arXiv subjects

Jimin Lin

Publications and source records attributed to Jimin Lin.

8 recordsLinked to original sources

arXiv2026

One Other Option Pricing Scheme

We present a distinctive approach to parameterizing the risk neutral distribution. Using parsimonious and interpretable parameters, the model provides direct and localized control over the shape of the implied volatility curve. It captures a wide variety of shapes, including those with local concavity. Empirical results demonstrate accurate calibration across a quarter million curves from a two-year Standard and Poor's 500 index option dataset. The fitted parameters exhibit stable patterns across tenors, enabling term structure interpolation and dynamic process construction without static arbitrage.

q-fin.CP↗

arXiv2026

Shallow Representation of Option Implied Information

Option prices encode the market's collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter to rule out static arbitrage. Despite earlier recognition of their parity, the two had been studied in isolation for decades until the recent demand in implied volatility modeling rejuvenated such parity. This paper provides a systematic approach to build neural representations of option implied information. As a preliminary, we first revisit the explicit link between implied density and implied volatility through an alternative and minimalist lens, where implied volatility is viewed not as volatility but as a pointwise corrector mapping the Black-Scholes quasi-density into the implied risk-neutral density. Building on this perspective, we propose the neural representation that incorporates arbitrage constraints through the differentiable corrector. With an additive logistic model as the synthetic benchmark, extensive experiments reveal that deeper or wider network structures do not necessarily improve the model performance due to the nonlinearity of both arbitrage constraints and neural derivatives. By contrast, a shallow feedforward network with a single hidden layer and a specific activation effectively approximates implied density and implied volatility.

q-fin.CP↗

arXiv2024

Neural Term Structure of Additive Process for Option Pricing

The additive process generalizes the L\'evy process by relaxing its assumption of time-homogeneous increments and hence covers a larger family of stochastic processes. Recent research in option pricing shows that modeling the underlying log price with an additive process has advantages in easier construction of the risk-neural measure, an explicit option pricing formula and characteristic function, and more flexibility to fit the implied volatility surface. Still, the challenge of calibrating an additive model arises from its time-dependent parameterization, for which one has to prescribe parametric functions for the term structure. For this, we propose the neural term structure model to utilize feedforward neural networks to represent the term structure, which alleviates the difficulty of designing parametric functions and thus attenuates the misspecification risk. Numerical studies with S\&P 500 option data are conducted to evaluate the performance of the neural term structure.

q-fin.CP↗

arXiv2024

NeuralBeta: Estimating Beta Using Deep Learning

Traditional approaches to estimating beta in finance often involve rigid assumptions and fail to adequately capture beta dynamics, limiting their effectiveness in use cases like hedging. To address these limitations, we have developed a novel method using neural networks called NeuralBeta, which is capable of handling both univariate and multivariate scenarios and tracking the dynamic behavior of beta. To address the issue of interpretability, we introduce a new output layer inspired by regularized weighted linear regression, which provides transparency into the model's decision-making process. We conducted extensive experiments on both synthetic and market data, demonstrating NeuralBeta's superior performance compared to benchmark methods across various scenarios, especially instances where beta is highly time-varying, e.g., during regime shifts in the market. This model not only represents an advancement in the field of beta estimation, but also shows potential for applications in other financial contexts that assume linear relationships.

q-fin.ST↗

arXiv2022

Reinforcement Learning for Intra-and-Inter-Bank Borrowing and Lending Mean Field Control Game

We propose a mean field control game model for the intra-and-inter-bank borrowing and lending problem. This framework allows to study the competitive game arising between groups of collaborative banks. The solution is provided in terms of an asymptotic Nash equilibrium between the groups in the infinite horizon. A three-timescale reinforcement learning algorithm is applied to learn the optimal borrowing and lending strategy in a data driven way when the model is unknown. An empirical numerical analysis shows the importance of the three-timescale, the impact of the exploration strategy when the model is unknown, and the convergence of the algorithm.

math.OC↗

arXiv2022

Bootstrap Percolation in Random Graphs of Unbounded Rank

Bootstrap percolation in (random) graphs is a contagion dynamic among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$ gets infected as soon as the number of its infected neighbors reaches $k$. This process has been studied extensively in \textit{rank one} models. These models can generate random graphs with heavy-tailed degree sequences but they are not capable of generating networks with a flexible stochastic block structure. In this paper, we treat a class of random graphs of unbounded rank that can generate flexible stochastic block structures. Our main result determines the limit in probability of the final fraction of infected vertices from the fixed point of a non-linear operator defined on a suitable function space. We propose a neural network based algorithm to calculate this fixed point efficiently. We further derive criteria based on the Fr\'echet derivative of the operator that allow one to determine whether small infections spread through the entire graph or rather stay local.

math.PR↗

arXiv2022

Reinforcement Learning Algorithm for Mixed Mean Field Control Games

We present a new combined \textit{mean field control game} (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between groups. Players coordinate their strategies within each group. An example is a modification of the classical trader's problem. Groups of traders maximize their wealth. They face cost for their transactions, for their own terminal positions, and for the average holding within their group. The asset price is impacted by the trades of all agents. We propose a three-timescale reinforcement learning algorithm to approximate the solution of such MFCG problems. We test the algorithm on benchmark linear-quadratic specifications for which we provide analytic solutions.

math.OC↗

arXiv2018

On Carr and Lee's correlation immunization strategy

In their seminal work Carr and Lee (2008) show how to robustly price and replicate a variety of claims written on the quadratic variation of a risky asset under the assumption that the asset's volatility process is independent of the Brownian motion that drives the asset's price. Additionally, they propose a correlation immunization strategy that minimizes the pricing and hedging error that results when the correlation between the risky asset's price and volatility is nonzero. In this paper, we show that the correlation immunization strategy is the only strategy among the class of strategies discussed in Carr and Lee (2008) that results in real-valued hedging portfolios when the correlation between the asset's price and volatility is nonzero. Additionally, we perform a number of Monte Carlo experiments to test the effectiveness of Carr and Lee's immunization strategy. Our results indicate that the correlation immunization method is an effective means of reducing pricing and hedging errors that result from nonzero correlation.

q-fin.MF↗