arXiv subjects

Indranil SenGupta

Publications and source records attributed to Indranil SenGupta.

14 recordsLinked to original sources

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↗

arXiv2023

Some asymptotics for short maturity Asian options

Most of the existing methods for pricing Asian options are less efficient in the limit of small maturities and small volatilities. In this paper, we use the large deviations theory for the analysis of short-maturity Asian options. We present a local volatility model for the underlying market that incorporates a jump term in addition to the drift and diffusion terms. We estimate the asymptotics for the out-of-the-money, in-the-money, and at-the-money short-maturity Asian call and put options. Under appropriate assumptions, we show that the asymptotics for out-of-the-money Asian call and put options are governed by rare events. For the at-the-money Asian options, the result is more involved and in that case, we find the upper and lower bounds of the asymptotics of the Asian option price.

q-fin.PR↗

arXiv2022

Stochastic volatility modeling of high-frequency CSI 300 index and dynamic jump prediction driven by machine learning

This paper models stochastic process of price time series of CSI 300 index in Chinese financial market, analyzes volatility characteristics of intraday high-frequency price data. In the new generalized Barndorff-Nielsen and Shephard model, the lag caused by asynchrony of market information is considered, and the problem of lack of long-term dependence is solved. To speed up the valuation process, several machine learning and deep learning algorithms are used to estimate parameter and evaluate forecast results. Tracking historical jumps of different magnitudes offers promising avenues for simulating dynamic price processes and predicting future jumps. Numerical results show that the deterministic component of stochastic volatility processes would always be captured over short and longer-term windows. Research finding could be suitable for influence investors and regulators interested in predicting market dynamics based on realized volatility.

q-fin.ST↗

arXiv2021

A data-science-driven short-term analysis of Amazon, Apple, Google, and Microsoft stocks

In this paper, we implement a combination of technical analysis and machine/deep learning-based analysis to build a trend classification model. The goal of the paper is to apprehend short-term market movement, and incorporate it to improve the underlying stochastic model. Also, the analysis presented in this paper can be implemented in a \emph{model-independent} fashion. We execute a data-science-driven technique that makes short-term forecasts dependent on the price trends of current stock market data. Based on the analysis, three different labels are generated for a data set: $+1$ (buy signal), $0$ (hold signal), or $-1$ (sell signal). We propose a detailed analysis of four major stocks- Amazon, Apple, Google, and Microsoft. We implement various technical indicators to label the data set according to the trend and train various models for trend estimation. Statistical analysis of the outputs and classification results are obtained.

q-fin.ST↗

arXiv2021

Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging

In this paper, we introduce and analyze the fractional Barndorff-Nielsen and Shephard (BN-S) stochastic volatility model. The proposed model is based upon two desirable properties of the long-term variance process suggested by the empirical data: long-term memory and jumps. The proposed model incorporates the long-term memory and positive autocorrelation properties of fractional Brownian motion with $H>1/2$, and the jump properties of the BN-S model. We find arbitrage-free prices for variance and volatility swaps for this new model. Because fractional Brownian motion is still a Gaussian process, we derive some new expressions for the distributions of integrals of continuous Gaussian processes as we work towards an analytic expression for the prices of these swaps. The model is analyzed in connection to the quadratic hedging problem and some related analytical results are developed. The amount of derivatives required to minimize a quadratic hedging error is obtained. Finally, we provide some numerical analysis based on the VIX data. Numerical results show the efficiency of the proposed model compared to the Heston model and the classical BN-S model.

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↗

arXiv2021

Analysis of stock index with a generalized BN-S model: an approach based on machine learning and fuzzy parameters

In this paper we implement a combination of data-science and fuzzy theory to improve the classical Barndorff-Nielsen and Shephard model, and implement this to analyze the S&P 500 index. We pre-process the index data based on fuzzy theory. After that, S&P 500 stock index data for the past ten years are analyzed, and a deterministic parameter is extracted using various machine and deep learning methods. The results show that the new model, where fuzzy parameters are incorporated, can incorporate the long-term dependence in the classical Barndorff-Nielsen and Shephard model. The modification is based on only a few changes compared to the classical model. At the same time, the resulting analysis effectively captures the stochastic dynamics of the stock index time series.

q-fin.MF↗

arXiv2020

Multi-asset Generalised Variance Swaps in Barndorff-Nielsen and Shephard model

This paper proposes swaps on two important new measures of generalized variance, namely the maximum eigenvalue and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for Barndorff-Nielsen and Shephard model used in financial markets. We consider multiple assets in the portfolio for theoretical purpose and demonstrate our approach with numerical examples taking three stocks in the portfolio. The results obtained in this paper have important implications for the commodity sector where such swaps would be useful for hedging risk.

q-fin.MF↗

arXiv2020

First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process

In this paper, an approximate version of the Barndorff-Nielsen and Shephard model, driven by a Brownian motion and a L\'evy subordinator, is formulated. The first-exit time of the log-return process for this model is analyzed. It is shown that with certain probability, the first-exit time process of the log-return is decomposable into the sum of the first exit time of the Brownian motion with drift, and the first exit time of a L\'evy subordinator with drift. Subsequently, the probability density functions of the first exit time of some specific L\'evy subordinators, connected to stationary, self-decomposable variance processes, are studied. Analytical expressions of the probability density function of the first-exit time of three such L\'evy subordinators are obtained in terms of various special functions. The results are implemented to empirical S&P 500 dataset.

q-fin.MF↗

arXiv2020

Hedging and machine learning driven crude oil data analysis using a refined Barndorff-Nielsen and Shephard model

In this paper, a refined Barndorff-Nielsen and Shephard (BN-S) model is implemented to find an optimal hedging strategy for commodity markets. The refinement of the BN-S model is obtained with various machine and deep learning algorithms. The refinement leads to the extraction of a deterministic parameter from the empirical data set. The problem is transformed to an appropriate classification problem with a couple of different approaches: the volatility approach and the duration approach. The analysis is implemented to the Bakken crude oil data and the aforementioned deterministic parameter is obtained for a wide range of data sets. With the implementation of this parameter in the refined model, the resulting model performs much better than the classical BN-S model.

q-fin.MF↗

arXiv2020

Sequential hypothesis testing in machine learning, and crude oil price jump size detection

In this paper we present a sequential hypothesis test for the detection of general jump size distrubution. Infinitesimal generators for the corresponding log-likelihood ratios are presented and analyzed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. This is shown to be implementable in relation to various classification problems for a crude oil price data set. Machine and deep learning algorithms are implemented to extract a specific deterministic component from the crude oil data set, and the deterministic component is implemented to improve the Barndorff-Nielsen and Shephard model, a commonly used stochastic model for derivative and commodity market analysis.

stat.ME↗

arXiv2019

Refinements of Barndorff-Nielsen and Shephard model: an analysis of crude oil price with machine learning

A commonly used stochastic model for derivative and commodity market analysis is the Barndorff-Nielsen and Shephard (BN-S) model. Though this model is very efficient and analytically tractable, it suffers from the absence of long range dependence and many other issues. For this paper, the analysis is restricted to crude oil price dynamics. A simple way of improving the BN-S model with the implementation of various machine learning algorithms is proposed. This refined BN-S model is more efficient and has fewer parameters than other models which are used in practice as improvements of the BN-S model. The procedure and the model show the application of data science for extracting a "deterministic component" out of processes that are usually considered to be completely stochastic. Empirical applications validate the efficacy of the proposed model for long range dependence.

q-fin.ST↗

arXiv2019

Infinitesimal generators for two-dimensional L\'evy process-driven hypothesis testing

In this paper, we present the testing of four hypotheses on two streams of observations that are driven by L\'evy processes. This is applicable for sequential decision making on the state of two-sensor systems. In one case, each sensor receives or does not receive a signal obstructed by noise. In another, each sensor receives data-driven by L\'evy processes with large or small jumps. In either case, these give rise to four possibilities. Infinitesimal generators are presented and analyzed. Bounds for infinitesimal generators in terms of \emph{super-solutions} and \emph{sub-solutions} are computed. An application of this procedure for the stochastic model is also presented in relation to the financial market.

math.ST↗