Berms without Calibration
A new semi-analytical pricing model for Bermudan swaptions based on swap rates distributions and correlations between them. The model does not require product specific calibration.
q-fin.PR↗
arXiv subjects
K. E. Feldman
Publications and source records attributed to K. E. Feldman.
Analytic Calibration in Andreasen-Huge SABR Model
We derive analytic formulae which link $α$, $ν$ and $ρ$ parameters in Andreasen-Huge style SABR model to the ATM price and option prices at four strikes close to ATM. Based on these formulae we give a characterisation for the SABR parameters in terms of derivatives of the swap rate forward probability density function. We test the analytic result in the application to the interest rate futures option market.
q-fin.CP↗
Change of Measure in Midcurve Pricing
We derive measure change formulae required to price midcurve swaptions in the forward swap annuity measure with stochastic annuities' ratios. We construct the corresponding linear and exponential terminal swap rate pricing models and show how they capture the midcurve swaption correlation skew.
q-fin.PR↗
Miraculous Cancellation and Pick's Theorem
We show that the Cappell-Shaneson version of Pick's theorem for simple lattice polytopes is a consequence of a general relation between characteristic numbers of virtual submanifolds dual to the characteristic classes of a stably almost complex manifold. This relation is analogous to the miraculous cancellation formula of Alvarez-Gaume and Witten, and is imposed by the action of the Landweber-Novikov algebra in the complex cobordism ring of a point.
math.GT↗
Boundary Effects in Non-Uniform Spin Chains
We give an explicit comparison of eigenvalues and eigenvectors of XY Hamiltonians of an open linear spin-1/2 chain and a closed spin-1/2 ring with periodic in space coefficients. It is shown that the Hamiltonian of a k-periodic chain with nk-1 sites has (n-1)k multiplicity one eigenvalues which are eigenvalues of multiplicity two for a Hamiltonian of a k-periodic ring with 2kn sites. For the corresponding eigenvectors in the case of a chain an explicit expression in terms of eigenvectors of the ring Hamiltonian is given. The remaining k-1 eigenvalues of the chain Hamiltonian and 2k eigenvalues of the ring Hamiltonian, together with the corresponding eigenvectors, are responsible for the difference between chain and ring models which displays in the boundary effects at the ends of the chain and translation invariance of the periodic ring.
quant-ph↗
Exact Diagonalisation of The XY-Hamiltonian of Open Linear Chains with Periodic Coupling Constants and Its Application to Dynamics of One-Dimensional Spin Systems
A new method of diagonalisation of the XY-Hamiltonian of inhomogeneous open linear chains with periodic (in space) changing Larmor frequencies and coupling constants is developed. As an example of application, multiple quantum dynamics of an inhomogeneous chain consisting of 1001 spins is investigated. Intensities of multiple quantum coherences are calculated for arbitrary inhomogeneous chains in the approximation of the next nearest interactions. {\it Key words:} linear spin chain, nearest--neighbour approximation, three--diagonal matrices, diagonalisation, fermions, multiple--quantum NMR, multiple--quantum coherence, intensities of multiple--quantum coherences. {\it PACS numbers:} 05.30.-d; 76.20.+q
quant-ph↗
Functional Equations and the Generalised Elliptic Genus
We give a new derivation and characterisation of the generalised elliptic genus of Krichever-Höhn by means of a functional equation.
math-ph↗
Chern numbers of Chern submanifolds
We present a solution of the generalized Hirzebruch problem on the relations between the Chern numbers of a stably almost complex manifold and the Chern numbers of its virtual Chern submanifolds.
math.AT↗
Hirzebruch genera of manifolds equipped with a Hamiltonian circle action
In the paper we describe obstructions for the existence of symplectic and Hamiltonian symplectic circle actions on closed compact manifolds in terms of Hirzebruch genera and relations between differential and homotopic invariants of such manifolds.
math.AT↗
A new proof of the Frobenius conjecture on the dimensions of real algebras without zero divisors
A new simple way to prove the Frobenius conjecture on the dimensions of real algebras without zero divisors is given.
math.AT↗
An Index of an Equivariant Vector Field and Addition Theorems for Pontrjagin Characteristic Classes
The theory of indices of Morse--Bott vector fields on a manifold is constructed and the famous localization problem for the transfer map is solved on its base in the present paper. As a consequence, we obtained addition theorems for the universal Pontrjagin characteristic classes in cobordisms. These results gave us a possibility to complete the construction, which was begun more than twenty years ago, of the universal characteristic classes' theory.
math.AT↗