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Presenting state-of-the-art methods in the area, the book begins
with a presentation of weak discrete time approximations of
jump-diffusion stochastic differential equations for derivatives
pricing and risk measurement. Using a moving least squares
reconstruction, a numerical approach is then developed that allows
for the construction of arbitrage-free surfaces. Free boundary
problems are considered next, with particular focus on stochastic
impulse control problems that arise when the cost of control
includes a fixed cost, common in financial applications. The text
proceeds with the development of a fear index based on equity
option surfaces, allowing for the measurement of overall fear
levels in the market. The problem of American option pricing is
considered next, applying simulation methods combined with
regression techniques and discussing convergence properties.
Changing focus to integral transform methods, a variety of option
pricing problems are considered. The COS method is practically
applied for the pricing of options under uncertain volatility, a
method developed by the authors that relies on the dynamic
programming principle and Fourier cosine series expansions.
Efficient approximation methods are next developed for the
application of the fast Fourier transform for option pricing under
multifactor affine models with stochastic volatility and jumps.
Following this, fast and accurate pricing techniques are showcased
for the pricing of credit derivative contracts with discrete
monitoring based on the Wiener-Hopf factorisation. With an energy
theme, a recombining pentanomial lattice is developed for the
pricing of gas swing contracts under regime switching dynamics. The
book concludes with a linear and nonlinear review of the
arbitrage-free parity theory for the CDS and bond markets.
This open access Pivot demonstrates how a variety of technologies
act as innovation catalysts within the banking and financial
services sector. Traditional banks and financial services are under
increasing competition from global IT companies such as Google,
Apple, Amazon and PayPal whilst facing pressure from investors to
reduce costs, increase agility and improve customer retention.
Technologies such as blockchain, cloud computing, mobile
technologies, big data analytics and social media therefore have
perhaps more potential in this industry and area of business than
any other. This book defines a fintech ecosystem for the 21st
century, providing a state-of-the art review of current literature,
suggesting avenues for new research and offering perspectives from
business, technology and industry.
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