arXiv research

Modified BDT model includes zero rate jumps for crisis risk.

Study uses zero-shot models to forecast mortality rates globally.

Study uses VIX for zero-coupon Treasury rates, proving long-term stability and returns.

In this work, I generalize Merton's approach of pricing risky debt to the case where the interest rate risk is modeled by the CIR term structure. Closed form result for pricing the debt is given for the case where the firm value has non-zero correlation with the interest rate. This extends previous closed form pricing …

Gradient methods converge exponentially in concave network games.

We analyze analytic approximation formulae for pricing zero-coupon bonds in the case when the short-term interest rate is driven by a one-factor mean-reverting process with a volatility nonlinearly depending on the interest rate itself. We derive the order of accuracy of the analytical approximation due to Choi and Wir…

New algorithms converge faster to Nash equilibrium in zero-sum games with bandit feedback.

Gradient methods converge better for alternating updates in bilinear zero-sum games.

Paper studies MCCR models with scale parameters tending to zero, revealing optimal learning rate and comparing robustness.

Study compares ZBDT model to BDT for financial derivatives valuation.

We present a new approach for the pricing of interest rate derivatives which allows a direct computation of option premiums without deriving a (Black-Scholes type) partial differential equation and without explicitly solving the stochastic process for the underlying variable. The approach is tested by rederiving the pr…

Online learning makes sequence of decisions with partial data arrival where next movement of data is unknown. In this paper, we have presented a new technique as multiple times weight updating that update the weight iteratively forsame instance. The proposed technique analyzed with popular state-of-art algorithms from …

New algorithm optimizes convex functions with noisy evaluations in one dimension.

Proposes a new model to handle negative interest rates using CIR framework.

The paper analyzes how automated market makers can retain trading fees.

New method avoids saddle points without gradients.

New inflation model captures correlations and skew in interest rates.

We consider an individual or household endowed with an initial capital and an income, modeled as a deterministic process with a continuous drift rate. At first, we model the discounting rate as the price of a zero-coupon bond at zero under the assumption of a short rate evolving as an Ornstein-Uhlenbeck process. Then, …

Paper establishes a universal growth rate for smooth surrogate losses in classification.

We derive expressions for the predicitive information rate (PIR) for the class of autoregressive Gaussian processes AR(N), both in terms of the prediction coefficients and in terms of the power spectral density. The latter result suggests a duality between the PIR and the multi-information rate for processes with mutua…

The aim of this paper is to present a dual-term structure model of interest rate derivatives in order to solve the two hardest problems in financial modeling: the exact volatility calibration of the entire swaption matrix, and the calculation of bucket vegas for structured products. The model takes a series of long-ter…

In this paper, we establish a market model for the term structure of forward inflation rates based on the risk-neutral dynamics of nominal and real zero-coupon bonds. Under the market model, we can price inflation caplets as well as inflation swaptions with a formula similar to the Black's formula, thus justify the cur…

Wide neural networks converge linearly to zero loss with feature learning.

Using expander graphs, we construct a sequence of smooth compact surfaces with boundary of perimeter N, and with the first non-zero Steklov eigenvalue uniformly bounded away from zero. This answers a question which was raised in [9]. The genus grows linearly with N, this is the optimal growth rate.

The well-known theorem of Dybvig, Ingersoll and Ross shows that the long zero-coupon rate can never fall. This result, which, although undoubtedly correct, has been regarded by many as surprising, stems from the implicit assumption that the long-term discount function has an exponential tail. We revisit the problem in …

In this article, we consider a Markov-modulated model with jumps for short rate dynamics. We obtain closed formulas for the term structure and forward rates using the properties of the jump-telegraph process and the expectation hypothesis. The results are compared with the numerical solution of the corresponding partia…

The paper calibrates the G2++ model using deep learning for interest rates.

Study on L2-boosting behavior as learning rate approaches zero.

The paper analyzes how learning rate affects SGD and provides insights into optimal rates.

Optimizes gradual reduction of excess carbon emissions to net-zero.

The paper analyzes the efficiency of gradient estimation methods in noisy function evaluations.

The high-dimensional linear model $y = X β^0 + ε$ is considered and the focus is put on the problem of recovering the support $S^0$ of the sparse vector $β^0.$ We introduce Lasso-Zero, a new $\ell_1$-based estimator whose novelty resides in an "overfit, then threshold" paradigm and the use of noise dictionaries concate…

Study shows different initialization schemes for LoRA finetuning impact performance.

A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for the instantaneous forward rates and the prices of interest-rate derivatives. The model admits function…

Paper proposes a mean-field gradient descent for zero-sum games, proving convergence to Nash equilibrium.

Unified framework matches equity and bond yields.

Adam optimizer converges to zeros of a new vector field, not just gradient zeros.

KSG mutual information estimator, which is based on the distances of each sample to its k-th nearest neighbor, is widely used to estimate mutual information between two continuous random variables. Existing work has analyzed the convergence rate of this estimator for random variables whose densities are bounded away fr…

Study no-arbitrage conditions in 1D diffusion markets with interest rates.

Modeling longevity bonds with a Vasicek model for better risk management.

The ever-increasing number of parameters in deep neural networks poses challenges for memory-limited applications. Regularize-and-prune methods aim at meeting these challenges by sparsifying the network weights. In this context we quantify the output sensitivity to the parameters (i.e. their relevance to the network ou…

We present conditions under which positive alpha exists in the realm of active portfolio management- in contrast to the controversial result in Jarrow (2010, pg. 20) which implicates delegated portfolio management by surmising that positive alphas are illusionary. Specifically, we show that the critical assumption used…

Open manifolds with nonnegative Ricci curvature have virtually abelian fundamental groups if they escape from bounded balls at a small rate.

Paper reconciles minimax rates and optimal recovery rates for noisy observations.

The paper analyzes kNN density estimation's convergence rates under different conditions.

The study constructs models for SOFR term rates using futures data.

We investigate the learning rate of multiple kernel leaning (MKL) with elastic-net regularization, which consists of an $\ell_1$-regularizer for inducing the sparsity and an $\ell_2$-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large but the number of non…

The paper models stochastic interest rates for life insurance using phase-type distributions.