Zugl.: Siegen, Universiẗat, Diss., 2004.

Assignment (MComm)--University of Stellenbosch, 2007. / Bibliography. Also available via the Internet.

No description available.

The exotic options that are examined in this thesis have a combination of non-standard characteristics which can be found in shout, multi-callable, pathdependent and Bermudan options. These options are called reset options. A reset option is an option which allows the holder to reset, one or more times, certain terms of the contract based on pre-specified rules during the life of the option. Overall in this thesis, an attempt has been made to tackle the modeling challenges that arise from the exotic properties of the reset option embedded in segregated funds. Initially, the relevant literature was reviewed and the lack of published work, advanced enough to deal with the complexities of the reset option, was identified. Hence, there appears to be a clear and urgent need to have more sophisticated approaches which will model the reset option. The reset option on the maturity guarantee of segregated funds is formulated as a non-stationary finite horizon Markov Decision Process. The returns from the underlying asset are modeled using a discrete time approximation of the lognormal model. An Optimal Exercise Boundary of the reset option is derived where a threshold value is depicted such that if the value of the underlying asset price exceeds it then it is optimal for the policyholder to reset his maturity guarantee. Otherwise, it is optimal for the policyholder to rollover his maturity guarantee. It is noteworthy that the model is able to depict the Optimal Exercise Boundary of not just the first but of all the segregated fund contracts which can be issued throughout the planning horizon of the policyholder. The main finding of the model is that as the segregated fund contract approaches its maturity, the threshold value in the Optimal Exercise Boundary increases. However, in the last period before the maturity of the segregated fund, the threshold value decreases. The reason for this is that if the reset option is not exercised it will expire worthless. The model is then extended to re ect on the characteristics of the range of products which are traded in the market. Firstly, the issuer of the segregated fund contract is allowed to charge a management fee to the policyholder. The effect from incorporating this fee is that the policyholder requires a higher return in order to optimally reset his maturity guarantee while the total value of the segregated fund is diminished. Secondly, the maturity guarantee becomes a function of the number of times that the reset option has been exercised. The effect is that the policyholder requires a higher return in order to choose to reset his maturity guarantee while the total value of the segregated fund is diminished. Thirdly, the policyholder is allowed to reset the maturity guarantee at any point in time within each year from the start of the planning horizon, but only once. The effect is that the total value of the segregated fund is increased since the policyholder may lock in higher market gains as he has more reset decision points. In response to the well documented deficiencies of the lognormal model to capture the jumps experienced by stock markets, extensions were built which incorporate such jumps in the original model. The effect from incorporating such jumps is that the policyholder requires a higher return in order to choose to reset his maturity guarantee while the total value of the segregated fund is diminished due to the adverse effect of the negative jumps on the value of the underlying asset.

Chan Chun Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 63-66). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Volatility Smile and Stochastic Volatility Models --- p.6 / Chapter 2.1 --- Volatility Smile --- p.6 / Chapter 2.2 --- Stochastic Volatility Model --- p.9 / Chapter 2.3 --- Multiscale Stochastic Volatility Model --- p.12 / Chapter 3 --- Lookback Options --- p.14 / Chapter 3.1 --- Lookback Options --- p.14 / Chapter 3.2 --- Lookback Spread Option --- p.15 / Chapter 3.3 --- Dynamic Fund Protection --- p.16 / Chapter 3.4 --- Floating Strike Lookback Options under Black-Scholes Model --- p.17 / Chapter 4 --- Floating Strike Lookback Options under Multiscale Stochastic Volatility Model --- p.21 / Chapter 4.1 --- Multiscale Stochastic Volatility Model --- p.22 / Chapter 4.1.1 --- Model Settings --- p.22 / Chapter 4.1.2 --- Partial Differential Equation for Lookbacks --- p.24 / Chapter 4.2 --- Pricing Lookbacks in Multiscale Asymtoeics --- p.26 / Chapter 4.2.1 --- Fast Tirnescale Asymtotics --- p.28 / Chapter 4.2.2 --- Slow Tirnescale Asymtotics --- p.31 / Chapter 4.2.3 --- Price Approximation --- p.33 / Chapter 4.2.4 --- Estimation of Approximation Errors --- p.36 / Chapter 4.3 --- Floating Strike Lookback Options --- p.37 / Chapter 4.3.1 --- Accuracy for the Price Approximation --- p.39 / Chapter 4.4 --- Calibration --- p.40 / Chapter 5 --- Other Lookback Products --- p.43 / Chapter 5.1 --- Fixed Strike Lookback Options --- p.43 / Chapter 5.2 --- Lookback Spread Option --- p.44 / Chapter 5.3 --- Dynamic Fund Protection --- p.45 / Chapter 6 --- Numerical Results --- p.49 / Chapter 7 --- Conclusion --- p.53 / Appendix --- p.55 / Chapter A --- Verifications --- p.55 / Chapter A.1 --- Formula (4.12) --- p.55 / Chapter A.2 --- Formula (4.22) --- p.56 / Chapter B --- Proof of Proposition --- p.57 / Chapter B.1 --- Proof of Proposition (4.2.2) --- p.57 / Chapter C --- Black-Scholes Greeks for Lookback Options --- p.60 / Bibliography --- p.63

An Asian option is an example of exotic options. Its payoff depends on the average of the underlying asset prices. The average may be over the entire time period between initiation and expiration or may be over some period of time that begins later than the initiation of the option and ends with the options expiration. The average may be from continuous sampling or may be from discrete sampling. The primary reason to base an option payoff on an average asset price is to make it more difficult for anyone to significantly affect the payoff by manipulation of the underlying asset price. The price of Asian options is not known in closed form, in general, if the arithmetic average is taken into effect. In this dissertation, we shall investigate the pricing theory for Asian options. After a brief introduction to the Black-Scholes theory, we derive the partial differential equations for the value process of an Asian option to satisfy. We do this in several approaches, including the usual extension to Asian options of the Black-Scholes, and the sophisticated martingale approach. Both fixed and floating strike are considered. In the case of the geometric average, we derive a closed form solution for the Asian option. Moreover, we investigate the Asian option price theory under stochastic volatility which is a recent trend in the study of path-dependent option theory. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2007.

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 120-126). Also available in electronic version. Access restricted to campus users.

The Black-Scholes option pricing model has several well recognized deficiencies, one of which is its assumption of a constant and time-homogeneous stock return volatility term. The implied volatility smile has been studied by subsequent researchers and various models have been developed in an attempt to reproduce this phenomenon from within the models. However, few of these models yield closed-form pricing formulas that are easy to implement in practice. In this thesis, we study a Mixture Lognormal model (MLN) for European option pricing, which assumes that future stock prices are conditionally described by a mixture of lognormal distributions. The ability of mixture models in generating volatility smiles as well as delivering pricing improvement over the traditional Black-Scholes framework have been much researched under multi-component mixtures for many derivatives and high-volatility individual stock options. In this thesis, we investigate the performance of the model under the simplest two-component mixture in a market characterized by relative tranquillity and over a relatively stable period for broad-based index options. A careful interpretation is given to the model and the results obtained in the thesis. This di erentiates our study from many previous studies on this subject. Throughout the thesis, we establish the unique advantage of the MLN model, which is having closed-form option pricing formulas equal to the weighted mixture of Black-Scholes option prices. We also propose a robust calibration methodology to fit the model to market data. Extreme market states, in particular the so-called crash-o-phobia effect, are shown to be well captured by the calibrated model, albeit small pricing improvements are made over a relatively stable period of index option market. As a major contribution of this thesis, we extend the MLN model to price exotic options including binary, Asian, and barrier options. Closed-form formulas are derived for binary and continuously monitored barrier options and simulation-based pricing techniques are proposed for Asian and discretely monitored barrier options. Lastly, comparative results are analysed for various strike-maturity combinations, which provides insights into the formulation of hedging and risk management strategies.

The Black-Scholes option pricing model has several well recognized deficiencies, one of which is its assumption of a constant and time-homogeneous stock return volatility term. The implied volatility smile has been studied by subsequent researchers and various models have been developed in an attempt to reproduce this phenomenon from within the models. However, few of these models yield closed-form pricing formulas that are easy to implement in practice. In this thesis, we study a Mixture Lognormal model (MLN) for European option pricing, which assumes that future stock prices are conditionally described by a mixture of lognormal distributions. The ability of mixture models in generating volatility smiles as well as delivering pricing improvement over the traditional Black-Scholes framework have been much researched under multi-component mixtures for many derivatives and high-volatility individual stock options. In this thesis, we investigate the performance of the model under the simplest two-component mixture in a market characterized by relative tranquillity and over a relatively stable period for broad-based index options. A careful interpretation is given to the model and the results obtained in the thesis. This di erentiates our study from many previous studies on this subject. Throughout the thesis, we establish the unique advantage of the MLN model, which is having closed-form option pricing formulas equal to the weighted mixture of Black-Scholes option prices. We also propose a robust calibration methodology to fit the model to market data. Extreme market states, in particular the so-called crash-o-phobia effect, are shown to be well captured by the calibrated model, albeit small pricing improvements are made over a relatively stable period of index option market. As a major contribution of this thesis, we extend the MLN model to price exotic options including binary, Asian, and barrier options. Closed-form formulas are derived for binary and continuously monitored barrier options and simulation-based pricing techniques are proposed for Asian and discretely monitored barrier options. Lastly, comparative results are analysed for various strike-maturity combinations, which provides insights into the formulation of hedging and risk management strategies.

Diss. Univ. Rotterdam, 2008. / Mit niederländischer Zusammenfassung.