arXiv subjects

Sourav Majumdar

Publications and source records attributed to Sourav Majumdar.

7 recordsLinked to original sources

arXiv2026

Physical Extinction and Long-Run Pricing under Time-Varying Beliefs

An investor may be optimistic about aggregate endowment growth at some times and pessimistic at others. The weight placed on her forecast in bond valuation can therefore vary across maturities. We study whether this maturity dependence disappears at the long end of the yield curve. In a two-investor Arrow--Debreu economy, physical extinction follows when \emph{total disagreement} grows without bound. We find that bond valuation depends on net disagreement. If \emph{net disagreement} has no limit, neither the long-forward measure nor the long bond exists. Bond yields can converge along the same belief path. The long yield alone therefore cannot reveal whether valuation weights and bond returns converge across maturities. We also obtain finite-maturity error bounds for bond prices and forward densities.

q-fin.MF↗

arXiv2026

A stochastic correlation extension of the Vasicek credit risk model

In this paper we extend the Vasicek credit risk model by modelling the correlation as a continuous-time process. The models for correlation follow diffusion processes on the circle. In particular we work with the Circular Brownian motion and a mean-reverting von Mises process. The analytical and computational tractability of these circular diffusion enables us to derive terminal asset and loss distributions by averaging their conditional laws over the law of time-averaged correlation, and evaluate path-dependent probabilities by Monte Carlo simulation. Simulations distinguish terminal joint default, joint survival, first-to-default, and joint first passage, and show how stochastic correlation reallocates probability between concordant and discordant outcomes. We fit both specifications to U.S. bank charge-off data, demonstrating that the framework remains tractable for probabilistic analysis and statistical estimation.

q-fin.RM↗

arXiv2026

Exact conditional goodness-of-fit tests for the mixed membership stochastic block model

We propose exact conditional goodness-of-fit tests for directed mixed membership stochastic block models. Given dyad-level sender and receiver roles, the block-pair edge totals are sufficient for the block probability matrix; conditioning on these totals gives a nuisance-free uniform law on a finite fiber. This yields finite-sample randomization tests for residual sender and receiver heterogeneity, reciprocity, and directed transitive closure. The procedure uses an independent fiber sampler, Monte Carlo rank $p$-values, and can be applied after drawing latent block-pair assignments from the posterior distribution. Simulations and the Sampson monastery network show that the tests are calibrated under the null and diagnostically useful for directed model misspecification.

stat.ME↗

arXiv2026

A Circular Chatterjee's Correlation Coefficient

Chatterjee's rank correlation is a directed measure of association designed to detect whether one variable can be predicted as a function of another. While the original coefficient is naturally defined for real-valued data, circular data poses additional difficulty. Applying the usual construction requires cutting each circle at an arbitrary point and treating it as a line. Different choices of cut points can lead to different finite-sample values, even though the underlying circular relationship is unchanged. This paper proposes a circular version of Chatterjee's coefficient that removes this arbitrary choice. The population construction averages over response cuts in circular rank space, and the finite-sample construction averages over sample cut gaps and reduces to a simple statistic based only on cyclic ranks. The resulting coefficient is intrinsic to the circular ordering of the data, remains directed, and retains the key interpretation of Chatterjee's original coefficient. Under non-atomic circular marginals, it is zero exactly under independence and one exactly when the circular response is a measurable function of the circular predictor. We prove consistency and derive its distribution-free null behavior under independence. Simulations show that the proposed coefficient is especially useful for detecting multi-winding circular relationships, such as cases where the response goes around the circle twice or four times as the predictor goes around once, where standard circular correlations can be nearly blind.

math.ST↗

arXiv2026

Markov processes on a circular lattice

We develop a Markov process viewpoint for discrete circular distributions motivated by directional-statistics settings where angles are observed on a finite grid and evolve over time. On the $m$-point discrete circle, the cycle graph, we study diffusion-generated families, obtaining an explicit transition kernel, exact trigonometric moments, and convergence to uniformity. We present a simple approach to construct reversible nearest-neighbour chains with any prescribed strictly positive stationary pmf $π$, providing discrete analogues of Markov processes on the continuous circle. We construct processes whose stationary laws are the discrete von Mises and wrapped Cauchy distributions with closed-form normalizers and exact moments.

math.ST↗

arXiv2026

Asian option valuation under price impact

We develop a tractable framework for valuing Asian options when trading the underlying generates market impact and execution costs. Starting from a discrete-time, quote-level model, we construct a reference midpoint suitable for Asian payoffs and separate market impact into a transient component and a permanent drift distortion driven by signed trading. This specification admits continuous-time limits where the midpoint and impact state converge to a coupled system in which the midpoint drift depends on the transient impact state and in the endogenous regime on the hedger's trading rate, with correlated price and order-flow shocks. We study valuation in two complementary regimes. In an exogenous benchmark, the impact state evolves independently of the hedger. When the order-flow volatility is deterministic, we obtain a closed-form expression for the geometric Asian call. In an endogenous regime, trading volumes feed back into prices and costs, leading to a stochastic control problem and Hamilton-Jacobi-Bellman equations. We define reservation bid and ask prices via cost-based indifference which produces an impact-driven bid-ask spread. For computations, we propose a CRR-style tree-based Bellman algorithm. Numerical experiments show that exogenous impact effects are modest relative to frictionless benchmarks, while endogenous indifference prices generate nontrivial bid-ask spreads that grow super-linearly in impact parameters, widen when execution costs are lower, and shrink with faster mean reversion, highlighting the interaction between averaging in Asian options, price impact effects, and strategic trading.

q-fin.MF↗

arXiv2026

Diffusion on the circle and a stochastic correlation model

We develop diffusion models for time-varying correlation using stochastic processes defined on the unit circle. Specifically, we study Brownian motion on the circle and the von Mises diffusion, and propose their use as continuous-time models for correlation dynamics. The von Mises process, introduced by Kent (1975) as a characterization of the von Mises distribution in circular statistics, does not have a known closed-form transition density, which has limited its use in likelihood-based inference. We derive an accurate analytical approximation to the transition density of the von Mises diffusion, enabling practical likelihood-based estimation. We study inference for discretely observed circular diffusions, establish consistency and asymptotic normality of the resulting estimators, and propose a stochastic correlation model for financial applications. The methodology is illustrated through simulation studies and empirical applications to equity-foreign exchange market data.

math.ST↗