Martingale Methods in Financial Modelling

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Springer Science & Business Media, Jan 21, 2006 - Business & Economics - 638 pages
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In the 2nd edition some sections of Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk. As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility.

In the 3rd printing of the 2nd edition, the second Chapter on discrete-time markets has been extensively revised. Proofs of several results are simplified and completely new sections on optimal stopping problems and Dynkin games are added. Applications to the valuation and hedging of American-style and game options are presented in some detail.

The theme of stochastic volatility also reappears systematically in the second part of the book, which has been revised fundamentally, presenting much more detailed analyses of the various interest-rate models available: the authors' perspectiveáthroughout is that the choice of a model should be based on the reality of how a particular sector of the financial market functions, never neglecting to examine liquid primary and derivative assets and identifying the sources of trading risk associated. This long-awaited new edition of an outstandingly successful, well-established book, concentrating on the most pertinent and widely accepted modelling approaches, provides the reader with a text focused on practical rather than theoretical aspects of financial modelling.

 

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Implied vola approximation

Contents

An Introduction to Financial Derivatives
3
Discretetime Security Markets
35
Benchmark Models in Continuous Time
112
Foreign Market Derivatives
181
American Options
205
Exotic Options
229
Volatility Risk
253
Continuoustime Security Markets
315
ShortTerm Rate Models
382
Models of Instantaneous Forward Rates
417
Market LIBOR Models
469
Alternative Market Models
517
Crosscurrency Derivatives
572
Part III APPENDIX
608
An Overview of It˘ Stochastic Calculus
609
ReferencesReferencesReferences
657

Part II Fixedincome Markets
348
Interest Rates and Related Contracts
351

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Page 9 - FORWARD CONTRACTS A forward contract is an agreement to buy or sell an asset on a specified date for a specified price. One of the parties to the contract assumes a long position and agrees to buy the underlying asset on a certain specified future date, for a certain specified price. The other party assumes a short position and agrees to sell the asset on the same date for the same price. Other contract details like delivery date, price and quantity are negotiated bilaterally by the parties to the...
Page 6 - At the time the bid and the ask are quoted, the market maker does not know whether the trader who asked for the quotes wants to buy or sell the option. The...
Page 11 - A call option gives the holder the right to buy the underlying asset by a certain date, called the maturity or expiration date, for a certain price, called exercise or strike price.
Page 10 - An option is a contract that gives its holder the right, but not the obligation, to buy or sell an asset on or before a future date at a specified price.
Page 8 - If a call futures option is exercised, the holder gets a long position in the underlying futures contract plus a cash amount equal to the current futures price minus the exercise price. If a put futures option is exercised, the holder...

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