An Analytic Approach to the Valuation of American Path Dependent Options

An Analytic Approach to the Valuation of American Path Dependent Options
Author: Bin Gao
Publisher:
Total Pages: 47
Release: 2009
Genre:
ISBN:

In this paper, we propose a general method for pricing and hedging non-standard American options. The proposed method applies to any kind of American-style contract for which the payoff function has a Markovian representation in the state space. Specifically, we obtain an analytic solution for the value and hedge parameters of path-dependent American options such as barrier options. The solution includes standard American options as a special case. The analytic formula also allows us to identify and exploit two key properties of the optimal exercise boundary-homogeneity in price parameters and time-invariance acirc;not; for American options. In addition, some new put-call acirc;not;Ssymmetryacirc;not;? relations are also derived. These properties suggest a new, efficient and integrated approach to pricing and hedging a variety of standard and non-standard American options. From an implementation perspective, this approach avoids the current practice of repetitive computation of options prices and hedge ratios. Our implementation of the analytic formula for barrier options indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. In some cases, our method is faster by about four orders of magnitude than existing numerical methods with equal accuracy. In particular, the method overcomes the difficulty that existing numerical methods have in dealing with prices close to the barrier, the case where the barrier matters most.

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:

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.

Option Theory

Option Theory
Author: Peter James
Publisher: John Wiley & Sons
Total Pages: 388
Release: 2003-04-04
Genre: Business & Economics
ISBN: 0470857951

A unified development of the subject, presenting the theory of options in each of the different forms and stressing the equivalence between each of the methodologies. * Demystifies some of the more complex topics. * Derives practical, tangible results using the theory, to help practitioners in problem solving. * Applies the results obtained to the analysis and pricing of options in the equity, currency, commodity and interest rate markets. * Gives the reader the analytical tools and technical jargon to understand the current technical literature available. * Provides a user-friendly reference on option theory for practicing investors and traders.

The Statistical Mechanics of Financial Markets

The Statistical Mechanics of Financial Markets
Author: Johannes Voit
Publisher: Springer Science & Business Media
Total Pages: 385
Release: 2005-12-28
Genre: Mathematics
ISBN: 354026289X

The present third edition of The Statistical Mechanics of Financial Markets is published only four years after the ?rst edition. The success of the book highlights the interest in a summary of the broad research activities on the application of statistical physics to ?nancial markets. I am very grateful to readers and reviewers for their positive reception and comments. Why then prepare a new edition instead of only reprinting and correcting the second edition? The new edition has been signi?cantly expanded, giving it a more pr- tical twist towards banking. The most important extensions are due to my practical experience as a risk manager in the German Savings Banks’ As- ciation (DSGV): Two new chapters on risk management and on the closely related topic of economic and regulatory capital for ?nancial institutions, - spectively, have been added. The chapter on risk management contains both the basics as well as advanced topics, e. g. coherent risk measures, which have not yet reached the statistical physics community interested in ?nancial m- kets. Similarly, it is surprising how little research by academic physicists has appeared on topics relating to Basel II. Basel II is the new capital adequacy framework which will set the standards in risk management in many co- tries for the years to come. Basel II is responsible for many job openings in banks for which physicists are extemely well quali?ed. For these reasons, an outline of Basel II takes a major part of the chapter on capital.

Handbook in Monte Carlo Simulation

Handbook in Monte Carlo Simulation
Author: Paolo Brandimarte
Publisher: John Wiley & Sons
Total Pages: 620
Release: 2014-06-20
Genre: Business & Economics
ISBN: 1118594517

An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization. The Handbook in Monte Carlo Simulation features: An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials Carefully crafted examples in order to spot potential pitfalls and drawbacks of each approach An accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methods Numerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentation The Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation.

Financial Mathematics

Financial Mathematics
Author: Giuseppe Campolieti
Publisher: CRC Press
Total Pages: 826
Release: 2014-03-12
Genre: Business & Economics
ISBN: 1439892431

Versatile for Several Interrelated Courses at the Undergraduate and Graduate Levels Financial Mathematics: A Comprehensive Treatment provides a unified, self-contained account of the main theory and application of methods behind modern-day financial mathematics. Tested and refined through years of the authors’ teaching experiences, the book encompasses a breadth of topics, from introductory to more advanced ones. Accessible to undergraduate students in mathematics, finance, actuarial science, economics, and related quantitative areas, much of the text covers essential material for core curriculum courses on financial mathematics. Some of the more advanced topics, such as formal derivative pricing theory, stochastic calculus, Monte Carlo simulation, and numerical methods, can be used in courses at the graduate level. Researchers and practitioners in quantitative finance will also benefit from the combination of analytical and numerical methods for solving various derivative pricing problems. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. The book provides complete coverage of both discrete- and continuous-time financial models that form the cornerstones of financial derivative pricing theory. It also presents a self-contained introduction to stochastic calculus and martingale theory, which are key fundamental elements in quantitative finance.

Mathematical Techniques in Finance

Mathematical Techniques in Finance
Author: Amir Sadr
Publisher: John Wiley & Sons
Total Pages: 278
Release: 2022-04-21
Genre: Business & Economics
ISBN: 111983841X

Explore the foundations of modern finance with this intuitive mathematical guide In Mathematical Techniques in Finance: An Introduction, distinguished finance professional Amir Sadr delivers an essential and practical guide to the mathematical foundations of various areas of finance, including corporate finance, investments, risk management, and more. Readers will discover a wealth of accessible information that reveals the underpinnings of business and finance. You’ll learn about: Investment theory, including utility theory, mean-variance theory and asset allocation, and the Capital Asset Pricing Model Derivatives, including forwards, options, the random walk, and Brownian Motion Interest rate curves, including yield curves, interest rate swap curves, and interest rate derivatives Complete with math reviews, useful Excel functions, and a glossary of financial terms, Mathematical Techniques in Finance: An Introduction is required reading for students and professionals in finance.