CVA and vulnerable options pricing by correlation expansions

We consider the problem of computing the Credit Value Adjustment ({CVA}) of a European option in presence of the Wrong Way Risk ({WWR}) in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in \cite{AS}. We compare the numerical performance of such a method with that recently proposed by Brigo et al. (\cite{BR18}, \cite{BRH18}) in the case of a call option driven by a GBM correlated with the CIR default intensity. We additionally report some numerical evaluations obtained by other methods.Comment: 21 page

A moment matching method for option pricing under stochastic interest rates

In this paper we present a simple, but new, approximation methodology for pricing a call option in a Black & Scholes market characterized by stochastic interest rates. The method, based on a straightforward Gaussian moment matching technique applied to a conditional Black & Scholes formula, is quite general and it applies to various models, whether affine or not. To check its accuracy and computational time, we implement it for the CIR interest rate model correlated with the underlying, using the Monte Carlo simulations as a benchmark. The method's performance turns out to be quite remarkable, even when compared with analogous results obtained by the affine approximation technique presented in Grzelak and Oosterlee (2011) and by the expansion formula introduced in Kim and Kunimoto (1999), as we show in the last section

Two-particle bosonic-fermionic quantum walk via 3D integrated photonics

Quantum walk represents one of the most promising resources for the simulation of physical quantum systems, and has also emerged as an alternative to the standard circuit model for quantum computing. Up to now the experimental implementations have been restricted to single particle quantum walk, while very recently the quantum walks of two identical photons have been reported. Here, for the first time, we investigate how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk. Such experiment has been realized by adopting two-photon entangled states and integrated photonic circuits. The polarization entanglement was exploited to simulate the bunching-antibunching feature of non interacting bosons and fermions. To this scope a novel three-dimensional geometry for the waveguide circuit is introduced, which allows accurate polarization independent behaviour, maintaining a remarkable control on both phase and balancement.Comment: 4 pages, 5 figures + supplementary informatio

Integrated optical waveplates for arbitrary operations on polarization-encoded single-qubits

Integrated photonic technologies applied to quantum optics have recently enabled a wealth of breakthrough experiments in several quantum information areas. Path encoding was initially used to demonstrate operations on single or multiple qubits. However, a polarization encoding approach is often simpler and more effective. Two-qubits integrated logic gates as well as complex interferometric structures have been successfully demonstrated exploiting polarization encoding in femtosecond-laser-written photonic circuits. Still, integrated devices performing single-qubit rotations are missing. Here we demonstrate waveguide-based waveplates, fabricated by femtosecond laser pulses, capable to effectively produce arbitrary single-qubit operations in the polarization encoding. By exploiting these novel components we fabricate and test a compact device for the quantum state tomography of two polarization-entangled photons. The integrated optical waveplates complete the toolbox required for a full manipulation of polarization-encoded qubits on-chip, disclosing new scenarios for integrated quantum computation, sensing and simulation, and possibly finding application also in standard photonic devices

Anderson localization of entangled photons in an integrated quantum walk

Waves fail to propagate in random media. First predicted for quantum particles in the presence of a disordered potential, Anderson localization has been observed also in classical acoustics, electromagnetism and optics. Here, for the first time, we report the observation of Anderson localization of pairs of entangled photons in a two-particle discrete quantum walk affected by position dependent disorder. A quantum walk on a disordered lattice is realized by an integrated array of interferometers fabricated in glass by femtosecond laser writing. A novel technique is used to introduce a controlled phase shift into each unit mesh of the network. Polarization entanglement is exploited to simulate the different symmetries of the two-walker system. We are thus able to experimentally investigate the genuine effect of (bosonic and fermionic) statistics in the absence of interaction between the particles. We will show how different types of randomness and the symmetry of the wave-function affect the localization of the entangled walkers.Comment: 7 pages, 5 figures, revised version published on Nature Photonics 7, 322-328 (2013

Fermionic statistics suppresses Fano resonances

Fano resonances and bound states with energy in the continuum are ubiquitous phenomena in different areas of physics. Observations, however, have been limited so far to single-particle processes. In this work we experimentally investigate the multi-particle case and observe Fano interference in a non-interacting two-particle Fano-Anderson model by considering propagation of two-photon states in engineered photonic lattices. We demonstrate that the quantum statistics of the particles, either bosonic or fermionic, strongly affects the decay process. Remarkably, we find that the Fano resonance, when two discrete levels are coupled to a continuum, is suppressed in the fermionic case

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

Quantum simulation of bosonic-fermionic non-interacting particles in disordered systems via quantum walk

We report on the theoretical analysis of bosonic and fermionic non-interacting systems in a discrete two-particle quantum walk affected by different kinds of disorder. We considered up to 100-step QWs with a spatial, temporal and space-temporal disorder observing how the randomness and the wavefunction symmetry non-trivially affect the final spatial probability distribution, the transport properties and the Shannon entropy of the walkers.Comment: 13 pages, 10 figures. arXiv admin note: text overlap with arXiv:1101.2638 by other author