Arbitrage Theory: Introductory Lectures on Arbitrage-Based Financial Asset Pricing

ISBN-13: 9783540152415 / Angielski / Miękka / 1985 / 116 str.

Jochen E.M. Wilhelm

Opis

The present 'Introductory Lectures on Arbitrage-based Financial Asset Pricing' are a first attempt to give a comprehensive presentation of Arbitrage Theory in a discrete time framework (by the way: all the re sults given in these lectures apply to a continuous time framework but, probably, in continuous time we could achieve stronger results - of course at the price of stronger assumptions). It has been turned out in the last few years that capital market theory as derived and evolved from the capital asset pricing model (CAPM) in the middle sixties, can, to an astonishing extent, be based on arbitrage arguments only, rather than on mean-variance preferences of investors. On the other hand, ar bitrage arguments provided access to a wider range of results which could not be obtained by standard CAPM-methods, e. g. the valuation of contingent claims (derivative assets) Dr the_ investigation of futures prices. To some extent the presentation will loosely follow historical lines. A selected set of capital asset pricing models will be derived according to their historical progress and their increasing complexity as well. It will be seen that they all share common structural properties. After having made this observation the presentation will become an axiomatical one: it will be stated in precise terms what arbitrage is about and what the consequences are if markets do not allow for risk-free arbitrage opportunities. The presentation will partly be accompanied by an illus trating example: two-state option pricing."

Spis treści

0. Introduction.- 1. The Linear Structure of Capital Asset Pricing Models.- 1.1. The Basic Idea of Theories of Financial Asset Prices.- 1.2. Cash-Flow Analysis.- 1.3. The Classical CAPM.- 1.3.1. Some Assumptions and Notations.- 1.3.2. Mean-Variance Efficiency.- 1.3.3. The Valuation Formula and Related Issues.- 1.3.4. The CAPM Structure of Asset Returns.- 1.3.5. Synopsis of Results in the CAPM Theory.- 1.4. The CAPM-Version By Black.- 1.4.1. The Derivation of Valuation Formulas.- 1.4.2. The Structure of Asset Returns in BLACK’S Model.- 1.5. The CAPM-Version with Non-Marketable Income.- 1.5.1. The Derivation of Valuation Formulas.- 1.5.2. The Individual Portfolio Structure.- 1.6. The Segmented Markets Model.- 1.7. Synopsis of the Main Results.- The Role Arbitrage Played in the Described Asset Pricing Theories.- 2. Taxonomy of Arbitrage in Financial Markets.- 3. Modelling and First Consequences of Arbitrage and No-Arbitrage Conditions.- 3.1. Notational Conventions; Arbitration and Spreads.- 3.2. Arbitration and No Spreads: Results without Transaction Costs.- 3.3. Free Lunches.- 3.3.1. Concepts and Definitions.- 3.3.2. Transaction Costs and Free Lunches.- 4. No-Arbitrage Conditions and the Structure of Price Systems.- 4.1. The Law of One Price.- 4.2. Free Lunches and the Law of One Price.- 4.3. Valuation by Arbitrage.- 4.3.1. The General Concept.- 4.3.2. An Example: Two-State Option Pricing.- 4.4. The Structure of Asset Prices under No-Arbitrage Conditions.- 4.4.1. The Statement of No-Arbitrage Conditions.- 4.4.2. The Implications of “No Free Lunches” for the Two-State Option Pricing.- 4.4.3. The One-Period Case.- 4.4.4. The Multiperiod Case.- 5. The Structure of Asset Returns and Mean Variance Efficiency under No-Arbitrage Conditions.- 5.1. The Structure Of Asset Returns.- 5.2. Mean-Variance Efficiency.- 6. Some Selected Applications.- 6.1. Options.- 6.1.1. No Early Exercise of an American Call.- 6.1.2. Put-Call-Parity.- 6.1.3. The Valuation of Contingent Claims in Discrete Time.- 6.2. Forward ad Futures Contracts.- 6.2.1. Interest Rate Parity Theory of Foreign Exchange Rates.- 6.2.2. Forward and Futures Prices.- 6.3. Corporate Financial Policy.- 6.3.1. The Valuation of Levered Firms.- 6.3.2. The FISHER Separation Under Uncertainty.- 6.4. Arbitrage Theory And Ross’s Arbitrage Pricing Theory.- List of Assumptions.- Index of Frequently Used Symbols.- References.