Market-Conform Valuation of Options

1. Front Matter

   Pages I-VIII

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2. Introduction

   Pages 1-10

3. Construction of Arbitrage-Free Implied Trees: A New Approach

   Pages 11-38

4. Market-Conform Option Valuation: An Empirical Assessment of Alternative Approaches

   Pages 39-67

5. Market-Conform Valuation of American-Style Options via Monte Carlo Simulation

   Pages 69-93

6. Synopsis

   Pages 95-104

7. Back Matter

   Pages 105-106

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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.

• Arbitrage
• Barrier Options
• Computational Finance
• Financial Derivatives
• Numerical Methods
• Option Valuation
• Options
• quantitative finance

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)

• Graduate Program “Finance and Monetary Economics” Faculty of Economics and Business Administration, Johann Wolfgang Goethe University, Frankfurt am Main, Germany

  Tobias Herwig

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