arXiv subjects

Shashi Jain

Publications and source records attributed to Shashi Jain.

16 recordsLinked to original sources

arXiv2026

Recovering Structural Organization in Noisy Correlation Networks Using Financial Systems as a Testbed

Empirical correlation matrices estimated from financial return time series are contaminated by statistical noise arising from finite sample size, obscuring genuine interactions among assets. We apply spectral decomposition to separate the empirical correlation matrix into a structured component associated with eigenvalues exceeding the Marchenko-Pastur bounds and a random component representing statistical noise. Using daily returns from the NIFTY 200, NIFTY 500, and S&P 500 over 2010-2022, we show that the structured component, constructed from only 10-16 eigenmodes, reproduces the main statistical properties of the full correlation matrix while removing most noise-dominated eigenmodes. Financial networks derived from the structured component exhibit significantly stronger and more stable core-periphery organization than networks constructed from the full or random matrices. Degree-preserving randomization, Kolmogorov-Smirnov, and Wasserstein distance tests confirm a clear statistical separation between structured and random components. We further show that structured networks display pronounced scale-free degree distributions in the Indian markets. As a practical application, portfolios constructed from peripheral assets of the denoised networks consistently outperform portfolios based on unfiltered correlations and standard benchmarks on a risk-adjusted basis, with robustness verified through Monte Carlo subsampling. These results demonstrate that spectral denoising effectively recovers meaningful network structure from noisy financial correlations.

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arXiv2025

Robust Hedging of path-dependent options using a min-max algorithm

We consider an investor who wants to hedge a path-dependent option with maturity $T$ using a static hedging portfolio using cash, the underlying, and vanilla put/call options on the same underlying with maturity $ t_1$, where $0 < t_1 < T$. We propose a model-free approach to construct such a portfolio. The framework is inspired by the \textit{primal-dual} Martingale Optimal Transport (MOT) problem, which was pioneered by \cite{beiglbock2013model}. The optimization problem is to determine the portfolio composition that minimizes the expected worst-case hedging error at $t_1$ (that coincides with the maturity of the options that are used in the hedging portfolio). The worst-case scenario corresponds to the distribution that yields the worst possible hedging performance. This formulation leads to a \textit{min-max} problem. We provide a numerical scheme for solving this problem when a finite number of vanilla option prices are available. Numerical results on the hedging performance of this model-free approach when the option prices are generated using a \textit{Black-Scholes} and a \textit{Merton Jump diffusion} model are presented. We also provide theoretical bounds on the hedging error at $T$, the maturity of the target option.

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arXiv2025

Order-Flow Filtration and Directional Association with Short-Horizon Returns

Electronic markets generate dense order flow with many transient orders, which degrade directional signals derived from the limit order book (LOB). We study whether simple structural filters on order lifetime, modification count, and modification timing sharpen the association between order book imbalance (OBI) and short-horizon returns in BankNifty index futures, where unfiltered OBI is already known to be a strong short-horizon directional indicator. The efficacy of each filter is evaluated using a three-step diagnostic ladder: contemporaneous correlations, linear association between discretised regimes, and Hawkes event-time excitation between OBI and return regimes. Our results indicate that filtration of the aggregate order flow produces only modest changes relative to the unfiltered benchmark. By contrast, when filters are applied on the parent orders of executed trades, the resulting OBI series exhibits systematically stronger directional association. Motivated by recent regulatory initiatives to curb noisy order flow, we treat the association between OBI and short-horizon returns as a policy-relevant diagnostic of market quality. We then compare unfiltered and filtered OBI series, using tick-by-tick data from the National Stock Exchange of India, to infer how structural filters on the order flow affect OBI-return dynamics in an emerging market setting.

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arXiv2025

Event-Time Anchor Selection for Multi-Contract Quoting

When quoting across multiple contracts, the sequence of execution can be a key driver of implementation shortfall relative to the target spread~\cite{bergault2022multi}. We model the short-horizon execution risk from such quoting as variations in transaction prices between the initiation of the first leg and the completion of the position. Our quoting policy anchors the spread by designating one contract ex ante as a \emph{reference contract}. Reducing execution risk requires a predictive criterion for selecting that contract whose price is most stable over the execution interval. This paper develops a diagnostic framework for reference-contract selection that evaluates this stability by contrasting order-flow Hawkes forecasts with a Composite Liquidity Factor (CLF) of instantaneous limit order book (LOB) shape. We illustrate the framework on tick-by-tick data for a pair of NIFTY futures contracts. The results suggest that event-history and LOB-state signals offer complementary views of short-horizon execution risk for reference-contract selection.

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arXiv2024

Forecasting High Frequency Order Flow Imbalance

Market information events are generated intermittently and disseminated at high speeds in real-time. Market participants consume this high-frequency data to build limit order books, representing the current bids and offers for a given asset. The arrival processes, or the order flow of bid and offer events, are asymmetric and possibly dependent on each other. The quantum and direction of this asymmetry are often associated with the direction of the traded price movement. The Order Flow Imbalance (OFI) is an indicator commonly used to estimate this asymmetry. This paper uses Hawkes processes to estimate the OFI while accounting for the lagged dependence in the order flow between bids and offers. Secondly, we develop a method to forecast the near-term distribution of the OFI, which can then be used to compare models for forecasting OFI. Thirdly, we propose a method to compare the forecasts of OFI for an arbitrarily large number of models. We apply the approach developed to tick data from the National Stock Exchange and observe that the Hawkes process modeled with a Sum of Exponential's kernel gives the best forecast among all competing models.

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arXiv2024

Neural Networks for Portfolio-Level Risk Management: Portfolio Compression, Static Hedging, Counterparty Credit Risk Exposures and Impact on Capital Requirement

In this paper, we present an artificial neural network framework for portfolio compression of a large portfolio of European options with varying maturities (target portfolio) by a significantly smaller portfolio of European options with shorter or same maturity (compressed portfolio), which also represents a self-replicating static hedge portfolio of the target portfolio. For the proposed machine learning architecture, which is consummately interpretable by choice of design, we also define the algorithm to learn model parameters by providing a parameter initialisation technique and leveraging the optimisation methodology proposed in Lokeshwar and Jain (2024), which was initially introduced to price Bermudan options. We demonstrate the convergence of errors and the iterative evolution of neural network parameters over the course of optimization process, using selected target portfolio samples for illustration. We demonstrate through numerical examples that the Exposure distributions and Exposure profiles (Expected Exposure and Potential Future Exposure) of the target portfolio and compressed portfolio align closely across future risk horizons under risk-neutral and real-world scenarios. Additionally, we benchmark the target portfolio's Financial Greeks (Delta, Gamma, and Vega) against the compressed portfolio at future time horizons across different market scenarios generated by Monte-Carlo simulations. Finally, we compare the regulatory capital requirement under the standardised approach for counterparty credit risk of the target portfolio against the compressed portfolio and highlight that the capital requirement for the compact portfolio substantially reduces.

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arXiv2024

Optimizing Neural Networks for Bermudan Option Pricing: Convergence Acceleration, Future Exposure Evaluation and Interpolation in Counterparty Credit Risk

This paper presents a Monte-Carlo-based artificial neural network framework for pricing Bermudan options, offering several notable advantages. These advantages encompass the efficient static hedging of the target Bermudan option and the effective generation of exposure profiles for risk management. We also introduce a novel optimisation algorithm designed to expedite the convergence of the neural network framework proposed by Lokeshwar et al. (2022) supported by a comprehensive error convergence analysis. We conduct an extensive comparative analysis of the Present Value (PV) distribution under Markovian and no-arbitrage assumptions. We compare the proposed neural network model in conjunction with the approach initially introduced by Longstaff and Schwartz (2001) and benchmark it against the COS model, the pricing model pioneered by Fang and Oosterlee (2009), across all Bermudan exercise time points. Additionally, we evaluate exposure profiles, including Expected Exposure and Potential Future Exposure, generated by our proposed model and the Longstaff-Schwartz model, comparing them against the COS model. We also derive exposure profiles at finer non-standard grid points or risk horizons using the proposed approach, juxtaposed with the Longstaff Schwartz method with linear interpolation and benchmark against the COS method. In addition, we explore the effectiveness of various interpolation schemes within the context of the Longstaff-Schwartz method for generating exposures at finer grid horizons.

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arXiv2024

Non-Parametric Estimation of Multi-dimensional Marked Hawkes Processes

An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. While extensive literature has been dedicated to the non-parametric estimation of both the linear and non-linear Hawkes process, there remains a significant gap in the literature regarding the marked Hawkes process. In response to this, we propose a methodology for estimating the conditional intensity of the marked Hawkes process. We introduce two distinct models: \textit{Shallow Neural Hawkes with marks}- for Hawkes processes with excitatory kernels and \textit{Neural Network for Non-Linear Hawkes with Marks}- for non-linear Hawkes processes. Both these approaches take the past arrival times and their corresponding marks as the input to obtain the arrival intensity. This approach is entirely non-parametric, preserving the interpretability associated with the marked Hawkes process. To validate the efficacy of our method, we subject the method to synthetic datasets with known ground truth. Additionally, we apply our method to model cryptocurrency order book data, demonstrating its applicability to real-world scenarios.

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arXiv2024

Data-driven Approach for Static Hedging of Exchange Traded Options

This paper presents a data-driven interpretable machine learning algorithm for semi-static hedging of Exchange Traded options, considering transaction costs with efficient run-time. Further, we provide empirical evidence on the performance of hedging longer-term National Stock Exchange (NSE) Index options using a self-replicating portfolio of shorter-term options and cash position, achieved by the automated algorithm, under different modeling assumptions and market conditions, including Covid period. We also systematically assess the model's performance using the Superior Predictive Ability (SPA) test by benchmarking against the static hedge proposed by Peter Carr and Liuren Wu and industry-standard dynamic hedging. We finally perform a thorough Profit and Loss (PnL) attribution analysis on the target option and hedge portfolios (dynamic and static) to discern the factors explaining the superior performance of static hedging.

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arXiv2023

Multi-period static hedging of European options

We consider the hedging of European options when the price of the underlying asset follows a single-factor Markovian framework. By working in such a setting, Carr and Wu \cite{carr2014static} derived a spanning relation between a given option and a continuum of shorter-term options written on the same asset. In this paper, we have extended their approach to simultaneously include options over multiple short maturities. We then show a practical implementation of this with a finite set of shorter-term options to determine the hedging error using a Gaussian Quadrature method. We perform a wide range of experiments for both the \textit{Black-Scholes} and \textit{Merton Jump Diffusion} models, illustrating the comparative performance of the two methods.

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arXiv2023

Precision versus Shrinkage: A Comparative Analysis of Covariance Estimation Methods for Portfolio Allocation

In this paper, we perform a comprehensive study of different covariance and precision matrix estimation methods in the context of minimum variance portfolio allocation. The set of models studied by us can be broadly categorized as: Gaussian Graphical Model (GGM) based methods, Shrinkage Methods, Thresholding and Random Matrix Theory (RMT) based methods. Among these, GGM methods estimate the precision matrix directly while the other approaches estimate the covariance matrix. We perform a synthetic experiment to study the network learning and sample complexity performance of GGM methods. Thereafter, we compare all the covariance and precision matrix estimation methods in terms of their predictive ability for daily, weekly and monthly horizons. We consider portfolio risk as an indicator of estimation error and employ it as a loss function for comparison of the methods under consideration. We find that GGM methods outperform shrinkage and other approaches. Our observations for the performance of GGM methods are consistent with the synthetic experiment. We also propose a new criterion for the hyperparameter tuning of GGM methods. Our tuning approach outperforms the existing methodology in the synthetic setup. We further perform an empirical experiment where we study the properties of the estimated precision matrix. The properties of the estimated precision matrices calculated using our tuning approach are in agreement with the algorithm performances observed in the synthetic experiment and the empirical experiment for predictive ability performance comparison. Apart from this, we perform another synthetic experiment which demonstrates the direct relation between estimation error of the precision matrix and portfolio risk.

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arXiv2023

A neural network based model for multi-dimensional nonlinear Hawkes processes

This paper introduces the Neural Network for Nonlinear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit nonlinear Hawkes processes. Our method is suitable for analyzing large datasets in which events exhibit both mutually-exciting and inhibitive patterns. The NNNH approach models the individual kernels and the base intensity of the nonlinear Hawkes process using feed forward neural networks and jointly calibrates the parameters of the networks by maximizing the log-likelihood function. We utilize Stochastic Gradient Descent to search for the optimal parameters and propose an unbiased estimator for the gradient, as well as an efficient computation method. We demonstrate the flexibility and accuracy of our method through numerical experiments on both simulated and real-world data, and compare it with state-of-the-art methods. Our results highlight the effectiveness of the NNNH method in accurately capturing the complexities of nonlinear Hawkes processes.

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arXiv2022

A semi-static replication approach to efficient hedging and pricing of callable IR derivatives

We present a semi-static hedging algorithm for callable interest rate derivatives under an affine, multi-factor term-structure model. With a traditional dynamic hedge, the replication portfolio needs to be updated continuously through time as the market moves. In contrast, we propose a semi-static hedge that needs rebalancing on just a finite number of instances. We show, taking as an example Bermudan swaptions, that callable interest rate derivatives can be replicated with an options portfolio written on a basket of discount bonds. The static portfolio composition is obtained by regressing the target option's value using an interpretable, artificial neural network. Leveraging on the approximation power of neural networks, we prove that the hedging error can be arbitrarily small for a sufficiently large replication portfolio. A direct, a lower bound, and an upper bound estimator for the risk-neutral Bermudan swaption price is inferred from the hedging algorithm. Additionally, closed-form error margins to the price statistics are determined. We practically demonstrate the hedging and pricing performance through several numerical experiments.

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arXiv2021

Method of lines for valuation and sensitivities of Bermudan options

In this paper, we present a computationally efficient technique based on the \emph{Method of Lines} (MOL) for the approximation of the Bermudan option values via the associated partial differential equations (PDEs). The MOL converts the Black Scholes PDE to a system of ordinary differential equations (ODEs). The solution of the system of ODEs so obtained only requires spatial discretization and avoids discretization in time. Additionally, the exact solution of the ODEs can be obtained efficiently using the exponential matrix operation, making the method computationally attractive and straightforward to implement. An essential advantage of the proposed approach is that the associated Greeks can be computed with minimal additional computations. We illustrate, through numerical experiments, the efficacy of the proposed method in pricing and computation of the sensitivities for a European call, cash-or-nothing, powered option, and Bermudan put option.

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arXiv2020

Shallow Neural Hawkes: Non-parametric kernel estimation for Hawkes processes

Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes two major contributions, we first find an unbiased estimator for the log-likelihood estimator of the Hawkes process to enable efficient use of the stochastic gradient descent method for maximum likelihood estimation. The second contribution is, we propose a specific single hidden layered neural network for the non-parametric estimation of the underlying kernels of the MHP. We evaluate the proposed model on both synthetic and real datasets, and find the method has comparable or better performance than existing estimation methods. The use of shallow neural network ensures that we do not compromise on the interpretability of the Hawkes model, while at the same time have the flexibility to estimate any non-standard Hawkes excitation kernel.

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arXiv2019

Neural network for pricing and universal static hedging of contingent claims

We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for interpretability of the model, a feature that is often desirable in the financial context. Specifically, the interpretation leads us to demonstrate that any contingent claim -- possibly high dimensional and path-dependent -- under the Markovian and the no-arbitrage assumptions, can be semi-statically hedged using a portfolio of short maturity options. We show how the method can be used to obtain an upper and lower bound to the true price, where the lower bound is obtained by following a sub-optimal policy, while the upper bound by exploiting the dual formulation. Unlike other duality based upper bounds where one typically has to resort to nested simulation for constructing super-martingales, the martingales in the current approach come at no extra cost, without the need for any sub-simulations. We demonstrate through numerical examples the simplicity and efficiency of the method for both pricing and semi-static hedging of path-dependent options

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