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Discrete Time Term Structure Theory and Consistent Recalibration Models
(2014)arXivWe develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily formulated and implemented from the chosen discrete point of view. In mathematical terms we provide an algorithmic answer to the following question: describe a rich, still tractable class of discrete time ...Working Paper 

A convergence result for the Emery topology and a variant of the proof of the fundamental theorem of asset pricing
(2014)arXivWe show that No unbounded profit with bounded risk (NUPBR) implies predictable uniform tightness (PUT), a boundedness property in the Emery topology which has been introduced by C. Stricker [32]. Combining this insight with well known results from J. M´emin and L. S lominski [26] leads to a short variant of the proof of the fundamental theorem of asset pricing initially proved by F. Delbaen and W. Schachermayer [4]. The results are ...Working Paper 
The GärtnerEllis theorem, homogenization, and affine processes
(2014)arXivWe obtain a first order extension of the large deviation estimates in the GärtnerEllis theorem. In addition, for a given family of measures, we find a special family of functions having a similar Laplace principle expansion up to order one to that of the original family of measures. The construction of the special family of functions mentioned above is based on heat kernel expansions. Some of the ideas employed in the paper come from the ...Working Paper 
When rollovers do not qualify as numéraire
(2013)arXivWe investigate defaultfree bond markets where the standard relationship between a possibly existing bank account process and the term structure of bond prices is broken, i.e. the bank account process is not a valid num\'eraire. We argue that this feature is not the exception but rather the rule in bond markets when starting with, e.g., terminal bonds as num\'eraires. Our setting are general c\`adl\`ag processes as bond prices, where we ...Working Paper 
Consistent LongTerm Yield Curve Prediction
(2012)arXivWe present an arbitragefree nonparametric yield curve prediction model which takes the full (discretized) yield curve as state variable. We believe that absence of arbitrage is an important model feature in case of highly correlated data, as it is the case for interest rates. Furthermore, the model structure allows to separate clearly the tasks of estimating the volatility structure and of calibrating market prices of risk. The empirical ...Working Paper 
Affine processes on symmetric cones
(2011)arXivWe 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\'evyKhintchine 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).Working Paper 
A Semigroup Point Of View On Splitting Schemes For Stochastic (Partial) Differential Equations
(2010)We construct normed spaces of realvalued functions with controlled growth on possibly infinitedimensional state spaces such that semigroups of positive, bounded operators $(P_t)_{t\ge 0}$ thereon with $\lim_{t\to 0+}P_t f(x)=f(x)$ are in fact strongly continuous. This result applies to prove optimal rates of convergence of splitting schemes for stochastic (partial) differential equations with linearly growing characteristics and for ...Working Paper 
Term Structure Models Driven by Wiener Process and Poisson Measures: Existence and Positivity
(2009)arXivIn the spirit of Bj\"orkDiMasiKabanovRunggaldier, we investigate term structure models driven by Wiener process and Poisson measures with forward curve dependent volatilities. This includes a full existence and uniqueness proof for the corresponding HeathJarrowMorton type term structure equation. Furthermore, we characterize positivity preserving models by means of the characteristic coefficients, which was open for jumpdiffusions. ...Working Paper