Market-Conform Valuation of Options

  • Tobias Herwig

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 571)

About this book

Introduction

1. 1 The Area of Research In this thesis, we will investigate the 'market-conform' pricing of newly issued contingent claims. A contingent claim is a derivative whose value at any settlement date is determined by the value of one or more other underlying assets, e. g. , forwards, futures, plain-vanilla or exotic options with European or American-style exercise features. Market-conform pricing means that prices of existing actively traded securities are taken as given, and then the set of equivalent martingale measures that are consistent with the initial prices of the traded securities is derived using no-arbitrage arguments. Sometimes in the literature other expressions are used for 'market-conform' valuation - 'smile-consistent' valuation or 'fair-market' valuation - that describe the same basic idea. The seminal work by Black and Scholes (1973) (BS) and Merton (1973) mark a breakthrough in the problem of hedging and pricing contingent claims based on no-arbitrage arguments. Harrison and Kreps (1979) provide a firm mathematical foundation for the Black-Scholes- Merton analysis. They show that the absence of arbitrage is equivalent to the existence of an equivalent martingale measure. Under this mea­ sure the normalized security price process forms a martingale and so securities can be valued by taking expectations. If the securities market is complete, then the equivalent martingale measure and hence the price of any security are unique.

Keywords

Arbitrage Barrier Options Computational Finance Financial Derivatives Numerical Methods Option Valuation Options

Authors and affiliations

  • Tobias Herwig
    • 1
  1. 1.Graduate Program “Finance and Monetary Economics” Faculty of Economics and Business AdministrationJohann Wolfgang Goethe UniversityFrankfurt am MainGermany

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-30838-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Business and Economics
  • Print ISBN 978-3-540-30837-9
  • Online ISBN 978-3-540-30838-6
  • Series Print ISSN 0075-8442
  • About this book