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.

From the reviews:

"This book is the author's doctoral thesis. It is for students and professionals in option pricing and related topics. The focus of this book lays on the development of new approaches of market-conform valuation of derivatives. The new approaches are demonstrated by some examples." (Klaus Ehemann, Zentralblatt MATH, Vol. 1116 (18), 2007)

Klappentext
The focus of this volume is on the development of new approaches for the market-conform valuation of newly issued derivatives. The first chapter presents a flexible approach to construct the binomial process of the underlying asset price by using a simultaneously backward and forward induction algorithm. This framework can be used to price and hedge a wide range of plain-vanilla and exotic options. In the second chapter this new approach is compared to existing models using a sample of plain-vanilla options, American call options and European Barrier options from two competing markets. In the third chapter new methods to value American-style options via Monte Carlo simulations in accordance with given market prices are discussed. After a short introduction to Monte Carlo methods, two new approaches are proposed. These new frameworks are illustrated via pricing examples for standard American put options. TOC:Introduction.- Construction of Arbitrage-Free Implied Trees: A New Approach.- Market-Conform Option Valuation: An Empirical Assessment of Alternative Approaches.- Market-Conform Valuation of American-Style Options via Monte Carlo Simulation.- Synopsis.

Inhalt
Construction of Arbitrage-Free Implied Trees: A New Approach.- Market-Conform Option Valuation: An Empirical Assessment of Alternative Approaches.- Market-Conform Valuation of American-Style Options via Monte Carlo Simulation.- Synopsis.