AuthorsT. Gillberg
TitleWorst Case Hedges for Derivative Contracts
AfilliationScientific Computing, Scientific Computing, Scientific Computing
Publication TypeMaster's thesis
Year of Publication2009
Date PublishedJanuary
PublisherLund Institute of Technology

There is a wide range of stocks, commodities and banks to invest in on the market. In addition there are numerous bets on future rates and prices. Those bets are called derivatives. A reasonable price of a derivative is the expected profit from the bet. Financial mathematics aim at specifying the prices of derivatives. Almost all financial models assume the underlying (price or rate) to behave as a certain stochastic process. In this way all future values of the underlying is assigned a probability, and one may calculate the expected profit. This thesis investigates a model assuming nothing of that kind. No assumptions on the underlyings probability distribution are made. Instead one speci- fies what is not allowed to happen by having bounds on the evolution of the underlying. Such a model was introduced by Paul Wilmott and David Epstein in 1999. We search for a value spread of a portfolio on one underlying. The portfolio may consist of any simple derivatives as well as the underlying. Assuming the underlying takes the 'worst' possible path allowed by the bounds, one gets a lower value of a contract. This value is called the worst value. Similarly the worst value for a negative share of a contract, a sold contract, is called the best value. The model is derived in a very general setting so that the underlying may refer to either a stock, rate or commodity price process. The works from Epstein and Wilmott are solely dedicated to interest rate markets, why the result section focuses on a stock market.

Citation KeySimula.simula.624