Originally presented as the author's thesis (Ph.D. - Goethe-University, Frankfurt am Main) titled "Pricing in (in)complete markets : structural analysis and applications," May 2003. / Includes bibliographical references (p. [105]-107) and index.

Zugl.: Frankfurt (Main), Univ., Diplomarbeit, 2006

Thesis (PhD)--Macquarie University, Division of Economic and Financial Studies, Dept. of Statistics, 2008. / Bibliography: p. 73-77.

Univ., Diss.--Frankfurt (Main), 2003. / Literaturverz. S. [105] - 107.

There is a growing number of applications of machine learning and deep learning in quantitative and computational finance. In this thesis, we focus on two of them. In the first application, we employ machine learning and deep learning in derivative pricing. The models considering jumps or stochastic volatility are more complicated than the Black-Merton-Scholes model and the derivatives under these models are harder to be priced. The traditional pricing methods are computationally intensive, so machine learning and deep learning are employed for fast pricing. I n Chapter 2, we propose a method for pricing American options under the variance gamma model. We develop a new fast and accurate approximation method inspired by the quadratic approximation to get rid of the time steps required in finite difference and simulation methods, while reducing the error by making use of a machine learning technique on pre-calculated quantities. We compare the performance of our method with those of the existing methods and show that this method is efficient and accurate for practical use. In Chapters 3 and 4, we propose unsupervised deep learning methods for option pricing under Lévy process and stochastic volatility respectively, with a special focus on barrier options in Chapter 4. The unsupervised deep learning approach employs a neural network as the candidate option surface and trains the neural network to satisfy certain equations. By matching the equation and the boundary conditions, the neural network would yield an accurate solution. Special structures called singular terms are added to the neural networks to deal with the non-smooth and discontinuous payoff at the strike and barrier levels so that the neural networks can replicate the asymptotic behaviors of options at short maturities. Unlike supervised learning, this approach does not require any labels. Once trained, the neural network solution yields fast and accurate option values. The second application focuses on financial time series simulation utilizing deep learning techniques. Simulation extends the limited real data for training and evaluation of trading strategies. It is challenging because of the complex statistical properties of the real financial data. In Chapter 5, we introduce two generative adversarial networks, which utilize the convolutional networks with attention and the transformers, for financial time series simulation. The networks learn the statistical properties in a data-driven manner and the attention mechanism helps to replicate the long-range dependencies. The proposed models are tested on the S&P 500 index and its option data, examined by scores based on the stylized facts and are compared with the pure convolutional network, i.e. QuantGAN. The attention-based networks not only reproduce the stylized facts, including heavy tails, autocorrelation and cross-correlation, but also smooth the autocorrelation of returns.

The first essay, "Market Integration and Side by Side Trading of Derivative and Cash Instruments" inquires into the microstructure of integrated trading of derivative and cash instruments and proposes a spatial differentiation model as a framework for analysis. The model illustrates that when broker-dealers can execute cash and derivative transactions proximately they can increase their returns by serving a larger proportion of investors who hold diverse portfolios thereby helping investors to economize on transactions costs. The model predicts that transactions involving a cash and derivative will be effected through an integrated system. The second essay, "Stock Index Futures Trading and Stock Market Volatility," reviews theoretical models and empirical evidence on the relationships between the level of futures trading and volatility. An empirical investigation is conducted by examining the relationship between the daily trading value of the S&P 500 stock index futures contract and the traded value of New York Stock Exchange stocks and considers whether there is higher price volatility in the stock markets when the level of trading in the futures markets is high relative to trading in the cash market. No evidence, theoretical or empirical, is found to support the notion that futures trading leads to greater volatility in the underlying cash market. The third essay, "Liquidation and Delivery Under Conditions of Manipulation models how strategic traders would respond to manipulation given an option to liquidate or deliver on the contract. A perfect Bayesian equilibrium concept is used in which traders must decide whether to liquidate or deliver given the realization of the first period equilibrium futures price. If detected by floor brokers who competitively bid prices to their expected value, the manipulator will cause prices to move against him, raising the equilibrium price when he puts in orders to buy and lowering the price when he seeks to selL Revelation of manipulation through prices also alters the behavior of other traders. An analysis of reactions in a simplified extensive form game indicates that detection of manipulation allows other market participants to stategically adjust their plans regarding liquidation and avoid incurring losses to the manipulator. / Ph. D.

In the first essay, this thesis provides a new methodology for pricing the fixed income derivatives using the arbitrage-free Heath-Jarrow-Morton model (hereafter HJM model). While, most previous empirical implementations of HJM model like that by Amin and Morton (1994) are focused on one-factor model only, the essay attempts to extend the test to a two-factor model that could further capture the subtleties of the forward rate process. The two-factor Poisson-Gaussian version of HJM model derived by Das (1999) that incorporates a jump component as the second state variables is used to value the actively traded Eurodollar futures call option under the jump diffusion lattice. The one-factor and two-factor models are compared with five volatility functions to evaluate the degree of pricing improvement by the inclusion of one more state variable. / The essay also addresses the critical issues on the volatility structure of forward rates that affect the pricing performance of option under the HJM framework. Three new volatility specifications are constructed to estimate the traded options. The first volatility function is the humped & curvature adjusted model that allows for humped shape in volatility structure and better adjustment to the curvature of the term structure. The second is the humped & proportional model that exhibits humped volatility feature and is proportional to the forward rate. The third function is the linear exponential model that is extended from Vasicek's exponential model. They are compared with two other volatility structures developed by previous researchers on their pricing performances. The alternative models are examined from the perspectives of in-sample fit, out-of-sample pricing and hedging. / The second essay develops an approach for estimating the Value-at-Risk (hereafter VaR) with jumps using the Monte Carlo simulation method. It is by far the first paper to estimate VaR using the HJM model. The paper takes the framework of the Poisson Gaussian version of HJM model (hereafter, HJM jump-diffusion model) from Das (1999). The model is incorporated with a jump component to capture the kurtosis effect in the daily price changes. As a result, the HJM jump-diffusion model allows for the fat tailed and skewed distribution of return in most financial markets. The simulation process is expedited by using variance reduction method. The model is used for calculating the VaR of a portfolio consisting of the fixed income derivatives. The accuracy of the VaR estimates is examined statistically at the VaR at confidence level of both 95 and 99 percent. / This thesis is a collection of two essays that explore issues related to the pricing and the risk management of fixed income securities and derivatives in US markets. In the context of the pricing of derivatives, the arbitrage-free pricing approach is adopted. For the issue of risk management, the estimation of Value-at-Risk is presented. / by Ze-To Yau Man. / Source: Dissertation Abstracts International, Volume: 62-09, Section: A, page: 3138. / Supervisors: Jia He; Ying-foon Chow. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (p. 145-151). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2007. / The use of options on various stock markets over the world has introduced a unique opportunity for investors to hedge, speculate, create synthetic financial instruments and reduce funding and other costs in their trading strategies. The power of options lies in their versatility. They enable an investor to adapt or adjust her position according to any situation that arises. Another benefit of using options is that they provide leverage. Since options cost less than stock, they provide a high-leverage approach to trading that can significantly limit the overall risk of a trade, or provide additional income. This versatility and leverage, however, come at a price. Options are complex securities and can be extremely risky. In this document several aspects of trading and valuing some exotic options are investigated. The aim is to give insight into their uses and the risks involved in their trading. Two volatility-dependent derivatives, namely compound and chooser options; two path-dependent derivatives, namely barrier and Asian options; and lastly binary options, are discussed in detail. The purpose of this study is to provide a reference that contains both the mathematical derivations and detail in valuating these exotic options, as well as an overview of their applicability and use for students and other interested parties.

Thesis (MBA)--Stellenbosch University, 2002. / ENGLISH ABSTRACT: This study reviews the development and current status of the weather derivative market in the world. As technology has improved, man's potential to model the unpredictable has come to the fore. Changes in the macro economic environment have prompted business to diversify. Deregulation in the American energy market and the advent of weather phenomenon like EI Nino and La Nina enticed large business to hedge their risk exposure in a different way than traditional diversification. Risk for the agriculture sector can be divided into three categories: Price risk, event risk and yield risk. Price risk has been managed by the incorporation of options and futures in the marketing of produce and acquiring of requisites. In conclusion the research finds that the SA market has the potential to grow faster than its American and European counterparts partly because techniques developed can be "leap frogged", but mostly because the SA environment induces smaller contracts that will lead to more market participants and eventually to higher liquidity. / AFRIKAANSE OPSOMMING: Hierdie studie bespreek die ontwikkeling en huidige stand van die Weer afgeleide instrumente mark in die wêreld. Soos tegnology verbeter het, het die mens se vermoeë om die onsekere te voorspel na vore getree. Veranderings in die makro ekonomiese omgewing het besighede genoodsaak om te diversifiseer. Deregulasie van die Amerikaanse energy mark en weerverskynsels soos EI Nino en La Nina het groot besighede verplig om risiko te verskans deur middel van 'n ander metode as tradisionele diversifikasie. Risiko in die landbou sektor kan verdeel word in drie kategorie; prys risiko, gebeurtenis risiko en laastens opbrengs risiko. In die verlede is prys risiko bestuur deur die insluiting van afgeleide opsies in die bemarkingsaksie van kommoditeite. Gebeurtenis risiko is beheer deur oes versekering en die laaste word deesdae deur weer afgeleide instrumente bestuur. In samevatting bevind die navorsing dat die Suid Afrikaanse mark die potensiaal bevat om vinnig te groei. Deels omdat tegnieke wat ontwikkel is gebruik kan word en deels omdat die Suid Afrikaanse omgewing kleiner kontrakte, dog meer deelnemers in die mark stimuleer.

A credit default swap is a contract that ensures protection against losses occurring due to a default event of an certain entity. It is crucial to know how default should be modelled for valuation or estimating of credit derivatives. In this dissertation, we first review the structural approach for modelling credit risk. The model is an approach for assessing the credit risk of a firm by typifying the firms equity as a European call option on its assets, with the strike price (or exercise price) being the promised debt repayment at the maturity. The model can be used to determine the probability that the firm will default (default probability) and the Credit Spread. We second concentrate on the valuation of credit derivatives, in particular the Credit Default Swap (CDS) when the hazard rate (or even of default) is modelled as the Vasicek-type model. The other objective is, by using South African credit spread data on defaultable bonds to estimate parameters on CIR and Vasicek-type Hazard rate models such as stochastic differential equation models of term structure. The parameters are estimated numerically by the Moment Method. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2013.