Mathematical Finance最新文献

In this article, we show how to analyze the covariation of bond prices nonparametrically and robustly, staying consistent with a general no-arbitrage setting. This is, in particular, motivated by the problem of identifying the number of statistically relevant factors in the bond market under minimal conditions. We apply our method in an empirical study, which suggests that a high number of factors is needed to describe the term structure evolution and that the term structure of volatility varies over time.

We develop a cross-border market model for two countries based on a continuous trading mechanism, in which the transmission capacities that enable transactions between market participants from different countries are limited. Our market model can be described by a regime-switching process alternating between active and inactive regimes, in which cross-border trading is possible, respectively prohibited. Starting from a reduced-form representation of the two national limit order books, we derive a high-frequency approximation of the microscopic model, assuming that the size of an individual order converges to zero while the order arrival rate tends to infinity. If transmission capacities are available, the limiting dynamics are as follows: the queue size processes at the top of the two limit order books follow a four-dimensional linear Brownian motion in the positive orthant with oblique reflection at the axes. Each time the two best ask queues or the two best bid queues simultaneously hit zero, the queue size process is reinitialized. The capacity process can be described as a linear combination of local times and ishence of finite variation. The analytic tractability of the limiting dynamics allows us to compute key quantities of interest.

The London Interbank Offered Rate (LIBOR) has served since the 1970s as a fundamental measure for floating term rates across multiple currencies and maturities. However, in 2017, the Financial Conduct Authority announced the discontinuation of LIBOR from the end of 2021, and the New York Fed declared the Treasury repo financing rate, called the Secured Overnight Financing Rate (SOFR), as a candidate for a new reference rate for IRSs denominated in U.S. dollars. We examine arbitrage-free pricing and hedging of swaps referencing SOFR without and with collateral backing. As hedging instruments, we take SOFR futures and idiosyncratic funding rates for the hedge and margin account. For simplicity, a one-factor model based on Vasicek's equation is used to specify the joint dynamics of several overnight interest rates, including the SOFR and unsecured funding rate.

We examine the shapes attainable by the forward- and yield-curve in the widely-used Svensson family, including the Nelson-Siegel and Bliss subfamilies. We provide a complete classification of all attainable shapes and partition the parameter space of each family according to these shapes. Building upon these results, we then examine the consistent dynamic evolution of the Svensson family under absence of arbitrage. Our analysis shows that consistent dynamics further restrict the set of attainable shapes, and we demonstrate that certain complex shapes can no longer appear after a deterministic time horizon. Moreover, a single shape (either inverse of normal curves) must dominate in the long-run.

In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multimarginal couplings, as a generalization of well-known correlation statistics such as the Pearson correlation. The first main result states that even an arbitrarily small positive dependence between losses can result in perfectly correlated tails beyond a certain threshold and seemingly complete independence before this threshold. In a second step, we focus on the aggregation of individual risks with known marginal distributions by means of arbitrary nondecreasing left-continuous aggregation functions. In this context, we show that under an arbitrarily small positive dependence, the tail risk of the aggregate loss might coincide with the one of perfectly correlated losses. A similar result is derived for expectiles under mild conditions. In a last step, we discuss our results in the context of credit risk, analyzing the potential effects on the value at risk for weighted sums of Bernoulli distributed losses.

We study Pareto efficiency in a pure-exchange economy where agents' preferences are represented by risk-averse monetary utilities. These coincide with law-invariant monetary utilities, and they can be shown to correspond to the class of monotone, (quasi-)concave, Schur concave, and translation-invariant utility functionals. This covers a large class of utility functionals, including a variety of law-invariant robust utilities. Given that Pareto optima exist and are comonotone, we provide a crisp characterization thereof in the case of law-invariant positively homogeneous monetary utilities. This characterization provides an easily implementable algorithm that fully determines the shape of Pareto-optimal (PO) allocations. In the special case of law-invariant comonotone-additive monetary utility functionals (concave Yaari-dual utilities), we provide a closed-form characterization of Pareto optima. As an application, we examine risk-sharing markets where all agents evaluate risk through law-invariant coherent risk measures, a widely popular class of risk measures. In a numerical illustration, we characterize PO risk-sharing for some special types of coherent risk measures.

Reppen, A. M., H. M. Soner, and V. Tissot-Daguette. 2025. “Neural Optimal Stopping Boundary.” Mathematical Finance 35, no. 2: 441–469. https://doi.org/10.1111/mafi.12450

The name of Anders Max Reppen was incorrectly written as Andres Max Reppen.

We apologize for this error.

This paper investigates the optimal investment problem in a market with two types of illiquidity: transaction costs and search frictions. We analyze a power-utility maximization problem where an investor encounters proportional transaction costs and trades only when a Poisson process triggers trading opportunities. We show that the optimal trading strategy is described by a no-trade region. We introduce a novel asymptotic framework applicable when both transaction costs and search frictions are small. Using this framework, we derive explicit asymptotics for the no-trade region and the value function along a specific parametric curve. This approach unifies existing asymptotic results for models dealing exclusively with either transaction costs or search frictions.

Whereas data on implied volatilities are available for a large number of assets, this is less frequently the case of implied covolatilities. We introduce a new approach based on static and dynamic Wishart models to solve this problem of missing data. We first discuss the identification of the parameter of the (nonlinear state-space) Wishart models from observed implied volatilities. It is shown that the parameter of the Wishart models is identified, possibly up to some signs. Then we derive the filtering approach for implied covolatilities and apply it to different financial applications. The identification issues in other dynamic models based on spectral decomposition, matrix logarithm, and volatility–correlation decomposition are also discussed. We also discuss the implication of this result for the modeling of realized covariance matrices, when this latter is fully observable, by proposing new specification tests for Wishart type models.