msc projects 2012

8/2/2019 MSc Projects 2012

1/5

1. British Put and Call Options-------------------------------

The objective is to examine and present the valuation of British putand call options where the holder enjoys the early exercise featureof American put and call options whereupon his payoff is the bestprediction of the European payoff under the hypothesis that the truedrift of the stock price equals a contract drift. This includes aderivation of the arbitrage-free price and a financial analysis ofthe option returns.

2. Path Dependent British Options---------------------------------

The objective is to examine and present the valuation of Britishpath dependent options where the holder enjoys the early exercisefeature of American path dependent options whereupon his payoff isthe best prediction of the European payoff under the hypothesis thatthe true drift of the stock price equals a contract drift. Thisincludes a derivation of the arbitrage-free price and a financialanalysis of the option returns.

3. Compound Options-------------------

The objective is to examine and present the valuation of compoundoptions which are contracts where the payoff depends on the value ofanother option. This includes a derivation of the arbitrage-freeprice and a financial analysis of the option returns.

4. Cancellable American Options-------------------------------

The objective is to examine and present the valuation of cancellableAmerican options which are contracts where the writer is allowed toterminate the option at any time for a fixed penalty amount paiddirectly to the holder. This includes a derivation of thearbitrage-free price and a financial analysis of the option returns.

5. Installment Options----------------------

The objective is to examine and present the valuation of installmentoptions which are contracts where the price is paid in installmentsover the lifetime of the option, rather than as a lump-sum at thetime of purchase, and where the holder can be allowed to lapse thecontract at any payment date before maturity. This includes a

derivation of the arbitrage-free price and a financial analysis ofthe option returns.

6. Implied Volatility and Performance of the BS model-----------------------------------------------------

Select a portfolio of options from the market and look for evidenceof volatility smiles, frowns etc using market data. Using historicaldata, the student can analyse how well the classic BS hedgingstrategy is at replicating the option payoff. Is the effectivenessof replicating the option reflected in the volatility smile?

7. Mine Options---------------

The standard method to value a finite resource (such as a mine) is


2/5

as a collection of futures options on the asset contained in theresource. The student can use either analytical or numericaltechniques to investigate the value of the option to expand capacityor use up stockpiles.

8. Pricing Exotic Options with Quadrature-----------------------------------------

Quadrature is a well known and effective tool used to price options.Its application on vanilla options is trivial but it is rather moredifficult to apply to more exotic options. The student will analyseand derive there own methods (if possible) to solve a choice ofexotic options.

9. Hedging Strategies with a Correlated Asset---------------------------------------------

In illiquid markets such as energy markets, where assets are nottraded, complex hedging strategies must be carried out on correlatedassets. This can lead to multiple prices contained within a bound.The student must develop a model to take account of the basis risk(that which cannot be hedged away) and investigate its effect onpricing options using Monte-Carlo or other numerical techniques.

10. Numerical Techniques for Jump Diffusions--------------------------------------------

It is well known that GBM is not sufficient to describe theevolution of asset prices in the market and jump diffusion models isone way to address this. The student will evaluate 2 or morenumerical techniques to solve European and American options when theunderlying price process contains jumps, and compare computedresults with market data.

11. Optimal Revenue Management for Events-----------------------------------------

Using binomial trees the students will solve optimal pre-book ticketpricing problems with stochastic arrival data and a perishableproduct. They will investigate solutions to the problem with avariety of underlying assumptions such as overbooking, to try togain insight into the problem.

12. The Long-Term Behaviour of American Options-----------------------------------------------

This project will study the long-term behaviour of American-styleoptions, in particular how (and how quickly) the well-known

`perpetual' limit is reached. A number of papers have been publishedin this area, however the precise details (rather than variousbounds) have yet to be fully understood.

13. Modelling Energy Prices---------------------------

Energy markets tend to have spikes in price caused by short termshortages in supply, meaning that they tend to be model the priceprocess with jumps. The student can evaluate current models of priceusing existing data of or try to implement something different whichtries to model supply and demand individually.

14. Modelling Storage on the Energy Markets

-------------------------------------------


3/5

Given shortages in supply caused by unexpected outages and a lack ofstorage the electricity markets tend to have spikes in price. Thestudent could use numerical techniques to model the value of storagein the market.

15. Structural Models for Bonds-------------------------------

The student may investigate existing structural models for bonds,testing them on data is it is available. They may then try to extendthe models using some occupation time derivatives to model thebankruptcy process or by adding the cash flows of the firm into theequation.

16. Pricing of Game Options---------------------------

We look at the pricing of so-called `game options'. In the case ofthe well known American option only the buyer can choose to exerciseand the seller has no influence on that, but in a game option boththe buyer and the seller can exercise. The seller has to pay theusual payoff plus a penalty if he decides to exercise. This givesthe seller of an option an extra protection, hence the game versionof an option will be cheaper than the American version of the sameoption. For game options both buyer and seller have to decide on anoptimal exercise strategy, hence it becomes a `game' between twoplayers and notions like saddle points are important. We will lookat some theory, some examples (possibly in a more general settingthan just Black-Scholes/Brownian motion) and you could analyse a newexample of a game option.

17. Risk Estimation using Extreme Value Theory----------------------------------------------

A common assumption is quantitative risk modelling is that assetprices are normally distributed. This assumption is not reasonableif the data has extreme tails. In this project, we shall use extremevalue theory methods to estimate extreme measures like Value-at-Riskand expected shortfall. We shall use real stock index data from someof the major economies.

18. Interest Rate Modelling with Affine Processes-------------------------------------------------

Affine processes are widely used in various areas of mathematicalfinance, like credit risk modelling, interest rate modelling andstochastic volatility models. In this project, we take a look at avery recently introduced subclass of affine processes for which fast

option pricing is possible via solving a linear, first orderordinary differential equation in combination with Laplace/Fourierinversion. This subclass forms a small extension of the class ofone-dimensional, positive affine process, the latter containing forinstance the popular Cox-Ingersoll-Ross model, and is suitable forinterest rate modelling. The central theme of the project is to seehow useful this particular extension is. The project can becomputational in flavour, like the computation of option pricesand/or calibration, or be more theoretical, like studying thepossible shapes of the yield curves.

19. Compound Poisson Process and its non-Markovian Generalisationsin Stock Price Modelling and Risk Management

------------------------------------------------------------------

In financial modelling, the compound Poisson process has been used


4/5

to model the jumps in underlying asset prices. In risk management,the jump processes have been used to model aggregate losses. Thepurpose of the project is to apply the compound Poisson process andits non-Markovian generalisations in stock price modelling and riskmanagement.

20. Semi-Markov Processes and Credit Risk Modelling---------------------------------------------------

The aim of this project is to use semi-Markov models in computingthe default probability of a company. The main idea is to look atthe credit risk as a reliability problem.

21. Memory Effects in Stochastic Volatility Modelling-----------------------------------------------------

The phenomenon of long memory in the stochastic volatility has beenobserved and extensively documented. The purpose of this project isuse the continuous time random walk models to describe the memoryeffects for the random volatility.

22. Fractional Diffusion Equations in Finance---------------------------------------------

The purpose of the project is to use the continuous time random walk(CTRW) models for the stock price dynamics. The aims are (1) toconsider the hydrodynamic limit, in which the models generatescaling form for the probability density function of the log-priceat time t and (2) to show the equivalence between CTRWs andfractional diffusion equations.

23. Weather Derivatives: Different Approaches to their Pricing--------------------------------------------------------------

Weather derivatives are used by businesses to protect themselvesagainst weather risk. Black-Scholes type pricing methods have beenderived. Other authors have suggested that these methods are notapplicable and have favoured the expected discounted value approach.

24. Mortality Bonds and Derivatives-----------------------------------

Life Insurance companies lose when people die early and pensionfunds and governments lose when people live longer. The longevitybond was first suggested in 2001 and the first was issued in 2004 bythe European Investment Bank/BNP. Stochastic longevity models areused to model longevity risk and enable the pricing of bond andderivatives.

25. Pricing and Hedging in Financial Markets with Jumps-------------------------------------------------------

The aim of the project is to study the problem of pricing andhedging in a financial market where the stock price fluctuations aremodelled by geometric Levy processes. Levy processes, stochasticintegration, Ito calculus for jump processes will play an importantrole.

26. Optimal Consumption and Portfolio in a Black-Scholes Market---------------------------------------------------------------

The purpose of this project is to study the optimal consumption and

portfolio problem in a Black-Scholes financial market. The dynamicprogramming approach and the martingale methods will be discussed.


5/5

Applications to specific examples will be given.

27. Fractional Brownian Motion in Finance-----------------------------------------

This project aims to study fractional Brownian motion and differenttypes of integrals against fractional Brownian motion. The role offractional Brownian motion in finance will be discussed,particularly the comparison of the Black-Scholes market driven byfractional Brownian motion and by standard Brownian motion.

28. Compound Poisson Processes and Applications to Finance----------------------------------------------------------

This project is concerned with stochastic calculus for compoundPoisson processes and its application in finance. Stochasticintegrals against compensated Poisson processes and Itos formulawill be discussed. Asset pricing in markets driven by compoundprocesses will be investigated.

29. Derivative Pricing in Electricity Markets---------------------------------------------

This projects aims to discuss spot price models in electricitymarket. Derivative pricing and various properties will be examined.

msc projects 2012

Documents