This book summarizes recent advances in applying saddlepoint
approximation methods to financial engineering. It addresses
pricing exotic financial derivatives and calculating risk
contributions to Value-at-Risk and Expected Shortfall in credit
portfolios under various default correlation models. These standard
problems involve the computation of tail probabilities and tail
expectations of the corresponding underlying state variables. The
text offers in a single source most of the saddlepoint
approximation results in financial engineering, with different sets
of ready-to-use approximation formulas. Much of this material may
otherwise only be found in original research publications. The
exposition and style are made rigorous by providing formal proofs
of most of the results. Starting with a presentation of the
derivation of a variety of saddlepoint approximation formulas in
different contexts, this book will help new researchers to learn
the fine technicalities of the topic. It will also be valuable to
quantitative analysts in financial institutions who strive for
effective valuation of prices of exotic financial derivatives and
risk positions of portfolios of risky instruments.
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