arXiv subjects

Christa Cuchiero

Publications and source records attributed to Christa Cuchiero.

45 records · Page 3Linked to original sources

arXiv2016

Cover's universal portfolio, stochastic portfolio theory and the numeraire portfolio

Cover's celebrated theorem states that the long run yield of a properly chosen "universal" portfolio is as good as the long run yield of the best retrospectively chosen constant rebalanced portfolio. The "universality" pertains to the fact that this result is model-free, i.e., not dependent on an underlying stochastic process. We extend Cover's theorem to the setting of stochastic portfolio theory as initiated by R. Fernholz: the rebalancing rule need not to be constant anymore but may depend on the present state of the stock market. This model-free result is complemented by a comparison with the log-optimal numeraire portfolio when fixing a stochastic model of the stock market. Roughly speaking, under appropriate assumptions, the optimal long run yield coincides for the three approaches mentioned in the title of this paper. We present our results in discrete and continuous time.

q-fin.MF↗

arXiv2015

A general HJM framework for multiple yield curve modeling

We 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 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. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling.

q-fin.MF↗

arXiv2014

A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing

We show that \emph{No unbounded profit with bounded risk} (NUPBR) implies \emph{predictable uniform tightness} (P-UT), a boundedness property in the Emery topology which has been introduced by C. Stricker \cite{S:85}. Combining this insight with well known results from J. Mémin and L. Słominski \cite{MS:91} leads to a short variant of the proof of the fundamental theorem of asset pricing initially proved by F. Delbaen and W. Schachermayer \cite{DS:94}. The results are formulated in the general setting of admissible portfolio wealth processes as laid down by Y. Kabanov in \cite{kab:97}.

math.PR↗

arXiv2014

Fourier transform methods for pathwise covariance estimation in the presence of jumps

We provide a new non-parametric Fourier procedure to estimate the trajectory of the instantaneous covariance process (from discrete observations of a multidimensional price process) in the presence of jumps extending the seminal work Malliavin and Mancino~\cite{MM:02, MM:09}. Our approach relies on a modification of (classical) jump-robust estimators of integrated realized covariance to estimate the Fourier coefficients of the covariance trajectory. Using Fourier-Féjer inversion we reconstruct the path of the instantaneous covariance. We prove consistency and central limit theorem (CLT) and in particular that the asymptotic estimator variance is smaller by a factor $ 2/3$ in comparison to classical local estimators. The procedure is robust enough to allow for an iteration and we can show theoretically and empirically how to estimate the integrated realized covariance of the instantaneous stochastic covariance process. We apply these techniques to robust calibration problems for multivariate modeling in finance, i.e., the selection of a pricing measure by using time series and derivatives' price information simultaneously.

math.ST↗

arXiv2013

Path properties and regularity of affine processes on general state spaces

We provide a new proof for regularity of affine processes on general state spaces by methods from the theory of Markovian semimartingales. On the way to this result we also show that the definition of an affine process, namely as stochastically continuous time-homogeneous Markov process with exponential affine Fourier-Laplace transform, already implies the existence of a càdlàg version. This was one of the last open issues in the fundaments of affine processes.

math.PR↗

arXiv2012

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 methods.

math.PR↗

arXiv2011

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 Lévy-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).

math.PR↗

arXiv2011

Affine processes on positive semidefinite matrices

This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatility and correlation structures, and fixed-income models with stochastically correlated risk factors and default intensities.

math.PR↗

arXiv2008

Affine Models

Affine term structure models have gained significant attention in the finance literature, mainly due to their analytical tractability and statistical flexibility. The aim of this article is to present both theoretical foundations as well as empirical aspects of the affine model class. Starting from the original one-factor short-rate models of Vasiček and Cox \emph{et al,} we provide an overview of the properties of regular affine processes and explain their relationship to affine term structure models. Methods for securities pricing and for parameter estimation are also discussed, demonstrating how the analytical tractability of affine models can be exploited for practical purposes.

q-fin.PR↗