Identifies smooth curves for financial models.
problem Consistent term structures with flexible diffusion.
method Analyzes manifolds of curves for Heath-Jarrow-Morton models.
result Term structures cannot be affine but must be linear-rational.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “Morton curves”
New method uses space-filling curves to represent crystal structures for machine learning.
problem Representing molecular crystals for machine learning.
method SFC-M feature representations based on Morton curves, reduced by LSI.
result Promising results in predicting crystal properties.
Characterizes diagrams achieving Morton-Franks-Williams inequality for positive knots and links.
problem Understanding when the Morton-Franks-Williams inequality holds for positive knots and links.
method Combinatorial characterisation and generating examples.
result Examples of diagrams achieving crossing number, braid index, and maximal self-linking number.
The paper analyzes the Heath-Jarrow-Morton-Musiela equation with Lévy perturbation.
problem Analyzing the Heath-Jarrow-Morton-Musiela equation with Lévy perturbation in weighted spaces.
method The paper studies the Heath-Jarrow-Morton-Musiela equation in weighted spaces of functions defined on , obtaining sufficient conditions for local and global existence.
result Conditions for global existence are close to necessary conditions for the linear diffusion term.
Two new models for forward power prices capture clustering jumps.
problem Describing forward power prices with clustering jumps.
method Continuous branching processes with immigration and Hawkes processes with exponential kernel.
result Models adequately describe forward prices evolution in French power market.
Calibrates historical and implied correlations in energy markets.
problem Challenges in aligning historical correlations of futures contracts with implied volatility smiles.
method Multiplicative multi-factor Heath-Jarrow-Morton model combined with stochastic volatility from lifted Heston model, using Kemna-Vorst approximation and Fourier-based techniques.
result Remarkable joint historical and implied calibration fits on the German power market.
Designs a Heath-Jarrow-Morton framework for forward contracts in power and gas markets.
problem Designing a framework for forward contracts in power and gas markets.
method Heath-Jarrow-Morton framework, affine functions, Girsanov kernel, measure changes.
result Validates measure changes for forward contracts in power and gas markets.
This paper considers the single factor Heath-Jarrow-Morton model for the interest rate curve with stochastic volatility. Its natural formulation, described in terms of stochastic differential equations, is solved through Monte Carlo simulations, that usually involve rather large computation time, inefficient from a pra…
The Long Bond, Long Forward Measure and Long-Term Factorization in Heath-Jarrow-Morton Modelsq-fin.MF
Proves existence of long bond, long forward measure, and long-term factorization in HJM models.
problem Existence of long bond, long forward measure, and long-term factorization in HJM models.
method Function space framework of Filipovic (2001) and sufficient condition on the weight in the Hilbert space of forward rate volatility curves.
result Existence of long bond volatility process, long bond process, and long-term factorization of SDF.
The paper studies multi-curve interest rate models and their consistency and finite-dimensional realizations.
problem Consistency and existence of finite-dimensional realizations for multi-curve interest rate models.
method Geometric approach, characterizing consistency and existence of finite-dimensional realizations for multi-curve models.
result Characterization of consistency and existence of finite-dimensional realizations for multi-curve models.
Kernel-based collocation methods for Heath-Jarrow-Morton models with Musiela parametrizationq-fin.CP
Kernel-based methods solve Heath-Jarrow-Morton models with Musiela parametrization.
problem Solving Heath-Jarrow-Morton models with Musiela parametrization.
method Kernel-based collocation methods as Euler-Maruyama approximations of stochastic differential equations.
result Derivation of a rate of convergence bound under specified conditions.
Suppose that a topological space is the union of an increasing sequence of open subsets each of which is homeomorphic to the Euclidean space . Then itself is homeomorphic to . This is an old theorem of Morton Brown. We observe that this theorem is an immediate consequence of other two theorems of Mort…
This paper applies Heath-Jarrow-Morton framework to energy markets for practical use.
problem Applying complex financial models to energy markets for practical use.
method Calibration by PCA, Monte Carlo simulations, derivatives pricing.
result Calibrated model accurately simulates European power and gas markets.
We give conditions on a knot on which the Morton-Franks-Williams inequality is not sharp. As applications, we show infinitely many examples of knots where the inequality is not sharp and also prove (by giving examples) that the deficit of the inequality can be arbitrarily large.
The paper approximates forward curve models in commodity markets using finite dimensional models.
problem Approximating forward curve models in commodity markets with finite dimensional arbitrage-free models.
method Construction of a convenient Riesz basis on the state space of the term structure dynamics.
result Recovery of a closed form representation of the forward price dynamics in the approximation models and uniform convergence to the true dynamics.
The paper is concerned with the problem of existence of solutions for the Heath-Jarrow-Morton equation with linear volatility. Necessary conditions and sufficient conditions for the existence of weak solutions and strong solutions are provided. It is shown that the key role is played by the logarithmic growth condition…
We generalize the Morton-Franks-Williams inequality to the colored link homology defined in arXiv:0907.0695, which gives infinitely many new bounds for the braid index and the self linking number. A key ingredient of our proof is a composition product for the general MOY graph polynomial, which gener…
Study variance-optimal hedging of forward curve derivatives under stochastic volatility.
problem Variance-optimal hedging of forward curve derivatives with stochastic volatility.
method Assumes HJM-Musiela dynamics modulated by stochastic covariance, uses Galtchouk-Kunita-Watanabe projection.
result Density of finite-maturity strategies, convergence of finite-rank projections, decomposition of hedging error.
Deep learning framework for bond and yield curve forecasting with no-arbitrage constraints.
problem Arbitrage-free yield curve and bond price forecasting.
method Combines Kalman, extended Kalman, and particle filters with LSTM/CLSTM, and introduces AER term.
result Arbitrage regularization improves forecast accuracy, especially at short maturities.
A new model captures forward curve dynamics with stochastic volatility.
problem Modeling continuous-time evolution of forward curves in financial markets.
method Affine stochastic volatility model with modulated dynamics.
result Model allows for maturity-specific risk and volatility clustering.
We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive permutation braids). This allows to prove, in a simple way, that the set of simple braids is a orthonormal basis for the inner product of the Hecke algebra of the braid group defined by Kálmán, who first obtained this r…
Short note on braid index and quasipositivity of certain pretzel knots.
problem Calculating braid index and identifying quasipositive status for specific pretzel knots.
method Used Morton-Franks-Williams inequalities and Khovanov-Rozansky concordance homomorphisms.
result Determined braid index and identified quasipositivity for knots with even crossings in one strand.
Paper proves existence of Lévy term structure models.
problem Existence proof for Lévy term structure models.
method Proof of existence and uniqueness for Heath-Jarrow-Morton type equation.
result Full proof of existence and uniqueness of Lévy term structure models.
Study stochastic equations in Banach spaces, applying to HJM equation.
problem Existence and uniqueness of solutions to stochastic evolution equations in Banach spaces.
method Proving existence and uniqueness of solutions to stochastic evolution equations in martingale-type 2 Banach spaces.
result Existence and uniqueness of solutions to the Heath-Jarrow-Morton-Musiela equation in weighted Lebesgue and Sobolev spaces.
This work reconstructs knot invariants from Alexander polynomials, proving consistency with known theorems.
problem Reconstructing knot invariants from Alexander polynomials.
method Quantization, deformation, and rewriting of Alexander polynomials.
result Derives new formulae for colored superpolynomials and proves consistency with Melvin-Morton-Rozansky theorem.
Develops a new method for financial term structure modeling.
problem Analyzing financial term structures with discontinuities.
method Cylindrical stochastic integration approach.
result Establishes a Heath-Jarrow-Morton framework.
Paper introduces a flexible HJM framework for consistent electricity prices.
problem Consistent modeling of intraday, spot, futures, and option prices.
method Flexible HJM-type framework with economic interpretations.
result Allows existing spot price models to be used in HJM setting.
New minimal link diagrams found, including torus links and homogeneous ones.
problem Finding minimal link diagrams with new classes.
method Morton-Franks-Williams inequality approach.
result New classes of minimal link diagrams, including previously unproven ones.
Positivity of mild solution to stochastic evolution equations with an application to forward ratesmath.AP
Maximum principle proves positivity of forward rates in stochastic models.
problem Proving positivity of forward rates in stochastic models.
method Maximum principle for mild solutions to SPDEs with Lipschitz coefficients and Wiener noise.
result Sufficient conditions for positivity of forward rates in the Heath-Jarrow-Morton model.
Deep learning calibrates HJM forward curves for commodity options pricing.
problem Calibrating HJM forward curves for accurate option pricing in commodity markets.
method Introduced a neural network to approximate true option prices from model parameters, calibrated using observed option prices.
result Neural network calibration yields high accuracy in recovering option prices, even with model parameter approximation loss.
This paper aims at transferring the philosophy behind Heath-Jarrow-Morton to the modelling of call options with all strikes and maturities. Contrary to the approach by Carmona and Nadtochiy (2009) and related to the recent contribution Carmona and Nadtochiy (2012) by the same authors, the key parametrisation of our app…
A new model for forward curves captures behavior through a single equation.
problem Modeling forward curves in a complex function space.
method Developed a stochastic partial differential equation with locally state-dependent coefficients.
result The model retains simplicity while capturing entire forward curve behavior.
We study the optimal stopping problem of pricing an American Put option on a Zero Coupon Bond (ZCB) in the Musiela's parametrization of the Heath-Jarrow-Morton (HJM) model for forward interest rates. First we show regularity properties of the price function by probabilistic methods. Then we find an infinite dimensional…
The paper develops stochastic models for mortality rates using infinite dimensional processes.
problem Uncertainty in demographic projections of future mortality rates.
method Forward mortality models driven by Wiener process and Poisson random measure.
result Consistency conditions for forward mortality improvements and mortality rates.
We study three-dimensional Chern-Simons theory with complex gauge group SL(2,C), which has many interesting connections with three-dimensional quantum gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence of a single knotted Wilson loop in an infinite-dimensional representation of the gauge grou…
New derivation of knot invariants from universal invariant.
problem Deriving knot invariants from universal invariant.
method Using Hopf algebra and a Mathematica implementation to compute .
result Derivation of large-color expansion from universal invariant.
Study pricing options on forward contracts using infinite-dimensional affine models.
problem Pricing European-style options on forward contracts in complex stochastic volatility models.
method Model forward price curves using stochastic partial differential equations modulated by stochastic volatility processes. Analyze two classes of affine stochastic volatility models: Gaussian and pure-jump. Derive conditions for existence of exponential moments and develop semi-closed pricing formulas.
result Developed semi-closed Fourier-based pricing formulas for vanilla call and put options in infinite-dimensional affine models.
In a recent paper, McMullen showed an inequality between the Thurston norm and the Alexander norm of a 3-manifold. This generalizes the well-known fact that twice the genus of a knot is bounded from below by the degree of the Alexander polynomial. We extend the Bennequin inequality for links to an inequality for all po…
Study on monotonicity in CDO term structure models using Lévy processes.
problem Existence of arbitrage-free and monotone CDO term structure models.
method Conditions for positivity and monotonicity of Heath-Jarrow-Morton-Musiela equation formulated using Milian type result and regularity results for Sobolev space.
result Characterization of arbitrage-free and monotone models in terms of volatility and driving Lévy process characteristics.
Experimentally identified 22 L-space knots with tunnel number >1, some having high genus and braid index.
problem Identifying L-space knots with tunnel number greater than 1.
method Cataloging hyperbolic manifolds, using SnapPy and KLO to find knot presentations as closures of positive braids.
result Found 9 asymmetric L-space knot complements with tunnel number 2, and 22 with tunnel number 1.
We show that 3-braid links with given (non-zero) Alexander or Jones polynomial are finitely many, and can be effectively determined. We classify among closed 3-braids strongly quasipositive and fibered ones, and show that 3-braid links have a unique incompressible Seifert surface. We also classify the positive braid wo…
The abstract discusses solutions to bond market equations with linear volatility and Lévy noise.
problem Existence and non-existence of solutions to Heath-Jarrow-Morton equations with linear volatility and Lévy noise.
method Analyzes conditions for existence and non-existence of solutions in the class of bounded fields, considering Lévy processes without Gaussian and negative jumps.
result Necessary and sufficient conditions for the existence of solutions are formulated in terms of Lévy measure behavior near the origin or Laplace exponent behavior at infinity.
We propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM) model. To construct the methods, we first discretize the infinite dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite dimensional system of stochastic dif…
Study four ways to define braided open book decompositions of the 3-sphere.
problem Define and compare different ways to make open book decompositions of the 3-sphere 'braided'.
method Analyze four specific definitions of braided open book decompositions and prove their equivalence.
result All four definitions of braided open book decompositions are equivalent.
In this paper, a generalized version of Morton's formula is proved. Using this formula, one can write down the colored Jones polynomials of cabling of an knot in terms of the colored Jones polynomials of the original knot.
We give criteria for an invariant of lens space links to bound the maximal self-linking number in certain tight contact lens spaces. As a corollary we extend the Franks-Williams-Morton inequality to the setting of lens spaces.
We describe a procedure for creating infinite families of knots, each having the maximum degree of their HOMFLY polynomial strictly less than twice their canonical genus. These families build upon examples first found by Stoimenow.
To a knot in 3-space, one can associate a sequence of Laurent polynomials, whose th term is the th colored Jones polynomial. The Volume Conjecture for small angles states that the value of the -th colored Jones polynomial at $e^{\a/n}$ is a sequence of complex numbers that grows subexponentially, for a fixed s…