Financial Derivatives in Theory and Practice, Revised EditionISBN: 9780470863589
468 pages
July 2004

The book originally published in March 2000 to widespread acclaim. This revised edition has been updated with minor corrections and new references, and now includes a chapter of exercises and solutions, enabling use as a course text.
 Comprehensive introduction to the theory and practice of financial derivatives.
 Discusses and elaborates on the theory of interest rate derivatives, an area of increasing interest.
 Divided into two selfcontained parts ? the first concentrating on the theory of stochastic calculus, and the second describes in detail the pricing of a number of different derivatives in practice.
 Written by well respected academics with experience in the banking industry.
A valuable text for practitioners in research departments of all banking and finance sectors. Academic researchers and graduate students working in mathematical finance.
Preface.
Acknowledgements.
Part I: Theory.
1 SinglePeriod Option Pricing.
1.1 Option pricing in a nutshell.
1.2 The simplest setting.
1.3 General oneperiod economy.
1.4 A twoperiod example.
2 Brownian Motion.
2.1 Introduction.
2.2 Definition and existence.
2.3 Basic properties of Brownian motion.
2.4 Strong Markov property.
3 Martingales.
3.1 Definition and basic properties.
3.2 Classes of martingales.
3.3 Stopping times and the optional sampling theorem.
3.4 Variation, quadratic variation and integration.
3.5 Local martingales and semimartingales.
3.6 Supermartingales and the Doob—Meyer decomposition.
4 Stochastic Integration.
4.1 Outline.
4.2 Predictable processes.
4.3 Stochastic integrals: the L2 theory.
4.4 Properties of the stochastic integral.
4.5 Extensions via localization.
4.6 Stochastic calculus: Itô’s formula.
5 Girsanov and Martingale Representation.
5.1 Equivalent probability measures and the Radon—Nikodým derivative.
5.1.1 Basic results and properties.
5.2 Girsanov’s theorem.
5.3 Martingale representation theorem.
6 Stochastic Differential Equations.
6.1 Introduction.
6.2 Formal definition of an SDE.
6.3 An aside on the canonical setup.
6.4 Weak and strong solutions.
6.5 Establishing existence and uniqueness: Itô theory.
6.6 Strong Markov property.
6.7 Martingale representation revisited.
7 Option Pricing in Continuous Time.
7.1 Asset price processes and trading strategies.
7.2 Pricing European options.
7.3 Continuous time theory.
7.4 Extensions.
8 Dynamic Term Structure Models.
8.1 Introduction.
8.2 An economy of pure discount bonds.
8.3 Modelling the term structure.
Part II: Practice.
9 Modelling in Practice.
9.1 Introduction.
9.2 The real world is not a martingale measure.
9.3 Productbased modelling.
9.4 Local versus global calibration.
10 Basic Instruments and Terminology.
10.1 Introduction.
10.2 Deposits.
10.3 Forward rate agreements.
10.4 Interest rate swaps.
10.5 Zero coupon bonds.
10.6 Discount factors and valuation.
11 Pricing Standard Market Derivatives.
11.1 Introduction.
11.2 Forward rate agreements and swaps.
11.3 Caps and floors.
11.4 Vanilla swaptions.
11.5 Digital options.
12 Futures Contracts.
12.1 Introduction.
12.2 Futures contract definition.
12.3 Characterizing the futures price process.
12.4 Recovering the futures price process.
12.5 Relationship between forwards and futures.
Orientation: Pricing Exotic European Derivatives.
13 Terminal SwapRate Models.
13.1 Introduction.
13.2 Terminal time modelling.
13.3 Example terminal swaprate models.
13.4 Arbitragefree property of terminal swaprate models.
13.5 Zero coupon swaptions.
14 Convexity Corrections.
14.1 Introduction.
14.2 Valuation of ‘convexityrelated’ products.
14.3 Examples and extensions.
15 Implied Interest Rate Pricing Models.
15.1 Introduction.
15.2 Implying the functional form DTS.
15.3 Numerical implementation.
15.4 Irregular swaptions.
15.5 Numerical comparison of exponential and implied swaprate models.
16 MultiCurrency Terminal SwapRate Models.
16.1 Introduction.
16.2 Model construction.
16.3 Examples.
16.3.1 Spread options.
Orientation: Pricing Exotic American and PathDependent Derivatives.
17 ShortRate Models.
17.1 Introduction.
17.2 Wellknown shortrate models.
17.3 Parameter fitting within the Vasicek—Hull—White model.
17.4 Bermudan swaptions via Vasicek—Hull—White.
18 Market Models.
18.1 Introduction.
18.2 LIBOR market models.
18.3 Regular swapmarket models.
18.4 Reverse swapmarket models.
19 MarkovFunctional Modelling.
19.1 Introduction.
19.2 Markovfunctional models.
19.3 Fitting a onedimensional Markovfunctional model to swaption prices.
19.4 Example models.
19.5 Multidimensional Markovfunctional models.
19.5.1 Lognormally driven Markovfunctional models.
19.6 Relationship to market models.
19.7 Mean reversion, forward volatilities and correlation.
19.7.1 Mean reversion and correlation.
19.7.2 Mean reversion and forward volatilities.
19.7.3 Mean reversion within the Markovfunctional LIBOR model.
19.8 Some numerical results.
20 Exercises and Solutions.
Appendix 1: The Usual Conditions.
Appendix 2: L^{2} Spaces.
Appendix 3: Gaussian Calculations.
References.
Index.
 Comprehensive introduction to the theory and practice of financial derivatives.
 Discusses and elaborates on the theory of interest rate derivatives, an area of increasing interest.
 Divided into two selfcontained parts – the first concentrating on the theory of stochastic calculus, and the second describes in detail the pricing of a number of different derivatives in practice.
 Written by well respected academics with experience in the banking industry.
 Now includes a new chapter of exercises and solutions, enabling use for selfstudy or as a course text.
 Text has been updated with new references and many
corrections.