Path-dependent Option Valuation when the Underlying Path is Discontinuous

Path-dependent Option Valuation when the Underlying Path is Discontinuous
Author: Chunsheng Zhou
Publisher:
Total Pages: 21
Release: 1997
Genre:
ISBN:

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The payoffs of path-dependent options depend not only on the nal values, but also on the sample paths of the prices of the underlying assets. A rigorous modeling of the under-lying asset price processes which can appropriately describe the sample paths is therefore critical for pricing path-dependent options. This paper allows for discontinuities in the sample paths of the underlying asset prices by assuming that these prices follow jump di usion processes. A general yet tractable approach is presented to value a variety of path-dependent options with discontinuous processes. The numerical examples show that ignoring the jump risk may lead to serious biases in path- dependent option pricing.

Dynamic Asset Pricing Theory

Dynamic Asset Pricing Theory
Author: Darrell Duffie
Publisher: Princeton University Press
Total Pages: 488
Release: 2010-01-27
Genre: Business & Economics
ISBN: 1400829208

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This is a thoroughly updated edition of Dynamic Asset Pricing Theory, the standard text for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimality, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis, so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models. Readers will be particularly intrigued by this latest edition's most significant new feature: a chapter on corporate securities that offers alternative approaches to the valuation of corporate debt. Also, while much of the continuous-time portion of the theory is based on Brownian motion, this third edition introduces jumps--for example, those associated with Poisson arrivals--in order to accommodate surprise events such as bond defaults. Applications include term-structure models, derivative valuation, and hedging methods. Numerical methods covered include Monte Carlo simulation and finite-difference solutions for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. A system of appendixes reviews the necessary mathematical concepts. And references have been updated throughout. With this new edition, Dynamic Asset Pricing Theory remains at the head of the field.

Financial Derivatives

Financial Derivatives
Author: Jamil Baz
Publisher: Cambridge University Press
Total Pages: 358
Release: 2004-01-12
Genre: Business & Economics
ISBN: 9780521815109

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Stochastic Models

Stochastic Models
Author: Donald Andrew Dawson
Publisher: American Mathematical Soc.
Total Pages: 492
Release: 2000
Genre: Mathematics
ISBN: 9780821810637

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This book presents the refereed proceedings of the International Conference on Stochastic Models held in Ottawa (ON, Canada) in honor of Professor Donald A. Dawson. Contributions to the volume were written by students and colleagues of Professor Dawson, many of whom are eminent researchers in their own right. A main theme of the book is the development and study of the Dawson-Watanabe "superprocess", a fundamental building block in modelling interaction particle systems undergoing reproduction and movement. The volume also contains an excellent review article by Professor Dawson and a complete list of his work. This comprehensive work offers a wide assortment of articles on Markov processes, branching processes, mathematical finance, filtering, queueing networks, time series, and statistics. It should be of interest to a broad mathematical audience.

Derivative Products and Pricing

Derivative Products and Pricing
Author: Satyajit Das
Publisher: John Wiley & Sons
Total Pages: 873
Release: 2005-10-06
Genre: Business & Economics
ISBN: 0470821647

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Derivative Products & Pricing consists of 4 Parts divided into 16 chapters covering the role and function of derivatives, basic derivative instruments (exchange traded products (futures and options on future contracts) and over-the-counter products (forwards, options and swaps)), the pricing and valuation of derivatives instruments, derivative trading and portfolio management.

Unified Financial Analysis

Unified Financial Analysis
Author: Willi Brammertz
Publisher: John Wiley & Sons
Total Pages: 463
Release: 2011-11-04
Genre: Business & Economics
ISBN: 1119991102

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Unified Financial Analysis arrives at the right time, in the midst of the current financial crisis where the call for better and more efficient financial control cannot be overstated. The book argues that from a technical perspective, there is no need for more, but for better and more efficiently organized information. The title demonstrates that it is possible with a single but well organized set of information and algorithms to derive all types of financial analysis. This reaches far beyond classical risk and return or profitability management, spanning all risk categories, all valuation techniques (local GAAP, IFRS, full mark-to-market and so on) and static, historic and dynamic analysis, just to name the most important dimensions. The dedication of a complete section to dynamic analysis, which is based on a going concern view, is unique, contrasting with the static, liquidation-based view prevalent today in banks. The commonly applied arbitrage-free paradigm, which is too narrow, is expanded to real world market models. The title starts with a brief history of the evolution of financial analysis to create the current industry structure, with the organisation of many banks following a strict silo structure, and finishes with suggestions for the way forward from the current financial turmoil. Throughout the book, the authors advocate the adoption of a 'unified financial language' that could also be the basis for a new regulatory approach. They argue that such a language is indispensable, if the next regulatory wave – which is surely to come – should not end in an expensive regulatory chaos. Unified Financial Analysis will be of value to CEOs and CFOs in banking and insurance, risk and asset and liability managers, regulators and compliance officers, students of Finance or Economics, or anyone with a stake in the finance industry.