Rituparna Sen - Academia.edu (original) (raw)

Papers by Rituparna Sen

Computational Finance with R

In this paper, the estimation of the Integrated Covariance matrix from high-frequency data, for h... more In this paper, the estimation of the Integrated Covariance matrix from high-frequency data, for high dimensional stock price process, is considered. The Hayashi-Yoshida covolatility estimator is an improvement over Realized covolatility for asynchronous data and works well in low dimensions. However it becomes inconsistent and unreliable in the high dimensional situation. We study the bulk spectrum of this matrix and establish its connection to the spectrum of the true covariance matrix in the limiting case where the dimension goes to infinity. The results are illustrated with simulation studies in finite, but high, dimensional cases. An application to real data with tick-by-tick data on 50 stocks is presented.

We develop a multivariate functional autoregressive model (MFAR), which captures the cross-correl... more We develop a multivariate functional autoregressive model (MFAR), which captures the cross-correlation among multiple functional time series and thus improves forecast accuracy. We estimate the parameters under the Bayesian dynamic linear models (DLM) framework. In order to capture Granger causality from one FAR series to another we employ Bayes Factor. Motivated by the broad application of functional data in finance, we investigate the causality between the yield curves of two countries. Furthermore, we illustrate a climatology example, examining whether the weather conditions Granger cause pollutant daily levels in a city.

arXiv: Statistical Finance, 2019

Spectral risk measures (SRMs) belongs to the family of coherent risk measures. A natural estimato... more Spectral risk measures (SRMs) belongs to the family of coherent risk measures. A natural estimator for the class of spectral risk measures (SRMs) has the form of LLL-statistics. In the literature, various authors have studied and derived the asymptotic properties of the estimator of SRM using the empirical distribution function. But no such estimator of SRM is studied considering distribution function estimator other than empirical cdf. We propose a kernel based estimator of SRM. We try to investigate the large sample properties of general LLL-statistics based on i.i.d cases and apply them to our kernel based estimator of SRM. We prove that the estimator is strongly consistent and the estimator is asymptotically normal. We compare the finite sample performance of the kernel based estimator with that of empirical estimator of SRM using Monte Carlo simulation, where appropriate choice of smoothing parameter and the user's coefficient of risk aversion plays an important role. Based...

Economic Modelling, 2018

Financial interdependence indicates a process through which transmission of shock originating in ... more Financial interdependence indicates a process through which transmission of shock originating in the financial market of one economy spreads to others. This paper provides a new idea of Residual and Recurrence Times of high or low values for bivariate time series to detect extreme dependence or contagion. In presence of financial extreme dependence, the distributions of residual and recurrence times are not the same. We examine the equality of two distributions using the permutation test. In comparison to other methods in multivariate extreme value theory, our proposed method does not need the i.i.d. assumption. Our method can handle the situation where the extremes for different components do not occur at the same time. We justify our methods in two ways: first using thorough simulation studies and then applying the proposed method to real data on weekly stock indices from sixteen markets.

An important aspect of the stock price process, which has often been ignored in the financial lit... more An important aspect of the stock price process, which has often been ignored in the financial literature, is that prices on organized exchanges are restricted to lie on a grid. We consider continuous-time models for the stock price process with random waiting times of jumps and discrete jump size. We consider a class of jump processes that arè`close'' to the Black-Scholes model in the sense that as the jump size goes to zero, the jump model converges to geometric Brownian motion. We study the changes in pricing and hedging caused by discretization. The convergence, estimation, discrete time approximation, and uniform integrability conditions for this model are studied. Upper and lower bounds on option prices are developed. We study the performance of the model with real data. In general, jump models do not admit self-financing strategies for derivative securities. Birth-death processes have the virtue that they allow perfect hedging of derivative securities. The effect of st...

arXiv: Portfolio Management, 2019

For a long investment time horizon, it is preferable to rebalance the portfolio weights at interm... more For a long investment time horizon, it is preferable to rebalance the portfolio weights at intermediate times. This necessitates a multi-period market model in which portfolio optimization is usually done through dynamic programming. However, this assumes a known distribution for the parameters of the financial time series. We consider the situation where this distribution is unknown and needs to be estimated from the data that is arriving dynamically. We applied Bayesian filtering through dynamic linear models to sequentially update the parameters. We considered uncertain investment lifetime to make the model more adaptive to the market conditions. These updated parameters are put into the dynamic mean-variance problem to arrive at optimal efficient portfolios. Extensive simulations are conducted to study the effect of varying underlying parameters and investment horizon on the performance of the method. An implementation of this model to the S&P500 illustrates that the Bayesian up...

Copula is a powerful tool to model multivariate data. Due to its several merits Copula modelling ... more Copula is a powerful tool to model multivariate data. Due to its several merits Copula modelling has become one of the most widely used methods to model financial data. We discuss the problem of modelling intraday financial data through Copula. The problem originates due to the nonsynchronous nature of intraday financial data whereas to estimate the Copula, we need synchronous observations. We show that this problem may lead to serious underestimation of the Copula parameter. We propose a modification to obtain a consistent estimator in case of Elliptical Copula or to reduce the bias significantly in case of general copulas.

New Perspectives and Challenges in Econophysics and Sociophysics, 2019

For high dimensional data some of the standard statistical techniques do not work well. So modifi... more For high dimensional data some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper we explore these modifications. We start with important problem of estimating high dimensional covariance matrix. Then we explore some of the important statistical techniques such as high dimensional regression, principal component analysis, multiple testing problems and classification. We describe some of the fast algorithms that can be readily applied in practice.

The stock price process is modelled as a continuous time jump process with exponential waiting ti... more The stock price process is modelled as a continuous time jump process with exponential waiting time. The exponential parameter is proportional to the value of the stock at that time. Conditions are obtained on the jump distribution so that as the minimum jump ...

Mathematical and Statistical Methods for Actuarial Sciences and Finance

Econometrics and Statistics

Applied Stochastic Models in Business and Industry

We develop time series analysis of functional data observed discretely, treating the whole curve ... more We develop time series analysis of functional data observed discretely, treating the whole curve as a random realization from a distribution on functions that evolve over time. The method consists of principal components analysis of functional data and subsequently modeling the principal component scores as vector autoregressive moving averag (VARMA) process. We justify the method by showing that an underlying ARMAH structure of the curves leads to a VARMA structure on the principal component scores. We derive asymptotic properties of the estimators, fits, and forecast. For term structures of interest rates, these provide a unified framework for studying the time and maturity components of interest rates under one setup with few parametric assumptions. We apply the method to the yield curves of USA and India. We compare our forecasts to the parametric model that is based on Nelson-Siegel curves. In another application, we study the dependence of long term interest rate on the short term interest rate using functional regression.

Asia-Pacific Financial Markets

Historical daily data for eleven years of the fifty constituent stocks of the NIFTY index traded ... more Historical daily data for eleven years of the fifty constituent stocks of the NIFTY index traded on the National Stock Exchange have been analyzed to check for the stylized facts in the Indian market. It is observed that while some stylized facts of other markets are also observed in Indian market, there are significant deviations in three main aspects, namely leverage, asymmetry and autocorrelation. Leverage and asymmetry are both reversed making this a more promising market to invest in. While significant autocorrelation observed in the returns points towards market inefficiency, the increased predictive power is better for investors.

Communications in Statistics - Simulation and Computation

An important component of the models for stock price process is volatility. It is necessary to es... more An important component of the models for stock price process is volatility. It is necessary to estimate volatility in many practical applications like option pricing, portfolio selection and risk management. Now-a-days stock price data is available at very high frequency and the most common estimator of volatility using such data is the realized variance. However in the presence of microstructure noise, realized variance diverges to infinity. The paper proposes principal component analysis of functional data approach to separate the volatility of a process from microstructure noise. This approach can be used to detect days on which the stock price process has jumps and to measure the size of jumps. Thus we can separate the jump component from the daily integrated volatility in the quadratic variation process. This separation leads to better understanding and prediction of integrated volatility. We develop the theory and present simulation as well as real data examples. We demonstrate how this additional source of the return variation introduces bias in normalizing the returns, in particular, when the bipower variation method is used in detecting jumps. We also investigate the predictability of our proposed method in forecasting Value at Risk (VaR).

Journal of Data Analysis and Information Processing, 2016

Markowitz Portfolio theory underestimates the risk associated with the return of a portfolio in c... more Markowitz Portfolio theory underestimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.

Journal of Quantitative Economics, 2016