Zugl.: Trier, Univ., Diss., 2007

Bachelor-Arbeit Univ. St. Gallen, 2007.

No description available.

Master-Arbeit Univ. St. Gallen, 2008.

<p>This paper examines the pricing of barrier options using Monte Carlo Simulations. MATLAB based software is developed to estimate the price of the option using Monte Carlo simulation. We consider a generalized barrier option of knock out type, but we let the domain take the shape of a rectangular box. We investigate the price of this kind of barrier options. We investigate how the box is placed and what effect it will have on the price of the option. We compare the number of trajectories that are needed in order to achieve the same accuracy between this box barrier option and an ordinary option.</p>

This paper examines the pricing of barrier options using Monte Carlo Simulations. MATLAB based software is developed to estimate the price of the option using Monte Carlo simulation. We consider a generalized barrier option of knock out type, but we let the domain take the shape of a rectangular box. We investigate the price of this kind of barrier options. We investigate how the box is placed and what effect it will have on the price of the option. We compare the number of trajectories that are needed in order to achieve the same accuracy between this box barrier option and an ordinary option.

With the rapid increase in the usage of barrier options on the OTC markets, pricing and especially hedging of these exotic instruments became an important field of research. This paper aims to explain, apply and compare current methods used for pricing and hedging barrier options with a simulation approach. An overview of most popular methods for pricing and hedging is presented in the first part, followed by application of these pricing methods and comparing the performances of different dynamic and static hedging techniques in Black-Scholes environment by simulation in the second part. In the third part different models such as ARCH type and Stochastic Volatility are used with different jump terms to relax the assumptions of the Black-Scholes and examine the effects of these incomplete models on both pricing and performance of different hedging techniques. In the fourth part diffusion models such as Constant Variance Elasticity, Heston Stochastic Volatility and Merton Jump Diffusion are used to complete the picture.

Bachelor-Arbeit Univ. St. Gallen, 2007.

Contingent claims models have recently been applied to the field of corporate insolvency prediction in an attempt to provide the art with a theoretical methodology that has been lacking in the past. Limited studies have been carried out in order to empirically compare the performance of these “market” models with that of their accounting number-based counterparts. This thesis contributes to the literature in several ways: The thesis traces the evolution of the art of corporate insolvency prediction from its inception through to the present day, combining key developments and methodologies into a single document of reference. I use receiver operating characteristic curves and tests of economic value to assess the efficacy of sixteen models, carefully selected to represent key moments in the evolution of the art, and tested upon, for the first time, post-IFRS UK data. The variability of model efficacy is also measured for the first time, using Monte Carlo simulation upon 10,000 randomly generated training and validation samples from a dataset consisting of over 12,000 firmyear observations. The results provide insights into the distribution of model accuracy as a result of sample selection, which is something which has not appeared in the literature prior to this study. I find overall that the efficacy of the models is generally less than that reported in the prior literature; but that the theoretically driven, market-based models outperform models which use accounting numbers; the latter showing a relatively larger efficacy distribution. Furthermore, I obtain the counter-intuitive finding that predictions based on a single ratio can be as efficient as those which are based on models which are far more complicated – in terms of variable variety and mathematical construction. Finally, I develop and test a naïve version of the down-and-out-call barrier option model for insolvency prediction and find that, despite its simple formulation, it performs favourably compared alongside other market-based models.

Barrier options have become increasingly popular financial instruments due to the lower costs and the ability to more closely match speculating or hedging needs. In addition, barrier options play a significant role in modeling and managing risks in insurance and finance as well as in refining insurance products such as variable annuities and equity-indexed annuities. Motivated by these immediate applications arising from actuarial and financial contexts, the thesis studies the pricing of barrier options and some exotic variations, assuming that the underlying asset price follows the Black-Scholes model or jump-diffusion processes. Barrier options have already been well treated in the classical Black-Scholes framework. The first part of the thesis aims to develop a new valuation approach based on the technique of exponential stopping and/or path counting of Brownian motions. We allow the option's boundaries to vary exponentially in time with different rates, and manage to express our pricing formulas properly as combinations of the prices of certain binary options. These expressions are shown to be extremely convenient in further pricing some exotic variations including sequential barrier options, immediate rebate options, multi-asset barrier options and window barrier options. Many known results will be reproduced and new explicit formulas will also be derived, from which we can better understand the impact on option values of various sophisticated barrier structures. We also consider jump-diffusion models, where it becomes difficult, if not impossible, to obtain the barrier option value in analytical form for exponentially curved boundaries. Our model assumes that the logarithm of the underlying asset price is a Brownian motion plus an independent compound Poisson process. It is quite common to assign a particular distribution (such as normal or double exponential distribution) for the jump size if one wants to pursue closed-form solutions, whereas our method permits any distributions for the jump size as long as they belong to the exponential family. The formulas derived in the thesis are explicit in the sense that they can be efficiently implemented through Monte Carlo simulations, from which we achieve a good balance between solution tractability and model complexity.