arXiv subjects

Yunqi Liang

Publications and source records attributed to Yunqi Liang.

3 recordsLinked to original sources

arXiv2026

Corporate Bond Yield Curve Modeling: A Rating-Based Regime-Switching Generalized CIR Approach

Persistent shifts in term-structure dynamics undermine the stability of single-regime models in long samples. We develop an arbitrage-free regime-switching generalized CIR (RS-GCIR) model that jointly prices the Chinese government bond (CGB) curve and corporate bond curves. To capture the systematic transmission from interest-rate conditions to credit spreads, we structure the model into two blocks and price corporate bonds conditional on the prevailing rate regime. The rate block features a two-state RS-GCIR short-rate process estimated from CGB zero-coupon curves, while the credit block embeds CIR-type credit factors in an intensity-based framework for rating migration and default. We implement a block-recursive Unscented Kalman Filter (UKF) procedure--filtering the rate block first and the credit block next--using weekly data from 2014--2025, a period that begins with the onset of China's modern corporate default cycle. We identify two persistent rate regimes with distinct level--volatility profiles. Relative to single-regime benchmarks, regime switching improves joint curve fit, delivers economically interpretable filtered regime probabilities, and sharpens the decomposition of corporate yields into discounting and credit compensation.

q-fin.PR↗

arXiv2026

Beyond Picking Winners: Correlation-Driven Tail Risk in Venture Capital Portfolio Construction

We propose a Gaussian-copula-based framework that learns deal-level dependence directly from observed joint success frequencies across founder, geography, and market attributes. Holding marginal deal success probabilities fixed, deal-level correlation preserves expected portfolio outcomes but shifts the portfolio distribution toward heavier right tails and higher kurtosis. In portfolio simulations, correlation reduces the probability of modest success counts while sharply amplifying extreme upside outcomes, especially in structurally concentrated portfolios. Our findings suggest that extreme venture capital outcomes may partly reflect correlation-induced tail amplification rather than solely higher average deal quality, with potential implications for portfolio construction and risk management. We note that the observed dataset reflects selected deals with observable outcomes, which inflates apparent success rates relative to the true population base rate; however, the core finding that correlation reshapes the distributional shape while leaving the mean unchanged is structurally robust to the level of marginal success probabilities.

q-fin.PM↗

arXiv2023

Polynomial equations for matrices over integers modulo a prime power and the cokernel of a random matrix

Given a prime $p$ and a positive integer $k$, let $\mathrm{M}_{n}(\mathbb{Z}/p^{k}\mathbb{Z})$ be the ring of $n \times n$ matrices over $\mathbb{Z}/p^{k}\mathbb{Z}$. We consider the number of solutions $X \in \mathrm{M}_{n}(\mathbb{Z}/p^{k}\mathbb{Z})$ to the polynomial equation $P(X) = 0$, where $P(t)$ is a monic polynomial in $(\mathbb{Z}/p^{k}\mathbb{Z})[t]$ whose reduction modulo $p$ is square-free over the finite field $\mathbb{F}_{p}$ of $p$ elements. Noting that $P(X) = 0$ if and only if $\mathrm{cok}(P(X)) \simeq (\mathbb{Z}/p^{k}\mathbb{Z})^{n}$, we give a conjectural generalization of counting solutions to $P(X) = 0$ as the distribution of the cokernel $\mathrm{cok}(P(X))$ of $P(X)$ up to isomorphisms, where $X$ is a uniform random matrix in $\mathrm{M}_{n}(\mathbb{Z}/p^{k}\mathbb{Z})$. This distribution involves an explicit formula when we fix the residue class of $X$ modulo $p$. We prove this conjecture for the special case when the image of $P(t)$ in $\mathbb{F}_{p}[t]$ modulo $p$ is irreducible. We explain how the distribution we obtain is closely related to the Cohen-Lenstra distribution. Our proof involves algebraic and combinatorial arguments in linear algebra over $\mathbb{Z}/p^{k}\mathbb{Z}$ and builds upon a previous work of Cheong and Kaplan.

math.CO↗