Robust option replication for a Black-Scholes model extended with nondeterministic trends

Statistical analysis on various stocks reveals long range dependence behavior of the stock prices that is not consistent with the classical Black and Scholes model. This memory or nondeterministic trend behavior is often seen as a reflection of market sentiments and causes that the historical volatility estimator becomes unreliable in practice. We propose an extension of the Black and Scholes model by adding a term to the original Wiener term involving a smoother process which accounts for these effects. The problem of arbitrage will be discussed. Using a generalized stochastic integration theory [8], we show that it is possible to construct a self financing replicating portfolio for a European option without any further knowledge of the extension and that, as a consequence, the classical concept of volatility needs to be re-interpreted. AMS subject classifications: 60H05, 60H10, 90A09

The real multiple dual

In this paper we present a dual representation for the multiple stopping problem, hence multiple exercise options. As such it is a natural generalization of the method in Rogers (2002) and Haugh and Kogan (2004) for the standard stopping problem for American options. We consider this representation as the real dual as it is solely expressed in terms of an infimum over martingales rather than an infimum over martingales and stopping times as in Meinshausen and Hambly (2004). For the multiple dual representation we present three Monte Carlo simulation algorithms which require only one degree of nesting

The CMB Dipole and Circular Galaxy Distribution

The validity of Hubble's law defies the determination of the center of the big bang expansion, even if it exists. Every point in the expanding universe looks like the center from which the rest of the universe flies away. In this article, the author shows that the distribution of apparently circular galaxies is not uniform in the sky and that there exists a special direction in the universe in our neighborhood. The data is consistent with the assumption that the tidal force due to the mass distribution around the universe center causes the deformation of galactic shapes depending on its orientation and location relative to the center and our galaxy. Moreover, the cmb dipole data can also be associated with the center of the universe expansion, if the cmb dipole at the center of our supercluster is assumed to be due to Hubble flow. The location of the center is estimated from the cmb dipole data. The direction to the center from both sets of data is consistent and the distance to the center is computed from the cmb dipole data.Comment: 9 pages, 3 figures (10 figure captions), 1 tabl

Incremental structure building of preverbal PPs in Dutch

Incremental comprehension of head-final constructions can reveal structural attachment preferences for ambiguous phrases. This study investigates how temporarily ambiguous PPs are processed in Dutch verb-final constructions. In De aannemer heeft op het dakterras bespaard/gewerkt ‘The contractor has on the roof terrace saved/worked’, the PP is locally ambiguous between attachment as argument and as adjunct. This ambiguity is resolved by the sentence-final verb. In a self-paced reading task, we manipulated the argument/adjunct status of the PP, and its position relative to the verb. While we found no reading-time differences between argument and adjunct PPs, we did find that transitive verbs, for which the PP is an argument, were read more slowly than intransitive verbs, for which the PP is an adjunct. We suggest that Dutch parsers have a preference for adjunct attachment of preverbal PPs, and discuss our findings in terms of incremental parsing models that aim to minimize costly reanalysis

Calibration of LIBOR models to caps and swaptions: A way around intrinsic instabilities via parsimonious structures and a collateral market criterion

We expose an intrinsic stability problem in joint calibration of a LIBOR market model to caps and swaptions by direct least squares calibration. This problem typically encounters if one tries to identify jointly the volatility norm behaviour and the correlation structure of the forward LIBORs. As a remedy we propose collateral incorporation of a 'Market Swaption Formula', a rule-of-thumb formula which practitioners tend to use, in the calibration routine. It is shown by experiments with practical data that with this new calibration procedure and suitably parametrized volatility structures LIBOR model calibration to caps and swaptions is stable. The involved calibration routine is based on standard swaption approximation or its refinements by Hull & White, Jäckel & Rebonato. We deal with the issue of differently settled caps and swaptions by accordingly adapting the swap rate formula and give a respective modification of Jäckel and Rebonato's refined swaption approximation formula

Adverbial hurdles in Dutch scrambling

This paper addresses the role of the adverb in Dutch direct object scrambling constructions. We report four experiments in which we investigate whether the structural position and the scope sensitivity of the adverb affect acceptability judgments of scrambling constructions and native speakers' tendency to scramble definite objects. We conclude that the type of adverb plays a key role in Dutch word ordering preferences

Regression on particle systems connected to mean-field SDEs with applications

In this note we consider the problem of using regression on interacting particles to compute conditional expectations for McKean-Vlasov SDEs. We prove general result on convergence of linear regression algorithms and establish the corresponding rates of convergence. Application to optimal stopping and variance reduction are considered

Projected particle methods for solving McKean--Vlaslov equations

We study a novel projection-based particle method to the solution of the corresponding McKean-Vlasov equation. Our approach is based on the projection-type estimation of the marginal density of the solution in each time step. The projection-based particle method can profit from additional smoothness of the underlying density and leads in many situation to a significant reduction of numerical complexity compared to kernel density estimation algorithms. We derive strong convergence rates and rates of density estimation. The case of linearly growing coefficients of the McKean-Vlasov equation turns out to be rather challenging and requires some new type of averaging technique. This case is exemplified by explicit solutions to a class of McKean-Vlasov equations with affine drift

An iterative algorithm for multiple stopping: Convergence and stability

We present a new iterative procedure for solving the discrete multiple stopping problem and discuss the stability of the algorithm. The algorithm produces monotonically increasing approximations of the Snell envelope, which coincide with the Snell envelope after finitely many steps. Contrary to backward dynamic programming, the algorithm allows to calculate approximative solutions with only a few nestings of conditionals expectations and is, therefore, tailor-made for a plain Monte-Carlo implementation