This thesis investigated Stochastic Runge–Kutta Lawson (SRKL) schemes and their application to the Heston model. Two distinct SRKL discretization methods were used to simulate a single asset’s dynamics under the Heston model, notably the Euler–Maruyama and Midpoint schemes. Additionally, standard Monte Carlo and variance reduction techniques were implemented. European and Asian option prices were estimated and compared with a benchmark value regarding accuracy, effectiveness, and computational complexity. Findings showed that the SRKL Euler–Maruyama schemes exhibited promise in enhancing the price for simple and path-dependent options. Consequently, integrating SRKL numerical methods into option valuation provides notable advantages by addressing challenges posed by the Heston model’s SDEs. Given the limited scope of this research topic, it is imperative to conduct further studies to understand the use of SRKL schemes within other models.

Credit risk measurement and management has great importance in credit market. Credit derivative products are the major hedging instruments in this market and credit default swap contracts (CDSs) are the most common type of these instruments. As observed in credit crunch (credit crisis) that has started from the United States and expanded all over the world, especially crisis of Iceland, CDS premiums (prices) are better indicative of credit risk than credit ratings. Therefore, CDSs are important indicators for credit risk of an obligor and thus these products should be understood by market participants well enough. In this thesis, initially, advanced credit risk models firsts, the structural (firm value) models, Merton Model and Black-Cox constant barrier model, and the intensity-based (reduced-form) models, Jarrow-Turnbull and Cox models, are studied. For each credit risk model studied, survival probabilities are calculated. After explaining the basic structure of a single name CDS contract, by the help of the general pricing formula of CDS that result from the equality of in and out cash flows of these contracts, CDS price for each structural models (Merton model and Black-Cox constant barrier model) and CDS price for general type of intensity based models are obtained. Before the conclusion, default intensities are obtained from the distribution functions of default under two basic structural models / Merton and Black-Cox constant barrier. Finally, we conclude our work with some inferences and proposals.

The aim of this study is to compare the performance of the four interest rate models (Vasicek Model, Cox Ingersoll Ross Model, Ho Lee Model and Black Der- man Toy Model) that are commonly used in pricing zero coupon bond options. In this study, 1{5 years US Treasury Bond daily data between the dates June 1, 1976 and December 31, 2007 are used. By using the four interest rate models, estimated option prices are compared with the real observed prices for the begin- ing work days of each months of the years 2004 and 2005. The models are then evaluated according to the sum of squared errors. Option prices are found by constructing interest rate trees for the binomial models based on Ho Lee Model and Black Derman Toy Model and by estimating the parameters for the Vasicek and the Cox Ingersoll Ross Models.

NJ, Univ., Dep. of Economics, Diss.--Princeton, 2005. / Kopie, ersch. im Verl. UMI, Ann Arbor, Mich. - Enth. 3 Beitr.

The submitted work deals with option pricing. Mathematical approach is immediately followed by an economic interpretation. The main problem is to model the underlying uncertainities driving the stock price. Using two well-known valuation models, binomial model and Black-Scholes model, we explain basic principles, especially risk neutral pricing. Due to the empirical biases new models have been developped, based on pure jump process. Variance gamma process and its special symmetric case are presented.

Surrogate-model-based optimization is widely used to solve black-box optimization problems if the evaluation of a target system is expensive. However, when the optimization budget is limited to a single or several evaluations, surrogate-model-based optimization may not perform well due to the lack of knowledge about the search space. In this case, transfer learning helps to get a good optimization result due to the usage of experience from the previous optimization runs. And if the budget is not strictly limited, transfer learning is capable of improving the final results of black-box optimization. The recent work in surrogate-model-based optimization showed that using multiple surrogates (i.e., applying multi-surrogate-model optimization) can be extremely efficient in complex search spaces. The main assumption of this thesis suggests that transfer learning can further improve the quality of multi-surrogate-model optimization. However, to the best of our knowledge, there exist no approaches to transfer learning in the multi-surrogate-model context yet. In this thesis, we propose an approach to transfer learning for multi-surrogate-model optimization. It encompasses an improved method of defining the expediency of knowledge transfer, adapted multi-surrogate-model recommendation, multi-task learning parameter tuning, and few-shot learning techniques. We evaluated the proposed approach with a set of algorithm selection and parameter setting problems, comprising mathematical functions optimization and the traveling salesman problem, as well as random forest hyperparameter tuning over OpenML datasets. The evaluation shows that the proposed approach helps to improve the quality delivered by multi-surrogate-model optimization and ensures getting good optimization results even under a strictly limited budget.:1 Introduction 1.1 Motivation 1.2 Research objective 1.3 Solution overview 1.4 Thesis structure 2 Background 2.1 Optimization problems 2.2 From single- to multi-surrogate-model optimization 2.2.1 Classical surrogate-model-based optimization 2.2.2 The purpose of multi-surrogate-model optimization 2.2.3 BRISE 2.5.0: Multi-surrogate-model-based software product line for parameter tuning 2.3 Transfer learning 2.3.1 Definition and purpose of transfer learning 2.4 Summary of the Background 3 Related work 3.1 Questions to transfer learning 3.2 When to transfer: Existing approaches to determining the expediency of knowledge transfer 3.2.1 Meta-features-based approaches 3.2.2 Surrogate-model-based similarity 3.2.3 Relative landmarks-based approaches 3.2.4 Sampling landmarks-based approaches 3.2.5 Similarity threshold problem 3.3 What to transfer: Existing approaches to knowledge transfer 3.3.1 Ensemble learning 3.3.2 Search space pruning 3.3.3 Multi-task learning 3.3.4 Surrogate model recommendation 3.3.5 Few-shot learning 3.3.6 Other approaches to transferring knowledge 3.4 How to transfer (discussion): Peculiarities and required design decisions for the TL implementation in multi-surrogate-model setup 3.4.1 Peculiarities of model recommendation in multi-surrogate-model setup 3.4.2 Required design decisions in multi-task learning 3.4.3 Few-shot learning problem 3.5 Summary of the related work analysis 4 Transfer learning for multi-surrogate-model optimization 4.1 Expediency of knowledge transfer 4.1.1 Experiments’ similarity definition as a variability point 4.1.2 Clustering to filter the most suitable experiments 4.2 Dynamic model recommendation in multi-surrogate-model setup 4.2.1 Variable recommendation granularity 4.2.2 Model recommendation by time and performance criteria 4.3 Multi-task learning 4.4 Implementation of the proposed concept 4.5 Conclusion of the proposed concept 5 Evaluation 5.1 Benchmark suite 5.1.1 APSP for the meta-heuristics 5.1.2 Hyperparameter optimization of the Random Forest algorithm 5.2 Environment setup 5.3 Evaluation plan 5.4 Baseline evaluation 5.5 Meta-tuning for a multi-task learning approach 5.5.1 Revealing the dependencies between the parameters of multi-task learning and its performance 5.5.2 Multi-task learning performance with the best found parameters 5.6 Expediency determination approach 5.6.1 Expediency determination as a variability point 5.6.2 Flexible number of the most similar experiments with the help of clustering 5.6.3 Influence of the number of initial samples on the quality of expediency determination 5.7 Multi-surrogate-model recommendation 5.8 Few-shot learning 5.8.1 Transfer of the built surrogate models’ combination 5.8.2 Transfer of the best configuration 5.8.3 Transfer from different experiment instances 5.9 Summary of the evaluation results 6 Conclusion and Future work

Diplomová práce primárně řeší zda jsou exotické opce vhodné pro zajištění kurzových rizik a přináší návrh vhodné aplikace exotických opcí. Práce je zaměřena na úzkou skupinu exotických opcí, tzv. Path-Dependent opce. Tři často používané typy těchto opcí jsou analyzovány a testovány jak mezi sebou tak pro lepší porovnání i s klasickou vanilla opcí. Hlavním výstupem diplomové práce je návrh vhodného využití testovaných exotických opcí.