Portfolio theory, risk management and the evaluation of derivatives (Q2276044)

The book offers a fairly broad selection of material on (mainly discrete time) mathematical finance. Chapter 1 deals with no-arbitrage theory in the one-period model. By assuming, for most of the book, a finite probability space and discrete time trading, the presentation needs no functional analysis and few probabilistic prerequisites. Chapter 2 covers mean-variance portfolio analysis and the CAPM. In Chapters 3 and 4, options are introduced and priced by replication in a multi-period model. The Black-Scholes formula is obtained as a limiting case. American options, forwards, and futures are also discussed, as well as some exotics and basics of fixed income markets (bonds, swaps, duration). Chapter 5 introduces value at risk and coherent risk measures, like expected shortfall. Continuous time no-arbitrage theory is only briefly touched in this book (Chapter 8 on the Black-Scholes model), but Chapter 6 (discrete stochastic analysis) renders the reader well prepared for the technically more demanding continuous time theory. Chapter 8 is preceded by a stochastic formulation of no-arbitrage and pricing by replication (Chapter 7); note that Chapters 1, 3, and 4 totally avoid the language of probability. The text includes code fragments for binomial trees and the Black-Scholes formula, which are also available for download.