This book prepares students to execute the quantitative and computational needs of the finance industry. The quantitative methods are explained in detail with examples from real financial problems like option pricing, risk management, portfolio selection, etc. Codes are provided in R programming language to execute the methods. Tables and figures, often with real data, illustrate the codes. References to related work are intended to aid the reader to pursue areas of specific interest in further detail. The comprehensive background with economic, statistical, mathematical, and computational theory strengthens the understanding. The coverage is broad, and linkages between different sections are explained. The primary audience is graduate students, while it should also be accessible to advanced undergraduates. Practitioners working in the finance industry will also benefit.

Autorentext

Rituparna Sen is Associate Professor at the Applied Statistics Division, Indian Statistical Institute, Bangalore Centre, Karnataka, India. Earlier, she was Assistant Professor at the University of California at Davis from 2004-2011. With a Ph.D. in statistics from the University of Chicago, USA, she has been internationally recognized for her outstanding contributions to the applications of statistical theory and methods in finance and for her initiative and leadership in research, teaching, and mentoring in this area. She is on the editorial board of the Applied Stochastic Models in Business and Industry journal and several other journals. Rituparna is an elected member of the International Statistical Institute and a council member of the International Society for Business and Industrial Statistics. She has been awarded the Young Statistical Scientist Award by the International Indian Statistical Association in the Applications category and the Best Student Paper Award by the American Statistical Association section on the Statistical Computing and Women in Mathematical Sciences award by Technical University of Munich, Germany.

Sourish Das is Associate Professor of mathematics at Chennai Mathematical Institute (CMI), Tamil Nadu, India. At CMI, he teaches data science courses, including statistical finance using R and Python. His research interests are in Bayesian methodology, machine learning on big data in statistical finance, and environmental statistics. He did his Ph.D. in statistics from the University of Connecticut and postdoctoral work at Duke University, USA. He was awarded the UK Commonwealth Rutherford Fellowship to visit the University of Southampton, UK. He was awarded the Best Student Research Paper by the American Statistical Association section on Bayesian statistics.

Inhalt

Part I. Numerical Methods.- 1. Preliminaries.- 2. Solving a System of Linear Equations.- 3. Solving Non-Linear Equations.- 4. Numerical Integration.- 5. Numerical Differentiation.- 6. Numerical Methods for PDE.- 7. Optimization.- Part II. Simulation Methods.- 8. Monte-Carlo Methods.- 9. Lattice Models.- 10. Simulating Brownian Motion.- 11. Variance Reduction.- 12. Bayesian Computation with Stan.- 13. Resampling.- Part III. Statistical Methods.- 14. Descriptive Methods.- 15. Inferential Statistics.- 16. Statistical Risk Analysis.- 17. Multivariate Analysis.- 18. Univariate Time Series.- 19. Multivariate Time Series.- 20. High Frequency Data.- 21. Supervised Learning.- 22. Unsupervised Learning.- Appendix.- A. Basics of Mathematical Finance.- B. Introduction to R.- C. Extreme Value Theory in Finance.- Bibliography.