New directions in mathematical finance / edited by Paul Wilmott and Henrik Rasmussen.

Format:

Book

Contributor:

Wilmott, Paul.

Rasmussen, Henrik O., 1966-

Series:

Wiley finance series

Wiley finance

Language:

English

Subjects (All):

Securities--Mathematical models.

Securities.

Investments--Mathematical models.

Investments.

Risk management--Mathematical models.

Risk management.

Physical Description:

xii, 192 pages : illustrations ; 25 cm.

Place of Publication:

Chichester, West Sussex, England ; New York, NY, USA : J. Wiley & Sons, [2002]

Summary:

A compilation of the most respected authorities in financial engineering Based around a conference on financial modeling held in Milan in December 1999, New Directions in Mathematical Finance brings together the leading names in quantitative finance to discuss the most current modeling techniques in a variety of areas of financial engineering. The contributions featured in this volume are all new items, based on each speaker's topic of presentation at the convention. Editors Paul Wilmott and Henrik Rasmussen include an introduction which pulls together the themes of the book.

Contents:

1 The quantitative finance timeline / Paul Wilmott 1

1827 Brown 1

1900 Bachelier 1

1905 Einstein 1

1923 Wiener 1

1950s Samuelson 1

1951 Ito 2

1952 Markowitz 2

1963 Sharpe, Lintner and Mossin 3

1966 Fama 3

1960s Sobol', Faure, Hammersley, Haselgrove, Halton... 3

1968 Thorp 4

1973 Black, Scholes and Merton 4

1977 Boyle 5

1977 Vasicek 5

1979 Cox, Ross, Rubinstein 6

1979-81 Harrison, Kreps, Pliska 6

1986 Ho and Lee 7

1992 Heath, Jarrow and Morton 7

1990s Credit risk 7

1990s Cheyette, Barrett, Moore, Wilmott 7

1994 Dupire, Rubinstein, Derman and Kani 8

1996 Avellaneda and Paras 8

And the Nobel Prize for Economics goes to ... 9

Part 1 New Directions in Equity Modelling 11

Asymptotic analysis of stochastic volatility models 14

Passport options: a review 15

Equity dividend models 15

Isoperimetry, log-concavity and elasticity of option prices 16

Models needed 16

3 Asymptotic analysis of stochastic volatility models / Henrik Rasmussen, Paul Wilmott 19

Conditions on the models 20

Examples of models 21

Scott's model 21

The Heston/Ball-Roma model 22

Asymptotic analysis 23

Vanilla options: asymptotics for values 26

Vanilla options: implied volatilities 28

4 Passport options: a review / Antony Penaud 33

The vanilla passport option 34

The stochastic control approach 34

The martingale approach 36

Utility of trading passport 37

Exotic passport options 42

Multi-asset passport option 42

Discrete trading constraints 44

Vacation calls and vacation puts 47

Miscellaneous exotic 49

5 Equity dividend models / David Bakstein, Paul Wilmott 55

Effects of dividends on asset prices 56

Frictionless markets 56

Market frictions 57

Non-stochastic dividend models 58

Known dividends 58

Non-Markovian models 61

Non-linear models 62

Stochastic dividend models 66

Diffusive dividend processes 66

Random jump processes 68

Criteria for model choice and summary 69

Sensitivity ratios 70

Time to expiry 70

Computational cost 70

Type of instrument 70

6 Isoperimetry, log-concavity and elasticity of option prices / Christer Borell 73

A brief review of isoperimetry in option pricing 73

Log-concavity 76

Log-concavity applied to option pricing 84

Part 2 New Directions in Interest Rate Modelling 93

Dynamic, deterministic and static optimal portfolio strategies in a mean

variance framework under stochastic interest rates 96

Pricing bond options in a worst-case scenario 97

Models needed 98

8 Dynamic, deterministic and static optimal portfolio strategies in a mean

variance framework under stochastic interest rates / Isabelle Bajeux-Besnainou, Roland Portait 101

The framework 102

Mean

variance efficient strategies when stochastic rebalancing is allowed 104

Predetermined weights: deterministic mean

variance dynamic efficiency 105

Buy-and-hold strategies 106

Simulations and comparison of the different cases 107

9 Pricing bond options in a worst-case scenario / David Epstein, Paul Wilmott 117

A worst-case scenario valuation 118

The pricing problem with optionality 119

Pricing a European option on a zero-coupon bond 119

Hedging the European option with the underlying zero-coupon bond 121

Hedging the European option with other instruments 123

Pricing and hedging American options 128

Part 3 New Directions in Risk Management 135

Chapters 11 to 13 137

Implementing VaR by historical simulation 137

CrashMetrics 138

Herding in financial markets: a role for psychology in explaining investor behaviour? 138

Models needed 138

11 Implementing VaR by historical simulation / Aldo Nassigh, Andrea Piazzetta, Ferdinando Samaria 141

Historical simulation: the partial revaluation approach 141

Implementing Value at Risk: a practical example 144

12 CrashMetrics / Philip Hua, Paul Wilmott 153

Why do banks go broke? 153

Market crashes 153

CrashMetrics 154

CrashMetrics for one stock 155

Portfolio optimisation and the Platinum Hedge 157

The multi-asset/single-index model 157

Portfolio optimisation and the Platinum Hedge in the multi-asset model 161

The multi-index model 162

Crash dispersion 163

Bias effects 163

Analysis of data 164

Margin calls and margin hedging 165

What is margin? 165

Modelling margin 165

Counterparty risk 166

Simple extensions to CrashMetrics 166

The CrashMetrics Index 166

13 Herding in financial markets: a role for psychology in explaining investor behaviour? / Henriette Prast 169

Herding in economic theory 169

Psychology in finance: existing research 172

The psychology of crowd behaviour: the theory of cognitive dissonance 174

Principle of congruity 174

The theory of cognitive dissonance 174.

Notes:

Includes bibliographical references and index.

ISBN:

0471498173

OCLC:

48398965