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

The regions of the sequence most exposed to the solvent within the amyloidogenic state of a protein initiate the aggregation process.

Formation of misfolded aggregates is an essential part of what proteins can do. The process of protein aggregation is central to many human diseases and any aggregating event needs to be prevented within a cell and in protein design. In order to aggregate, a protein needs to unfold its native state, at least partially. The conformational state that is prone to aggregate is difficult to study, due to its aggregating potential and heterogeneous nature. Here, we use a systematic approach of limited proteolysis, in combination with electrospray ionisation mass spectrometry, to investigate the regions that are most flexible and solvent-exposed within the native, ligand-bound and amyloidogenic states of muscle acylphosphatase (AcP), a protein previously shown to form amyloid fibrils in the presence of trifluoroethanol. Seven proteases with different degrees of specificity have been used for this purpose. Following exposure to the aggregating conditions, a number of sites along the sequence of AcP become susceptible to proteolytic digestion. The pattern of proteolytic cleavages obtained under these conditions is considerably different from that of the native and ligand-bound conformations and includes a portion within the N-terminal tail of the protein (residues 6-7), the region of the sequence 18-23 and the position 94 near the C terminus. There is a significant overlap between the regions of the sequence found to be solvent-exposed from the present study and those previously identified to be critical in the rate-determining steps of aggregation from protein engineering approaches. This indicates that a considerable degree of solvent exposure is a feature of the portions of a protein that initiate the process of aggregation

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

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

Polarized micro-Raman studies of femtosecond laser written stress-induced optical waveguides in diamond

Understanding the physical mechanisms of the refractive index modulation induced by femtosecond laser writing is crucial for tailoring the properties of the resulting optical waveguides. In this work we apply polarized Raman spectroscopy to study the origin of stress-induced waveguides in diamond, produced by femtosecond laser writing. The change in the refractive index induced by the femtosecond laser in the crystal is derived from the measured stress in the waveguides. The results help to explain the waveguide polarization sensitive guiding mechanism, as well as providing a technique for their optimization.Comment: 5 pages, 4 figure