Financial risk management has become a popular practice amongst financial institutions to
protect against the adverse effects of uncertainty caused by fluctuations in interest
rates, exchange rates, commodity prices, and equity prices. New financial instruments and
mathematical techniques are continuously developed and introduced in financial practice.
These techniques are being used by an increasing number of firms, traders and financial
risk managers across various industries. Risk and Financial Management: Mathematical and
Computational Methods confronts the many issues and controversies, and explains the
fundamental concepts that underpin financial risk management.
- Provides a comprehensive
introduction to the core topics of risk and financial management.
- Adopts a pragmatic approach,
focused on computational, rather than just theoretical, methods.
- Bridges the gap between
theory and practice in financial risk management
- Includes coverage of utility
theory, probability, options and derivatives, stochastic volatility and value at risk.
- Suitable for students of
risk, mathematical finance, and financial risk management, and finance practitioners.
- Includes extensive reference
lists, applications and suggestions for further reading.
Risk and Financial
Management: Mathematical and Computational Methods is ideally suited to both students of
mathematical finance with little background in economics and finance, and students of
financial risk management, as well as finance practitioners requiring a clearer
understanding of the mathematical and computational methods they use every day. It
combines the required level of rigor, to support the theoretical developments, with a
practical flavour through many examples and applications.
Table of Contents
Preface.
Part I: Finance and Risk
Management.
Chapter 1: Potpourri.
1.1 Introduction.
1.2 Theoretical finance and
decision making.
1.3 Insurance and actuarial
science.
1.4 Uncertainty and risk in
finance.
1.4.1 Foreign exchange risk.
1.4.2 Currency risk.
1.4.3 Credit risk.
1.4.4 Other risks.
1.5 Financial physics.
Selected introductory
reading.
Chapter 2: Making Economic
Decisions under Uncertainty.
2.1 Decision makers and
rationality.
2.1.1 The principles of
rationality and bounded rationality.
2.2 Bayes decision making.
2.2.1 Risk management.
2.3 Decision criteria.
2.3.1 The expected value (or
Bayes) criterion.
2.3.2 Principle of (Laplace)
insufficient reason.
2.3.3 The minimax (maximin)
criterion.
2.3.4 The maximax (minimin)
criterion.
2.3.5 The minimax regret or
Savage's regret criterion.
2.4 Decision tables and
scenario analysis.
2.4.1 The opportunity loss
table.
2.5 EMV, EOL, EPPI, EVPI.
2.5.1 The deterministic
analysis.
2.5.2 The probabilistic
analysis.
Selected references and
readings.
Chapter 3: Expected Utility.
3.1 The concept of utility.
3.1.1 Lotteries and utility
functions.
3.2 Utility and risk
behaviour.
3.2.1 Risk aversion.
3.2.2 Expected utility
bounds.
3.2.3 Some utility
functions.
3.2.4 Risk sharing.
3.3 Insurance, risk
management and expected utility.
3.3.1 Insurance and premium
payments.
3.4 Critiques of expected
utility theory.
3.4.1 Bernoulli, Buffon,
Cramer and Feller.
3.4.2 Allais Paradox.
3.5 Expected utility and
finance.
3.5.1 Traditional valuation
3.5.2 Individual investment
and consumption.
3.5.3 Investment and the
CAPM.
3.5.4 Portfolio and utility
maximization in practice.
3.5.5 Capital markets and
the CAPM again.
3.5.6 Stochastic discount
factor, assets pricing and the Euler equation.
3.6 Information asymmetry.
3.6.1 'The lemon
phenomenon' or adverse selection.
3.6.2 'The moral hazard
problem'.
3.6.3 Examples of moral
hazard.
3.6.4 Signalling and
screening.
3.6.5 The principal-agent
problem.
References and further
reading.
Chapter 4: Probability and
Finance.
4.1 Introduction.
4.2 Uncertainty, games of
chance and martingales.
4.3 Uncertainty, random
walks and stochastic processes.
4.3.1 The random walk.
4.3.2 Properties of
stochastic processes.
4.4 Stochastic calculus.
4.4.1 Ito's Lemma.
4.5 Applications of Ito's
Lemma.
4.5.1 Applications.
4.5.2 Time discretization of
continuous-time finance models.
4.5.3 The Girsanov Theorem
and martingales*.
References and further
reading.
Chapter 5: Derivatives
Finance.
5.1 Equilibrium valuation
and rational expectations.
5.2 Financial instruments.
5.2.1 Forward and futures
contracts.
5.2.2 Options.
5.3 Hedging and
institutions.
5.3.1 Hedging and hedge
funds.
5.3.2 Other hedge funds and
investment strategies.
5.3.3 Investor protection
rules.
References and additional
reading.
Part II: Mathematical and
Computational Finance.
Chapter 6: Options and
Derivatives Finance Mathematics.
6.1 Introduction to call
options valuation.
6.1.1 Option valuation and
rational expectations.
6.1.2 Risk-neutral pricing.
6.1.3 Multiple periods with
binomial trees.
6.2 Forward and futures
contracts.
6.3 Risk-neutral
probabilities again.
6.3.1 Rational expectations
and optimal forecasts.
6.4 The Black-Scholes
options formula.
6.4.1 Options, their
sensitivity and hedging parameters.
6.4.2 Option bounds and
put-call parity.
6.4.3 American put options.
References and additional
reading.
Chapter 7: Options and
Practice.
7.1 Introduction.
7.2 Packaged options.
7.3 Compound options and
stock options.
7.3.1 Warrants.
7.3.2 Other options.
7.4 Options and practice.
7.4.1 Plain vanilla
strategies.
7.4.2 Covered call
strategies: selling a call and a share.
7.4.3 Put and protective put
strategies: buying a put and a stock.
7.4.4 Spread strategies.
7.4.5 Straddle and strangle
strategies.
7.4.6 Strip and strap
strategies.
7.4.7 Butterfly and condor
spread strategies.
7.4.8 Dynamic strategies and
the Greeks.
7.5 Stopping time
strategies*.
7.5.1 Stopping time sell and
buy strategies.
7.6 Specific application
areas.
7.7 Option misses.
References and additional
reading.
Appendix: First passage
time*.
Chapter 8: Fixed Income,
Bonds and Interest Rates.
8.1 Bonds and yield curve
mathematics.
8.1.1 The zero-coupon,
default-free bond.
8.1.2 Coupon-bearing bonds.
8.1.3 Net present values
(NPV).
8.1.4 Duration and
convexity.
8.2 Bonds and forward rates.
8.3 Default bonds and risky
debt.
8.4 Rated bonds and default.
8.4.1 A Markov chain and
rating.
8.4.2 Bond sensitivity to
rates - duration.
8.4.3 Pricing rated bonds
and the term structure risk-free rates*.
8.4.4 Valuation of
default-prone rated bonds*.
8.5 Interest-rate processes,
yields and bond valuation*.
8.5.1 The Vasicek
interest-rate model.
8.5.2 Stochastic volatility
interest-rate models.
8.5.3 Term structure and
interest rates.
8.6 Options on bonds*.
8.6.1 Convertible bonds.
8.6.2 Caps, floors, collars
and range notes.
8.6.3 Swaps.
References and additional
reading.
Mathematical appendix.
A.1: Term structure and
interest rates.
A.2: Options on bonds.
Chapter 9: Incomplete
Markets and Stochastic Volatility.
9.1 Volatility defined.
9.2 Memory and volatility.
9.3 Volatility, equilibrium
and incomplete markets.
9.3.1 Incomplete markets.
9.4 Process variance and
volatility.
9.5 Implicit volatility and
the volatility smile.
9.6 Stochastic volatility
models.
9.6.1 Stochastic volatility
binomial models*.
9.6.2 Continuous-time
volatility models.
9.7 Equilibrium, SDF and the
Euler equations*.
9.8 Selected Topics*.
9.8.1 The Hull and White
model and stochastic volatility.
9.8.2 Options and jump
processes.
9.9 The range process and
volatility.
References and additional
reading.
Appendix: Development for
the Hull and White model (1987)*.
Chapter 10: Value at Risk
and Risk Management.
10.1 Introduction.
10.2 VaR definitions and
applications.
10.3 VaR statistics.
10.3.1 The historical VaR
approach.
10.3.2 The analytic
variance-covariance approach.
10.3.3 VaR and extreme
statistics.
10.3.4 Copulae and portfolio
VaR measurement.
10.3.5 Multivariate risk
functions and the principle of maximum entropy.
10.3.6 Monte Carlo
simulation and VaR.
10.4 VaR efficiency.
10.4.1 VaR and portfolio
risk efficiency with normal returns.
10.4.2 VaR and regret.
References and additional
reading.
Author Index.
Subject Index.
338 pages