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Analytical Finance: The Mathematics of Equity Derivatives, Markets, Risk and Valuation


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Table of Contents

1.1. Clearing and settlement.- 1.2. About Risk.- 1.3. Credit and Counterparty Risk.- 1.4. Settlement Risk.- 1.5. Market Risk.- 1.6. Model Risk.- 2.1. Pricing via Arbitrage.- 2.2. Martingales.- 2.3. The Central Limit Theorem.- 2.4. A simple Random Walk.- 2.5. The Binomial model.- 2.6. Modern pricing theory based on risk-neutral valuation.- 2.7. More on Binomial models.- 2.8. Finite difference methods.- 2.9. Value-at-Risk - VaR.- 3.1. Introduction.- 3.2. A binomial model.- 3.3. Finite Probability Spaces.- 3.4. Properties of normal and log-normal distributions.- 3.5. The Ito Lemma.- 3.6. Stochastic integration.- 4.1. Classifications of Partial Differential Equations.- 4.2. Parabolic PDE's.- 4.3. The Black-Scholes-Merton model.- 4.4. Volatility.- 4.5. Parity relations.- 4.6. A practical guide to pricing.- 4.7. Currency options and the Garman-Kohlhagen model.- 4.8. Options on commodities.- 4.9. Black-Scholes and stochastic volatility.- 4.10. The Black-Scholes formulas.- 4.11. American versus European options.- 4.12. Analytical pricing formulas for American options.- 4.13. Poisson processes and jump diffusion.- 5.1. Martingale representation.- 5.2. Girsanov transformation.- 5.3. Securities paying dividends.- 5.4. Hedging.- 6.1. Contract for Difference - CFD.- 6.2. Binary options/ Digital options.- 6.3. Barrier options - Knock-out and Knock-in Options.- 6.4. Lookback Options.- 6.5. Asian Options.- 6.6. Chooser Options.- 6.7. Forward Options.- 6.8. Compound Options - Options on Options.- 6.9. Multi-Asset Options.- 6.10. Basket Options.- 6.11. Correlation Options.- 6.12. Exchange Options.- 6.13. Currency-Linked Options.- 6.14. Pay-Later Options.- 6.15. Extensible Options.- 6.16. Quantos.- 6.17. Structured products.- 6.18. Summary of exotic instruments.- 6.19. Something about weather derivatives.- 7.1. Introduction to deflators.- 8.1. Introduction.- 8.2. Strategies.- 8.3. A decreasing markets.- 8.4. An increasing market.- 8.5. Neutral markets.- 8.6. Volatile Markets.- 8.7. Using market indexes in pricing.- 8.8. Price direction matrix.- 8.9. Strategy matrix.- Appendix: Some source code

About the Author

Jan Roeman is Senior Lecturer, Malardaran University, where he teaches analytical finance and financial engineering. He is also a financial engineer in the Quantitative Risk Modelling Group at Swedbank Robur Funds, where he specializes in risk model validation, focusing on all inputs to front office systems including interest rates and volatility structures. Jan has over 16 years financial markets experience mostly in financial modeling and valuation in derivatives environments. He has held positions as Head of Market and Credit Risk, Swedbank Markets, Senior Risk Analyst at the Swedish financial Supervisory Authority, Senior Developer at SunGard and Senior Developer, OMX Stockholm Exchange. He holds a License degree in Theoretical Physics from Chalmers University of Technology and has received a scholarship of the Nordic Minister Council to research at NORDITA, the Nordic Institute for Theoretical Physics.


"The aim of this book is to cover the most essential elements of valuing derivatives on equity markets. ... The book may be used as a textbook for graduate students in mathematical and analytical finance, and also may be useful for practitioners working in this area of finance." (Anatoliy Swishchuk, zbMATH 1382.91001, 2018)

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