Mixture dynamics and regime switching diffusions with application to option pricing

In this paper we present a class of regime switching diffusion models described by a pair (X(t),Y(t)) ∈ Rn × S, S = {1, 2, . . . , N}, Y(t) being a Markov chain, for which the marginal probability of the diffusive component X(t) is a given mixture. Our main motivation is to extend to a multivariate setting the class of mixture models proposed by Brigo and Mercurio in a series of papers. Furthermore, a simple algorithm is available for simulating paths through a thinning mechanism. The application to option pricing is considered by proposing a mixture version for theMargrabe Option formula and the Heston stochastic volatility formula for a plain vanilla

Exchange option pricing under stochastic volatility: a correlation expansion

Efficient valuation of exchange options with random volatilities while challenging at analytical level, has strong practical implications: in this paper we present a new approach to the problem which allows for extensions of previous known results. We undertake a route based on a multi-asset generalization of a methodology developed in Antonelli and Scarlatti (Finan Stoch 13:269–303, 2009) to handle simple European one-asset derivatives with volatility paths described by Ito’s diffusive equations. Our method seems to adapt rather smoothly to the evaluation of Exchange options involving correlations among all the financial quantities that specify the model and it is based on expanding and approximating the theoretical evaluation formula with respect to correlation parameters. It applies to a whole range of models and does not require any particular distributional property. In order to test the quality of our approximation numerical simulations are provided in the last part of the paper

Polarization entangled state measurement on a chip

The emerging strategy to overcome the limitations of bulk quantum optics consists of taking advantage of the robustness and compactness achievable by the integrated waveguide technology. Here we report the realization of a directional coupler, fabricated by femtosecond laser waveguide writing, acting as an integrated beam splitter able to support polarization encoded qubits. This maskless and single step technique allows to realize circular transverse waveguide profiles able to support the propagation of Gaussian modes with any polarization state. Using this device, we demonstrate the quantum interference with polarization entangled states and singlet state projection.Comment: Revtex, 5+2 pages (with supplementary information), 4+1 figure

Hellinger vs. Kullback-Leibler multivariable spectrum approximation

In this paper, we study a matricial version of the Byrnes-Georgiou-Lindquist generalized moment problem with complexity constraint. We introduce a new metric on multivariable spectral densities induced by the family of their spectral factors which, in the scalar case, reduces to the Hellinger distance. We solve the corresponding constrained optimization problem via duality theory. A highly nontrivial existence theorem for the dual problem is established in the Byrnes-Lindquist spirit. A matricial Newton-type algorithm is finally provided for the numerical solution of the dual problem. Simulation indicates that the algorithm performs effectively and reliably.Comment: 32 pages, 1 figur

Random Time Forward Starting Options

We introduce a natural generalization of the forward-starting options, first discussed by M. Rubinstein. The main feature of the contract presented here is that the strike-determination time is not fixed ex-ante, but allowed to be random, usually related to the occurrence of some event, either of financial nature or not. We will call these options {\bf Random Time Forward Starting (RTFS)}. We show that, under an appropriate "martingale preserving" hypothesis, we can exhibit arbitrage free prices, which can be explicitly computed in many classical market models, at least under independence between the random time and the assets' prices. Practical implementations of the pricing methodologies are also provided. Finally a credit value adjustment formula for these OTC options is computed for the unilateral counterparty credit risk.Comment: 19 pages, 1 figur

Context-Based Defading of Archive Photographs

We present an algorithm for the enhancement of contrast in digitized archive photographic prints. It aims at producing an adaptive enhancement based on the local context of each pixel and is able to operate without direct user's intervention. A relation between the variation of contrast at different resolutions and the local Lipschitz regularity of the image is exploited. In this way, each pixel is defaded according to its nature: noise, edge, or smooth region. This strategy provides for an algorithm that drastically reduces typical, annoying artifacts like halo effects and noise amplification

Path-polarization hyperentangled and cluster states of photons on a chip

Encoding many qubits in different degrees of freedom (DOFs) of single photons is one of the routes towards enlarging the Hilbert space spanned by a photonic quantum state. Hyperentangled photon states (i.e. states showing entanglement in multiple DOFs) have demonstrated significant implications for both fundamental physics tests and quantum communication and computation. Increasing the number of qubits of photonic experiments requires miniaturization and integration of the basic elements and functions to guarantee the set-up stability. This motivates the development of technologies allowing the precise control of different photonic DOFs on a chip. We demonstrate the contextual use of path and polarization qubits propagating within an integrated quantum circuit. We tested the properties of four-qubit linear cluster states built on both DOFs. Our results pave the way towards the full integration on a chip of hybrid multiqubit multiphoton states.Comment: 7 pages, 7 figures, RevTex4-1, Light: Science & Applications AAP:http://aap.nature-lsa.cn:8080/cms/accessory/files/AAP-lsa201664.pd

Methyl trans geranate and farnesoate as markers for Gewürztraminer grape skins and related distillates

Methyl ester of trans geranic and farnesoic acids, farnesol and two alpha-farnesene isomers are remarkable compounds in skins of mature grapes as well as in marc distillates of Traminer variety. Considerations about their level in both products of other floral varieties, like Yellow and Rose Muscats and Müller-Thurgau, as well as about their relationships with the main skin monoterpenols and other compounds, including two unidentified stereoisomeric sesquiterpenes present only in distillates, were discussed. Finally, results of PCA data treatments as for the distillates are show

General rules for bosonic bunching in multimode interferometers

We perform a comprehensive set of experiments that characterize bosonic bunching of up to 3 photons in interferometers of up to 16 modes. Our experiments verify two rules that govern bosonic bunching. The first rule, obtained recently in [1,2], predicts the average behavior of the bunching probability and is known as the bosonic birthday paradox. The second rule is new, and establishes a n!-factor quantum enhancement for the probability that all n bosons bunch in a single output mode, with respect to the case of distinguishable bosons. Besides its fundamental importance in phenomena such as Bose-Einstein condensation, bosonic bunching can be exploited in applications such as linear optical quantum computing and quantum-enhanced metrology.Comment: 6 pages, 4 figures, and supplementary material (4 pages, 1 figure