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Market-Consistent Prices - An Introduction to Arbitrage Theory (Paperback, 1st ed. 2020)
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Market-Consistent Prices - An Introduction to Arbitrage Theory (Paperback, 1st ed. 2020)
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Arbitrage Theory provides the foundation for the pricing of
financial derivatives and has become indispensable in both
financial theory and financial practice. This textbook offers a
rigorous and comprehensive introduction to the mathematics of
arbitrage pricing in a discrete-time, finite-state economy in which
a finite number of securities are traded. In a first step, various
versions of the Fundamental Theorem of Asset Pricing, i.e.,
characterizations of when a market does not admit arbitrage
opportunities, are proved. The book then focuses on incomplete
markets where the main concern is to obtain a precise description
of the set of "market-consistent" prices for nontraded financial
contracts, i.e. the set of prices at which such contracts could be
transacted between rational agents. Both European-type and
American-type contracts are considered. A distinguishing feature of
this book is its emphasis on market-consistent prices and a
systematic description of pricing rules, also at intermediate
dates. The benefits of this approach are most evident in the
treatment of American options, which is novel in terms of both the
presentation and the scope, while also presenting new results. The
focus on discrete-time, finite-state models makes it possible to
cover all relevant topics while requiring only a moderate
mathematical background on the part of the reader. The book will
appeal to mathematical finance and financial economics students
seeking an elementary but rigorous introduction to the subject;
mathematics and physics students looking for an opportunity to get
acquainted with a modern applied topic; and mathematicians,
physicists and quantitatively inclined economists working or
planning to work in the financial industry.
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