Thesis (Ph. D.)--University of Massachusetts Amherst, 2009. / Open access. Includes bibliographical references (p. 142-149). Print copy also available.

Thesis (M.B.A.)--Naval Postgraduate School, 2003. / Title from title screen (viewed Apr. 5, 2004). "December 2003." "ADA420489"--URL. Includes bibliographical references (p. 67-69). Also issued in paper format.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 104). Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 167-172). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 167-172). Also available on the Internet.

published_or_final_version / abstract / Real Estate and Construction / Doctoral / Doctor of Philosophy

We present a tree algorithm, called the willow tree, for financial derivative pricing. The setup of the tree uses a fixed number of spatial nodes at each time step. The transition probabilities are determine by solving linear programming problems. The willow tree method is radically superior in numerical performance when compared to the binomial tree method.

This dissertation is in the form of three essays on the topic of component and long memory GARCH models. The unifying feature of the thesis is the focus on investigating European index option evaluation using these models. / The first essay presents a new model for the valuation of European options. In this model, the volatility of returns consists of two components. One of these components is a long-run component that can be modeled as fully persistent. The other component is short-run and has zero mean. The model can be viewed as an affine version of Engle and Lee (1999), allowing for easy valuation of European options. The model substantially outperforms a benchmark single-component volatility model that is well established in the literature. It also fits options better than a model that combines conditional heteroskedasticity and Poisson normal jumps. While the improvement in the component model's performance is partly due to its improved ability to capture the structure of the smirk and the path of spot volatility, its most distinctive feature is its ability to model the term structure. This feature enables the component model to jointly model long-maturity and short-maturity options. / The second essay derives two new GARCH variance component models with non-normal innovations. One of these models has an affine structure and leads to a closed-form option valuation formula. The other model has a non-affine structure and hence, option valuation is carried out using Monte Carlo simulation. We provide an empirical comparison of these two new component models and the respective special cases with normal innovations. We also compare the four component models against GARCH(1,1) models which they nest. All eight models are estimated using MLE on S&P500 returns. The likelihood criterion strongly favors the component models as well as non-normal innovations. The properties of the non-affine models differ significantly from those of the affine models. Evaluating the performance of component variance specifications for option valuation using parameter estimates from returns data also provides strong support for component models. However, support for non-normal innovations and non-affine structure is less convincing for option valuation. / The third essay aims to investigate the impact of long memory in volatility on European option valuation. We mainly compare two groups of GARCH models that allow for long memory in volatility. They are the component Heston-Nandi GARCH model developed in the first essay, in which the volatility of returns consists of a long-run and a short-run component, and a fractionally integrated Heston-Nandi GARCH (FIHNGARCH) model based on Bollerslev and Mikkelsen (1999). We investigate the performance of the models using S&P500 index returns and cross-sections of European options data. The component GARCH model slightly outperforms the FIGARCH in fitting return data but significantly dominates the FIHNGARCH in capturing option prices. The findings are mainly due to the shorter memory of the FIHNGARCH model, which may be attributed to an artificially prolonged leverage effect that results from fractional integration and the limitations of the affine structure.

Currency exposure has become a widespread issue as more corporations of all sizes source and sell in overseas markets and compete both at home and abroad with international companies. Very few companies are unaffected by currency risk, whether directly or indirectly. Businesses that source products from foreign countries face the risk that exchange rate movement will erode gross margins if competition prevents selling prices from rising in tandem, while resource-based companies face the uncertainty associated with the fact that the world's commodities markets are denominated in US Dollars or Pounds Sterling while their costs are often denominated in their local currencies. Businesses that ignore exchange rate volatility expose themselves to unnecessary risk, which could have significant consequences if exchange rates suddenly move unfavourably. The volatility of the South African Rand over the past few years is forcing treasurers and other managers responsible for international trade to look anew at how South African exchange rate fluctuations affect their company's results. Many companies have suffered from the effects of fluctuating exchange rates; some have reported losses running into millions of Rand. While more and more firms realize that they should manage foreign exchange risk, not all of them have come up with an appropriate management strategy. There has always been a great deal of debate over the best approach to hedging, or the best methods to forecast exchange rates; however hedging is of the utmost importance for companies. With the recent volatility of the rand, the multinational firm covered in this thesis, showed foreign exchange losses amounting to several millions, using forward exchange contracts to cover its high foreign exchange exposures. The major disadvantage of the forward contract as experienced by the firm and shown in this thesis is that it is a legally binding agreement and thus the firm was bound to accept the agreed exchange rate and also the fact that the exchange itself had to be done. If the commercial reason for the exchange disappeared, the cost of cancelling the forward contract would be quite high. In addition, if the exchange rate at maturity was more favourable to the firm than the one agreed to in the forward contract, the firm will still have to honour the contract and will not be able to take advantage of the favourable exchange rate. Thus, with FEC there is the elimination of the opportunity for profit, should exchange rates turn out favourably. When purchasing a currency option, however, the holder is protected from downward movements in the exchange rate whist still having the opportunity to benefit if the currency moves favourably. Hence, the purpose of this thesis was to evaluate the use of currency options as an alternative hedging strategy to forward exchange contracts to manage the firm's foreign exchange risk. It was found that, had the firm used currency options as compared to FEC over the last four years, the firm would have made significant saving in spite of the option premium. The firm would have enjoyed the flexibility offered by currency options, that is, to let the contract lapse when it would not be to the firm's advantage thus making a lower payment for its imports than would be paid under the forward exchange contract for the same period. The results were tested over a period of four years to prove that the difference in payments using the FEC and the currency options were statistically significant. What was apparent from the research, however, was that though the multinational firm could choose from a vast array of financial instruments and currency derivatives to manage its foreign exchange risk, the firm chose to stick to using forward exchange contracts. The reasons varied from fear of dealing with the complexities of the many instruments available on the market to the limited resources within the foreign exchange department to understand the technicalities of the various instruments. The investigation revealed though forward cover as used by the firm was more efficient in terms of ease of use. Currency options when applied to cover the firm's foreign imports resulted in less cash outflow, making it better and more profitable than forward exchange contracts. Options contract, though more expensive, would have allowed the firms to let the option lapse and therefore benefit from spot exchange rates if these were more favourable. / Thesis (M.B.A.)-University of KwaZulu-Natal, Pietermaritzburg, 2006.

Diss. (sammanfattning) Västerås : Mälardalens högskola, 2007. / Härtill 6 uppsatser.