"Financial Modelling - Theory, Implementation and Practice" is a
unique combination of quantitative techniques, the application to
financial problems and programming using Matlab. The book enables
the reader to model, design and implement a wide range of financial
models for derivatives pricing and asset allocation, providing
practitioners with complete financial modelling workflow, from
model choice, deriving prices and Greeks using (semi-) analytic and
simulation techniques, and calibration even for exotic options.
The book is split into three parts. The first part considers
financial markets in general and looks at the complex models needed
to handle observed structures, reviewing models based on diffusions
including stochastic-local volatility models and (pure) jump
processes. It shows the possible risk neutral densities, implied
volatility surfaces, option pricing and typical paths for a variety
of models including SABR, Heston, Bates, Bates-Hull-White,
Displaced-Heston, or stochastic volatility versions of Variance
Gamma, respectively Normal Inverse Gaussian models and finally,
multi-dimensional models. The stochastic-local-volatility Libor
market model with time-dependent parameters is considered and as an
application how to price and risk-manage CMS spread products is
The second part of the book deals with numerical methods which
enables the reader to use the models of the first part for pricing
and risk management, covering methods based on direct integration
and Fourier transforms, and detailing the implementation of the
COS, CONV, Carr-Madan method or Fourier-Space-Time Stepping. This
is applied to pricing of European, Bermudan and exotic options as
well as the calculation of the Greeks. The Monte Carlo simulation
technique is outlined and bridge sampling is discussed in a
Gaussian setting and for Levy processes. Computation of Greeks is
covered using likelihood ratio methods and adjoint techniques. A
chapter on state-of-the-art optimization algorithms rounds up the
toolkit for applying advanced mathematical models to financial
problems and the last chapter in this section of the book also
serves as an introduction to model risk.
The third part is devoted to the usage of Matlab, introducing
the software package by describing the basic functions applied for
financial engineering. The programming is approached from an
object-oriented perspective with examples to propose a framework
for calibration, hedging and the adjoint method for calculating
Greeks in a Libor Market model.
Source code used for producing the results and analysing the
models is provided on the author's dedicated website, http:
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