not require the existence of an equivalent risk neutral martingale measure. Fair prices for index derivatives when expressed in units of the index are martingales under the real world probability measure. 
  Reading:
  Heath, D. and E. Platen (2004). Local volatility function models under the benchmark model.
  E. Platen (2006) A Benchmark Approach to Finance Mathematical Finance, Vol. 16, No. 1 131-151

• Approximation of American put options by options with random expiry
  SUPERVISOR: Terence Chan, HWU School of Mathematical and Computer Sciences
  Number of students: 4
  Periods of absence:
  Summary: One of the main difficulties in pricing an American put with finite expiry is the computation of the optimal exercise level - this depends on the remaining life of the option and can only be computed numerically. In the case of American puts with infinite expiry (perpetual puts), the problem is much easier because the optimal exercise barrier is constant. An idea (due to Carr) is to consider a sequence of American puts with random exponentially distributed expiries. The memoryless property of the exponential distribution reduces the problem to that of a perpetual put. In this project, students will study the theory behind this and apply it compute the price of American puts where the underlying asset is modelled as the exponential of a simple Levy process (Brownian motion or BM + Poisson).
  
  This project is suitable for a group of up to 4 students working on the same theoretical aspects and applying them to slightly different models. There is a large practical computational component requiring the writing of suitable computer code (e.g. in Matlab). The balance of theoretical and practical is approx. 50/50.
  

• Continuous Time Stochastic Control
  SUPERVISOR: Tim Johnson, HWU School of Mathematical and Computer Sciences
  Number of students: 4
  Periods of absence:
  Summary: Stochastic control is one of the most important tools in financial mathematics.  In fact the Black-Scholes-Merton model, along with any dynamic portfolio management problem, can be viewed as the solution to a particular problem in stochastic control.
  
  The student will be expected to do some research into the ideas underpinning the theory of stochastic control and then investigate how those theories are applied in finance.  The student could take a number of paths, for example they could look at some contemporary theoretical issues or investigate the numerical solution of problems.
  
  Students will work as a group in developing their understanding of stochastic control and then work on specific issues individually. Students will be assessed on the clarity and depth of their dissertation if they choose to undertake a survey of theory.  If students address the numerical solution of a problem, they will be assessed on the  novelty of the approach or the problem being solved.
  
  
• Extensions to the Standard Vasicek Model of Portfolio Credit Risk
  SUPERVISOR: Alex McNeil, HWU School of Mathematical and Computer Sciences
  Number of students: 4
  Periods of absence:
  Summary: The Vasicek single factor model of portfolio credit risk is widely used in industry and has been influential in the development of the Basel II regulatory capital formula. Vasicek's model builds on Merton's idea that firm default is caused when a critical variable, often interpreted as a measure of asset value, lies below a critical threshold, often interpreted as a measure of short-term liabilities, at some designated time horizon. The Vasicek model extends Merton to a portfolio model by assuming that the critical variables for all obligors follow a one-factor Gaussian model, giving rise to a Gaussian copula dependence structure for joint defaults. One-factor portfolio versions of industrial models like KMV and CreditMetrics essentially follow the Vasicek  construction.
  
  In this project it will be of interest to investigate the effects of changing features of Vasicek's model and adding new features. The project is partly prompted by interest from Barrie & Hibbert who are employing a Vasicek-style model to capture credit dependence in their economic scenario generator (ESG).
  
  Computing component: ca 40%
  
  

• American options: Early exercise and pricing in incomplete markets
  SUPERVISOR: Mark Owen, HWU School of Mathematical and Computer Sciences
  Number of students: 4
  Periods of absence:
  Summary: In a complete market, where both the buyer and seller of an American option may completely hedge their position by trading the underlying security, the determination of the early exercise boundary has been thorougly studied; the literature goes back as far as work by McKean (1965) and Merton (1973). In many cases there are no exact formulae for the early exercise boundary, although a numerical determination of the boundary is fairly straightfoward. The notable exceptions to the lack of exact solutions are the cases of perpetual options (where the early exercise boundary is time-invariant), and the case of a call option on a non-dividend-paying asset (in which case early exercise is never optimal).
  
  This project will allow students to study the optimal exercise (and the pricing) of American options. The project will begin with a literature survey, and implementation of numerical methods to determine the early exercise boundary for both classical and perpetual options. Following this, students will consider some methods for determining the optimal exercise policy for the buyer and the seller in a incomplete markets (again, both theoretically and numerically). There is scope for investigation of separate sources of incompleteness.
  
  References:
  1. McKean, H.P. "Appendix: A free boundary problem for the heat equation arising from a problem in mathematical economics", Indust. Mang. Rev. 6 (1965) pp 32-39.
  2. Merton, R.C. "The theory of rational option pricing", Bell J. Economics, 4 (1973), pp 141-183.
  3. Wilmott, P. "Wilmott on quantitative finance", 2nd ed, Wiley (2006).
  Extent of the computing component: Very approximately, 40%.

• Utility Maximisation Problems in Incomplete Markets
  SUPERVISOR: Anke Wiese, HWU School of Mathematical and Computer Sciences
  Number of students: 4
  Periods of absence:
  Summary: In this project, we will investigate some key approaches for solving optimal portfolio problems in incomplete markets by maximising the expected utility of an individual investor. We will first review some of the existing approaches and further investigate concrete examples of financial derivative for which we compute values (prices) and hedging strategies analytially and numerically.
  
  Possible examples that can be investigated include
  - volatility derivatives in stochastic volatility models
  - insurance derivatives as they arise when the combination of insurance and financial risk is considered.
  
  The project will include the numerical implementation and investigation of resulting option prices.
  
  References:
  Henderson, V. and D. Hobson (2008): Utility Indifference Pricing - An Overview. in: Carmona, R. (ed). Indifference Pricing: Theory and Applications. Princeton University Press.
  Tehranchi, M. (2004): Explicit Solutions to some utility maximization problems in incomplete markets. Stochastic Processes and their applications 114, 109-125.
  Egami, M. and V. Young (2008): Indifference prices of structured catastrophe (CAT) bonds. Insurance: Mathematics and Economics 42, 771-778.

---

Page maintained by Anke Wiese .