Since arbitrage-free is a desirable theoretical feature in a healthy financial market, many efforts have been made to construct arbitrage-free models for yield curves. However, little attention is paid to review if such restriction will improve yield forecast. We evaluate the importance of arbitrage-free restriction on dynamic Nelson-Siegel term structure when forecasting yield curves. We find that it doesn’t help. We also compare these two Nelson-Siegel dynamic models with a benchmark dynamic model and show that Nelson-Siegel structure improve forecasts for long-maturity yields. / text

There had been a number of researches that investigated on the security market without transaction costs. The focus of this research is in the area that when the security market with transaction costs is fair and in such fair market how one chooses a suitable portfolio to optimize the financial goal. The research approach adopted in this thesis includes linear algebra and elementary probability. The thesis provides evidence that we can maximize expected utility function to achieve our goal (maximize expected return under certain risk tolerance). The main conclusions drawn from this study are under certain conditions the security market is arbitrage-free, and we can always find an optimal portfolio maximizing certain expected utility function.

In this thesis we formulate a model for foreign exchange (FX) exposure management and multi-currency cash management taking into consideration random fluctuations of exchange rates and net revenues of a multinational firm (MNF). The central decision model used in this thesis is a scenario-based stochastic programming (SP) recourse model. A critical review of alternative scenario generation methods is given followed by analysis of some desirable properties of the scenario tree. The application of matching statistical moments of a probability distribution to generate a multiperiod scenario tree for our problem is described in detail. A four-stage SP decision model is formulated using the random parameter values. This model evaluates currency / cash flows hedging strategies, which provide rolling decisions on the size and timing of the forward positions. We compute an efficient frontier from which an investor can choose an optimal strategy according to his risk and return preferences. The flexibility of the SP model allows an investor to analyse alternative risk-return trading strategies. The model decisions are investigated by making comparisons with decisions based purely on the expected value problem. The investigation shows that there is a considerable improvement to the "spot only" strategy and provides insight into how these decisions are made. The contributions of the thesis are summarised below. (i) The FX forward scenario trees are derived using an arbitrage-free pricing strategy and is in line with modem principles of finance. (ii) Use of the SP model and forward contracts as a tool for hedging decisions is novel. (iii) In particular smoothing of the effects in exchange rates and the smoothing of account receivables are examples of innovative modelling approaches for FX management.

The uncertainty attached to future movements of interest rates is an essential part of the Financial Decision Theory and requires an awareness of the stochastic movement of these rates. Several approaches have been proposed for modeling the one-factor short rate models where some lead to arbitrage-free term structures. However, no definite consensus has been reached with regard to the best approach for interest rate modeling. In this work, we briefly examine the existing one-factor interest rate models and calibrate Vasicek and Hull-White (Extended Vasicek) Models by using Turkey&#039 / s term structure. Moreover, a trinomial interest rate tree is constructed to represent the evolution of Turkey&rsquo / s zero coupon rates.

The Heath-Jarrow-Morton (HJM) model represents the latest in powerful arbitrage-free technology for modeling the term structure and managing interest rate risk. Yet risk management strategies in the form of immunization portfolios using duration, convexity, and M-square are still widely used in bond portfolio management today. This study addresses the question of how traditional risk measures and immunization strategies perform when the term structure evolves in the HJM manner. Using Monte Carlo simulation, I analyze four HJM volatility structures, four initial term structure shapes, three holding periods, and two traditional immunization approaches (duration-matching and duration-and-convexity-matching). I also examine duration and convexity measures derived specifically for the HJM framework. In addition I look at whether portfolios should be constructed randomly, by minimizing their M-squares or using barbell or bullet structures. I assess immunization performance according to three criteria. One of these criteria corresponds to active portfolio management, and the other two correspond to passive portfolio management. Under active portfolio management, an asset portfolio is successfully immunized if its holding period return is greater than or equal to the holding period return of the liability portfolio. Under passive portfolio management, the closer the returns of the asset portfolio to the returns of the liability portfolio, the better the immunization performance. The results of the study suggest that, under the active portfolio management criterion, and with the duration matching strategy, HJM and traditional duration measures have similar immunization performance when forward rate volatilities are low. There is a substantial deterioration in the immunization performance of traditional risk measures when there is high volatility. This deterioration is not observed with HJM duration measures. These results could be due to two factors. Traditional risk measures could be poor risk measures, or the duration matching strategy is not the most appropriate immunization approach when there is high volatility because yield curve shifts would often be large. Under the active portfolio management criterion and with the duration and convexity matching strategy, the immunization performance of traditional risk measures improves considerably at the high volatility segments of the yield curve. The improvement in the performance of the HJM risk measures is not as dramatic. The immunization performance of traditional duration and convexity measures, however, deteriorates at the low volatility segments of the yield curve. This deterioration is not observed when HJM risk measures are used. Overall, with the duration and convexity matching strategy, the immunization performance of portfolios matched with traditional risk measures is very close to that of portfolios matched with the HJM risk measures. This result suggests that the duration and convexity matching approach should be preferred to duration matching alone. Also the result shows that the underperformance of traditional risk measures under high volatility is not due to their being poor risk measures, but rather due to the reason that the duration matching strategy is not an appropriate immunization approach when there is high volatility in the market. Under the passive portfolio management criteria, the performances of traditional and HJM measures are similar with the duration matching strategy. Less than 29% of the duration matched portfolios have returns within one basis point of the target yield, whereas almost all are within 100 basis points of the target yield. These results suggest that the duration matching strategy might not be sufficient to generate cash flows close to those of the target bond. The duration measure assumes a linear relation between the bond price and the yield change, and the nonlinearities that are not captured by the duration measure might be important. When the duration and convexity matching strategy is used, more than 36% of the portfolios are within one basis point of the target with HJM risk measures. This dramatic improvement in the immunization performance of HJM measures is not guaranteed for traditional risk measures. In fact, there are certain cases in which the performance of traditional risk measures deteriorates with the duration and convexity matching strategy. In this respect, choosing the correct risk measure is more important than the immunization strategy when passive portfolio management is pursued. Under active portfolio management criterion, there is no significant difference among bullet, barbell, minimum M-square, and random portfolios with both duration matching and duration and convexity matching strategies. Under the passive portfolio management criterion, bullet portfolios produce closer returns to the target for short holding periods when the duration matching strategy is used. With the duration and convexity matching strategy, bullet, barbell and minimum M-square portfolios produce closer returns to the target for short holding periods. Random portfolios perform as well as bullet, barbell and minimum M-square portfolios for medium to long holding periods. These results suggest that when the duration matching strategy is used, bullet portfolios are preferable to other portfolio formation strategies for short holding periods. When the duration and convexity matching strategy is used, no portfolio formation strategy is better than the other. Under the active portfolio management criterion, minimum M-square portfolios are successfully immunized under each yield curve shape and volatility structure considered. Under the passive portfolio management criterion, minimum M-square portfolios perform better for short holding periods, and their performance deteriorates as the holding period increases, irrespective of the volatility level. This suggests that the performance of minimum M-square portfolios is more sensitive to the holding period rather than the volatility. Therefore, minimum M-square portfolios would be preferred in the markets when there are large changes in volatility. Overall, the results of the study suggest that, under the active portfolio management criterion and with the duration matching strategy, traditional duration measures underperform their HJM counterparts when forward rate volatilities are high. With the duration and convexity matching strategy, this underperformance is not as dramatic. Also no particular portfolio formation strategy is better than the other under the active portfolio management criterion. Under the passive portfolio management criterion, the duration matching strategy is not sufficient to generate cash flows closer to those of the target bond. The duration and convexity matching strategy, however, leads to substantial improvement in the immunization performance of the HJM risk measures. This improvement is not guaranteed for the traditional risk measures. Under the passive portfolio management criterion, bullet portfolios are preferred to other portfolio formation strategies for short holding periods. For medium to long holding periods, however, the portfolio formation strategy does not significantly affect immunization performance. Also, the immunization performance of minimum M-square portfolios is more sensitive to the holding period rather than the volatility. / Ph. D.

This work mainly studies modeling and existence issues for martingale models of option markets with one stock and a collection of European call options for one fixed maturity and infinetely many strikes. In particular, we study Dupire's and Schweizer-Wissel's models, especially the latter one. These two types of models have two completely different pricing approachs, one of which is martingale approach (in Dupire's model), and other one is a market approach (in Schweizer-Wissel's model). After arguing that Dupire's model suffers from the several lacks comparing to Schweizer-Wissel's model, we extend the latter one to get the variations for the case of options on interest rate indexes and futures options. Our models are based on the newly introduced definitions of local implied volatilities and a price level proposed by Schweizer and Wissel. We get explicit expressions of option prices as functions of the local implied volatilities and the price levels in our variations of models. Afterwards, the absence of the dynamic arbitrage in the market for such models can be described in terms of the drift restrictions on the models' coefficients. Finally we demonstrate the application of such models by a simple example of an investment portfolio to show how Schweizer-Wissel's model works generally.

With the exception of holders of default-free instruments, a key risk run by investors is credit risk. To meet the need of investors to hedge this risk, the market uses credit derivatives. The South African credit derivatives market is still in its infancy and only the very simplistic instruments are traded. One of the reasons is due to the technical sophistication required in pricing these instruments. This dissertation introduces the key concepts of risk neutral probabilities, arbitrage free pricing, martingales, default probabilities, survival probabilities, hazard rates and forward spreads. These mathematical concepts are then used as a building block to develop pricing formulae which can be used to infer valuations to the most popular credit derivatives in the South African financial markets. / Operations Research / M.Sc. (Operations Research)

The five essays in this dissertation are all concerned with how commodity price uncertainty affects the valuation of real and financial assets.  Focusing on the stochastic process approximating the price process of the commodity, a time-inhomogeneous mean reverting process is suggested and used in the valuation of a pulp mill.  Also an analytic approximation and a parameter estimation procedure to a stochastic volatility option-pricing model are developed.  Generally, the large valuation differences and hedging errors that occur for different assumptions about the price process indicate the importance of an appropriately specified price process.  The dissertation provides examples of this. The question of whether commodity prices are mean reverting or follow a random walk is also studied.  Using a large database with close to 300 different commodities, econometric tests favour a random walk.  There are very few exceptions.  However, when applied to an option pricing model, the time-inhomogeneous mean reverting process gives smaller hedging errors than the traditional Black-Scholes model based on a random walk.  The results are therefore inconclusive, although mean reversion seems more predominant than econometric tests reveal. / Diss. Stockholm : Handelshögskolan, 2003

With the exception of holders of default-free instruments, a key risk run by investors is credit risk. To meet the need of investors to hedge this risk, the market uses credit derivatives. The South African credit derivatives market is still in its infancy and only the very simplistic instruments are traded. One of the reasons is due to the technical sophistication required in pricing these instruments. This dissertation introduces the key concepts of risk neutral probabilities, arbitrage free pricing, martingales, default probabilities, survival probabilities, hazard rates and forward spreads. These mathematical concepts are then used as a building block to develop pricing formulae which can be used to infer valuations to the most popular credit derivatives in the South African financial markets. / Operations Research / M.Sc. (Operations Research)