This diploma thesis describes problem of change-points in volatility of the time-series and their impact on price of nancial assets. Those change-points are estimated by using statistical methods and tests. Change-point estimation was tested on simulated datas and real world driven datas. Simulation helped to discover signi cant characteristics of change-point test, those data were simulated with using stochastic calculus. Google share prices and prices of call options were chosen to analyse impact of volatility change on those prices. Also implied volatility and its impact to call option price was analysed.

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.

本篇論文旨在分析神經網路學習績效，並提出一套學習演算法，結合倒傳遞網路(BP)與理解神經網路(RN)，命名為RNBP，這套學習演算法將與傳統的BP做比較，以兩個不同的財務金融領域的應用，一個是選擇權上Black-Scholes訂價模式的模擬，一個是金融交換上利率的預測。主要績效的評估準則是以學習的效率與模擬、預測的準確度為依據。 此外，本論文的另一個重點是提出一套對於神經網路系統進一步分析的方法與工具，敏感度分析(Sensitivity Analysis)與滯留區(Dead Region)分析，藉以瞭解神經網路系統是否具有效地良好學習或被一般化的能力，從神經網路的角度來說，這也是BP與RNBP的另一個績效比較標準。本研究的結果顯示RNBP在預測準確度上較BP為優良，但是在學習效率與預測能力的穩定性上並沒有呈現一致性的結論；此外，敏感度分析與滯留區分析的結果也幫助神經網路在應用領域上有更深入的瞭解。 在過去，神經網路的應用者往往忽略了進一步瞭解神經網路的重要性與可行性，本論文的貢獻在於藉由分析神經網路所學習的知識，幫助應用者進一步瞭解神經網路表達的訊息在應用領域上所隱含的實質意義。 / The study attempts to analyze the learning performance of neural networks in applications, and propose a new learning procedure for the layered feedforward neural network systems, named KNBP, which binds RN and BP learning algorithms. Two artificial neural networks, BP and KNBP, here are both applied to two financial fields, the simulation of Black-Scholes pricing model for the call options and the midrates forecasting in financial swaps. The explicit performance comparison between the two artificial neural network systems is mainly based on two criteria, which are learning efficiency and forecasting effectiveness. Then we propound a mathematical methodology of sensitivity analysis and the dead regions to deeply explore inside the network structures to see whether the models of ANNS are actually well trained or valid, and thus setup an alternative comparable criterion. The results from this study show that RNBP performs better than BP in forecasting effectiveness, but RNBP obtains neither a consistent learning efficiency in cases nor a stable forecasting ability. Furthermore, the sensitivity analysis and the dead region analysis provide a deeper view of the ANNs in the applied fields. In the past, most studies applying neural networks ignored the importance that it is feasible and advantageous to obtain more useful information via analyzing neural networks. The purpose of the research is to help further understanding to the information discovery resulted from neural networks in practical applications.