arXiv subjects

Minglian Lin

Publications and source records attributed to Minglian Lin.

6 recordsLinked to original sources

arXiv2026

Enhancing the Black-Scholes Model for Option Valuation via L\'evy Processes and Malliavin Calculus

The Black-Scholes model has been extensively used for option pricing, but exhibits limitations in its reliance on geometric Brownian motion and fixed volatility assumptions. This paper proposes an enhanced model incorporating stochastic volatility with jumps modeled by a L\'evy process. Leveraging multidimensional It\^o calculus, we derive a pricing formula for European call options under the new framework. Additionally, Malliavin calculus enables the derivation of an exact expression for at-the-money implied volatility. The proposed model is shown to better capture empirical features like volatility smiles. Analysis of VIX data demonstrates the model's ability to match observed market volatility. The integration of L\'evy processes and Malliavin calculus represents a valuable advancement in addressing deficiencies in the classic Black-Scholes model. Further empirical testing is warranted to validate the approach across varying market conditions and option types.

q-fin.MF↗

arXiv2026

The interplay between network transitivity and community structure

Recent empirical observations suggest that network transitivity is highly correlated with community structure in many real-world networks. In this paper, we theoretically investigate this relationship by deriving the limits of the global and average clustering coefficients for the geometric block model (GBM). Both limits exhibit a phase transition; specifically, the functional forms of the limit functions differ between the weak and strong community structure strength regimes. For a GBM with balanced communities, the limits of the global and average clustering coefficients are identical, whereas these limits differ for unbalanced communities. In general, the clustering coefficients do not exhibit a monotonic relationship with community structure strength. Particularly, for a balanced GBM where the within-community edge probability is a constant multiple of the between-community edge probability, the limit decreases from $3/4$ to $3/5$ and subsequently increases toward an asymptotic upper bound of $3/4$ as the multiple grows from one. A similar pattern is observed for the global clustering coefficient in unbalanced settings, where both limits exhibit an explicit dependence on community size.

math.ST↗

arXiv2025

Pricing Variance Swap for Multi-Asset Stochastic Volatility Models

This paper develops a novel framework for modeling variance swap of multi-asset stochastic volatility models by employing determinant-based instantaneous generalized variance. In this setting the determinant of the covariance matrix captures the joint dispersion of the multivariate log-return dynamics. By specifying the distribution of the log returns of the underlying assets under the Heston and Barndorff-Nielsen & Shephard (BNS) stochastic volatility frameworks, we obtain an analytical pricing expression for multi-asset Heston formulation, while BNS formulation is treated through a tractable approximation. To evaluate the robustness of the proposed model, we conduct simulations using nine different assets generated via the quantmod package. For a three-asset portfolio, analytical expressions for the generalized variance swap are obtained under both the Heston and BNS models. Numerical experiments further demonstrate the effectiveness of the proposed model through parameter testing, calibration, and validation.

q-fin.MF↗

arXiv2023

Estimation of VaR with jump process: application in corn and soybean markets

Value at Risk (VaR) is a quantitative measure used to evaluate the risk linked to the potential loss of investment or capital. Estimation of the VaR entails the quantification of prospective losses in a portfolio of investments, using a certain likelihood, under normal market conditions within a specific time period. The objective of this paper is to construct a model and estimate the VaR for a diversified portfolio consisting of multiple cash commodity positions driven by standard Brownian motions and jump processes. Subsequently, a thorough analytical estimation of the VaR is conducted for the proposed model. The results are then applied to two distinct commodities -- corn and soybean -- enabling a comprehensive comparison of the VaR values in the presence and absence of jumps.

q-fin.MF↗

arXiv2023

Analysis of optimal portfolio on finite and small-time horizons for a stochastic volatility model with multiple correlated assets

In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton-Jacobi-Bellman equation including the correlations among the standard Brownian motions. We use an approximation method for the optimization of portfolios. With such approximation, the value function is analyzed using the first-order terms of expansion of the utility function in the powers of time to the horizon. The error of this approximation is controlled using the second-order terms of expansion of the utility function. It is also shown that the one-dimensional version of this analysis corresponds to a known result in the literature. We also generate a close-to-optimal portfolio near the time to horizon using the first-order approximation of the utility function. It is shown that the error is controlled by the square of the time to the horizon. Finally, we provide an approximation scheme to the value function for all times and generate a close-to-optimal portfolio.

q-fin.MF↗

arXiv2021

Analysis of optimal portfolio on finite and small time horizons for a stochastic volatility market model

In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change from its current value. We consider an incomplete stochastic volatility market model, that is driven by both a Brownian motion and a jump process. At first, we obtain a closed-form formula for an approximation to the optimal portfolio in a small-time horizon. This is obtained by finding the associated Hamilton-Jacobi-Bellman integro-differential equation and then approximating the value function by constructing appropriate super-solution and sub-solution. It is shown that the true value function can be obtained by sandwiching the constructed super-solution and sub-solution. We also prove the accuracy of the approximation formulas. Finally, we provide a procedure for generating a close-to-optimal portfolio for a finite time horizon.

q-fin.PM↗