10 research outputs found
Polynomial processes and their applications to mathematical finance
We introduce a class of Markov processes, called m-polynomial, for which the calculation of (mixed) moments up to order m only requires the computation of matrix exponentials. This class contains affine processes, processes with quadratic diffusion coefficients, as well as Lévy-driven SDEs with affine vector fields. Thus, many popular models such as exponential Lévy models or affine models are covered by this setting. The applications range from statistical GMM estimation procedures to new techniques for option pricing and hedging. For instance, the efficient and easy computation of moments can be used for variance reduction techniques in Monte Carlo method
Affine processes on symmetric cones
We consider affine Markov processes taking values in convex cones. In
particular, we characterize all affine processes taking values in an
irreducible symmetric cone in terms of certain L\'evy-Khintchine triplets. This
is the complete classification of affine processes on these conic state spaces,
thus extending the theory of Wishart processes on positive semidefinite
matrices, as put forward by Bru (1991)
Polynomial processes and their applications to mathematical finance
ISSN:0949-2984ISSN:1432-112
A general HJM framework for multiple yield curve modeling
46 pages, 4 figuresWe propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between (normalized) FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor's length. When the driving semimartingale is specified as an affine process, we obtain a flexible Markovian structure which allows for tractable valuation formulas for most interest rate derivatives. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling