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A masters-level introduction offering a unique compromise between intuition and the mathematics underlying derivatives pricing. Suitable for a broad readership ranging from management students to engineers, it starts from the foundations of probability, using examples, exercises and simulations to illustrate the key concepts.
List of contents
Foreword; General Introduction; Part I. Probability Theory: 1. Probability space; 2. Random variables and distributions; 3. Moments and measure changes; 4. Dealing with partial information; 5. Sampling and Monte Carlo simulation; 6. Solved exercises; Part II. Pricing by Risk-Neutral Expectation: 7. Stochastic process and related concepts; 8. The random walk; 9. Derivative pricing using CRR; 10. The Brownian motion; 11. Derivative pricing using GBM; 12. Solved exercises; Part III. Pricing by Dynamic Replication: 13. Stochastic integrals; 14. Stochastic differential equations; 15. Itô calculus; 16. The Black-Scholes-Merton equation; 17. Solved exercises; Part IV. Hedging and Beyond: 18. Replication and hedging; 19. Fundamental theorems of asset pricing; 20. Pricing via change of numéraire; 21. Beyond Black-Scholes-Merton; 22. Solved exercises; Part V. Appendices: Appendix A. Short-selling in a nutshell; Appendix B. Important functions of distributions; Appendix C. Covergence of random variables; Appendix D. Quadratic variation of smooth functions; Appendix E. Connections between CRR and GBM; Appendix F. Pricing Asian options via Monte Carlo; Appendix G. Itô vs Stratanovich integrals; Appendix H. Itô's lemma: sketch of proof; Appendix I. Acronyms; Bibliography; Index.
About the author
Frédéric D. Vrins has been a quantitative finance professor at the Louvain School of Management (UCLouvain) since 2014, where he coordinates the Financial Engineering track. Previously, he was Senior Quant in the trading room of a systemic bank. His research includes mathematical finance, credit risk and portfolio optimization.
