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Featuring international contributors from both industry and
academia, Numerical Methods for Finance explores new and relevant
numerical methods for the solution of practical problems in
finance. It is one of the few books entirely devoted to numerical
methods as applied to the financial field. Presenting
state-of-the-art methods in this area, the book first discusses the
coherent risk measures theory and how it applies to practical risk
management. It then proposes a new method for pricing
high-dimensional American options, followed by a description of the
negative inter-risk diversification effects between credit and
market risk. After evaluating counterparty risk for interest rate
payoffs, the text considers strategies and issues concerning
defined contribution pension plans and participating life insurance
contracts. It also develops a computationally efficient swaption
pricing technology, extracts the underlying asset price
distribution implied by option prices, and proposes a hybrid GARCH
model as well as a new affine point process framework. In addition,
the book examines performance-dependent options, variance
reduction, Value at Risk (VaR), the differential evolution
optimizer, and put-call-futures parity arbitrage opportunities.
Sponsored by DEPFA Bank, IDA Ireland, and Pioneer Investments, this
concise and well-illustrated book equips practitioners with the
necessary information to make important financial decisions.
This monograph deals with the asymptotic behaviour, and in
particular the largest fluctuations, of various classes of
stochastic differential equations (SDEs) and their discretisations.
Equations subject to Markovian switching are also studied, allowing
the drift and diffusion coefficients to switch randomly according
to a Markov jump process. The assumptions are motivated by the
large fluctuations experienced by financial markets which are
subjected to random regime shifts. Such results are then applied to
a variant of the classical Geometric Brownian Motion (GBM) market
model. Moreover it is shown that discrete approximations to these
equations, using standard and split-step implicit Euler-Maruyama
methods, exhibit asymptotic behaviour which is consistent with
their continuous-time counterparts.
The book deals with the asymptotic behaviour of stochastic
difference and functional differential equations of Ito type. The
equations have a form which make them suitable to model financial
markets in which agents use past prices. The main results of the
time sysyetms concern the almost sure largest fluctuations of the
cumulative returns. These results are robust to the
time-discretisation of the process and to the presence of
non-linearities in the traders' demand schedules. The conditions
for, and dynamics in, a market experiencing a bubble or crash are
also described. Numerical methods which both minimise error and
preserve the features of the underlying continuous equation are
studied and the methods are simulated on computer.
Featuring engaging narratives, this "how-to" book delves into
reflection as a concept and provides specific, replicable tools for
professional practice. Each chapter draws on a particular school
situation demonstrating the value of teacher reflection and
describing the nuts and bolts of the process, including protocols
for handling many different circumstances.
Featuring international contributors from both industry and
academia, Numerical Methods for Finance explores new and relevant
numerical methods for the solution of practical problems in
finance. It is one of the few books entirely devoted to numerical
methods as applied to the financial field. Presenting
state-of-the-art methods in this area, the book first discusses the
coherent risk measures theory and how it applies to practical risk
management. It then proposes a new method for pricing
high-dimensional American options, followed by a description of the
negative inter-risk diversification effects between credit and
market risk. After evaluating counterparty risk for interest rate
payoffs, the text considers strategies and issues concerning
defined contribution pension plans and participating life insurance
contracts. It also develops a computationally efficient swaption
pricing technology, extracts the underlying asset price
distribution implied by option prices, and proposes a hybrid GARCH
model as well as a new affine point process framework. In addition,
the book examines performance-dependent options, variance
reduction, Value at Risk (VaR), the differential evolution
optimizer, and put-call-futures parity arbitrage opportunities.
Sponsored by DEPFA Bank, IDA Ireland, and Pioneer Investments, this
concise and well-illustrated book equips practitioners with the
necessary information to make important financial decisions.
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