This book provides a first, basic introduction into the valuation of financial options via the numerical solution of partial differential equations (PDEs). It provides readers with an easily accessible text explaining main concepts, models, methods and results that arise in this approach. In keeping with the series style, emphasis is placed on intuition as opposed to full rigor, and a relatively basic understanding of mathematics is sufficient.

The book provides a wealth of examples, and ample numerical experiments are givento illustrate the theory. The main focus is on one-dimensional financial PDEs, notably the Black-Scholes equation. The book concludes with a detailed discussion of the important step towards two-dimensional PDEs in finance.

Engages the reader with an accessible account of a highly complex mathematical approach commonly applied in financial markets. Provides a first, basic introduction into the valuation of financial options via the numerical solution of partial differential equations (PDEs) Specializes in PDE - the author has written numerous papers on the application of numerical methods focusing on PDEs and is beginning to bring this expertise to practitioners, most recently through quanthub, a new training platform.

Autorentext

Karel in 't Hout is Associate Professor in the Department of Mathematics and Computer Science at University of Antwerp, specializing in the analysis and development of numerical methods for time-dependent partial differential equations with applications to finance. He has previously held positions as Visiting Professor at Arizona State University, Visiting Professor at Boise State University and Researcher at Leiden University and University of Auckland. Karel has also spent time in the industry, working as quantitative analyst at ABN Amro, Amsterdam. He holds a PhD in Mathematics from Leiden University.

Inhalt
Chapter1. Financial option valuation.-Chapter2. Partial differential equations.- Chapter3 Spatial discretization I.- Chapter4. Spatial discretization II.- Chapter5. Numerical study: space.- Chapter6. The Greeks.- Chapter7. Temporal discretization.- Chapter8. Numerical study: time.- Chapter9. Cash-or-nothing options.- Chapter10. Barrier options.- Chapter11. American-style options.- Chapter12. Merton model.- Chapter13. Two-asset options.