arXiv subjects

Nino Kordzakhia

Publications and source records attributed to Nino Kordzakhia.

13 recordsLinked to original sources

arXiv2025

PDSim: A Shiny App for Simulating and Estimating Polynomial Diffusion Models in Commodity Futures

PDSim is an R package that enables users to simulate commodity futures prices using the polynomial diffusion model introduced in Filipovic & Larsson (2016) through both a Shiny web application and R scripts. For user-supplied data, a standalone R routine has been developed to provide joint estimation of state variables and model parameters via the Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF). With its user-friendly interface, PDSim makes the features of simulations and estimations accessible. To date, it is the only package specifically designed for the simulation and estimation of the polynomial diffusion model. The Schwartz-Smith two-factor model (Schwartz & Smith, 2000) is also available within this package for both simulation and calibration. The package is validated through several tests, including replication of the results in Schwartz & Smith (2000), unit testing of the coverage rate, and verification of the outputs of the main functions.

q-fin.ST↗

arXiv2025

On Finite Time Span Estimators of Parameters for Ornstein-Uhlenbeck Processes

We study the bias and the mean-squared error of the maximum likelihood estimators (MLE) of parameters associated with a two-parameter mean-reverting process for a finite time $T$. Using the likelihood ratio process, we derive the expressions for MLEs, then compute the bias and the MSE via the change of measure and Ito's formula. We apply the derived expressions to the general Ornstein-Uhlenbeck process, where the bias and the MSE are numerically computed through a joint moment-generating function of key functionals of the O-U process. A numerical study is provided to illustrate the behaviour of bias and the MSE for the MLE of the mean-reverting speed parameter.

math.ST↗

arXiv2024

Multi-Factor Function-on-Function Regression of Bond Yields on WTI Commodity Futures Term Structure Dynamics

In the analysis of commodity futures, it is commonly assumed that futures prices are driven by two latent factors: short-term fluctuations and long-term equilibrium price levels. In this study, we extend this framework by introducing a novel state-space functional regression model that incorporates yield curve dynamics. Our model offers a distinct advantage in capturing the interdependencies between commodity futures and the yield curve. Through a comprehensive empirical analysis of WTI crude oil futures, using US Treasury yields as a functional predictor, we demonstrate the superior accuracy of the functional regression model compared to the Schwartz-Smith two-factor model, particularly in estimating the short-end of the futures curve. Additionally, we conduct a stress testing analysis to examine the impact of both temporary and permanent shocks to US Treasury yields on futures price estimation.

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arXiv2024

Multi-Factor Polynomial Diffusion Models and Inter-Temporal Futures Dynamics

In stochastic multi-factor commodity models, it is often the case that futures prices are explained by two latent state variables which represent the short and long term stochastic factors. In this work, we develop the family of stochastic models using polynomial diffusion to obtain the unobservable spot price to be used for modelling futures curve dynamics. The polynomial family of diffusion models allows one to incorporate a variety of non-linear, higher-order effects, into a multi-factor stochastic model, which is a generalisation of Schwartz and Smith (2000) two-factor model. Two filtering methods are used for the parameter and the latent factor estimation to address the non-linearity. We provide a comparative analysis of the performance of the estimation procedures. We discuss the parameter identification problem present in the polynomial diffusion case, regardless, the futures prices can still be estimated accurately. Moreover, we study the effects of different methods of calculating matrix exponential in the polynomial diffusion model. As the polynomial order increases, accurately and efficiently approximating the high-dimensional matrix exponential becomes essential in the polynomial diffusion model.

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arXiv2024

State-Space Dynamic Functional Regression for Multicurve Fixed Income Spread Analysis and Stress Testing

The Nelson-Siegel model is widely used in fixed income markets to produce yield curve dynamics. The multiple time-dependent parameter model conveniently addresses the level, slope, and curvature dynamics of the yield curves. In this study, we present a novel state-space functional regression model that incorporates a dynamic Nelson-Siegel model and functional regression formulations applied to multi-economy setting. This framework offers distinct advantages in explaining the relative spreads in yields between a reference economy and a response economy. To address the inherent challenges of model calibration, a kernel principal component analysis is employed to transform the representation of functional regression into a finite-dimensional, tractable estimation problem. A comprehensive empirical analysis is conducted to assess the efficacy of the functional regression approach, including an in-sample performance comparison with the dynamic Nelson-Siegel model. We conducted the stress testing analysis of yield curves term-structure within a dual economy framework. The bond ladder portfolio was examined through a case study focused on spread modelling using historical data for US Treasury and UK bonds.

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arXiv2021

On Modelling of Crude Oil Futures in a Bivariate State-Space Framework

We study a bivariate latent factor model for the pricing of commodity fu- tures. The two unobservable state variables representing the short and long term fac- tors are modelled as Ornstein-Uhlenbeck (OU) processes. The Kalman Filter (KF) algorithm has been implemented to estimate the unobservable factors as well as unknown model parameters. The estimates of model parameters were obtained by maximising a Gaussian likelihood function. The algorithm has been applied to WTI Crude Oil NYMEX futures data.

q-fin.ST↗

arXiv2021

On the Parameter Estimation in the Schwartz-Smiths Two-Factor Model

The two unobservable state variables representing the short and long term factors introduced by Schwartz and Smith in [16] for risk-neutral pricing of futures contracts are modelled as two correlated Ornstein-Uhlenbeck processes. The Kalman Filter (KF) method has been implemented to estimate the short and long term factors jointly with un- known model parameters. The parameter identification problem arising within the likelihood function in the KF has been addressed by introduc- ing an additional constraint. The obtained model parameter estimates are the conditional Maximum Likelihood Estimators (MLEs) evaluated within the KF. Consistency of the conditional MLEs is studied. The methodology has been tested on simulated data.

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arXiv2021

Tilted Nonparametric Regression Function Estimation

This paper provides the theory about the convergence rate of the tilted version of linear smoother. We study tilted linear smoother, a nonparametric regression function estimator, which is obtained by minimizing the distance to an infinite order flat-top trapezoidal kernel estimator. We prove that the proposed estimator achieves a high level of accuracy. Moreover, it preserves the attractive properties of the infinite order flat-top kernel estimator. We also present an extensive numerical study for analysing the performance of two members of the tilted linear smoother class named tilted Nadaraya-Watson and tilted local linear in the finite sample. The simulation study shows that tilted Nadaraya-Watson and tilted local linear perform better than their classical analogs in some conditions in terms of Mean Integrated Squared Error (MISE). Finally, the performance of these estimators as well as the conventional estimators were illustrated by curve fitting to COVID-19 data for 12 countries and a dose-response data set.

stat.ME↗

arXiv2017

On a representation of fractional Brownian motion and the limit distributions of statistics arising in cusp statistical models

We discuss some extensions of results from the recent paper by Chernoyarov et al. (Ann. Inst. Stat. Math., October 2016) concerning limit distributions of Bayesian and maximum likelihood estimators in the model "signal plus white noise" with irregular cusp-type signals. Using a new representation of fractional Brownian motion (fBm) in terms of cusp functions we show that as the noise intensity tends to zero, the limit distributions are expressed in terms of fBm for the full range of asymmetric cusp-type signals correspondingly with the Hurst parameter H, 0<H<1. Simulation results for the densities and variances of the limit distributions of Bayesian and maximum likelihood estimators are also provided.

math.ST↗

arXiv2016

Pricing of Asian-type and Basket Options via Upper and Lower Bounds

This paper sets out to provide a general framework for the pricing of average-type options via lower and upper bounds. This class of options includes Asian, basket and options on the volume-weighted average price. We demonstrate that in cases under discussion lower bounds allow for the dimensionality of the problem to be reduced and that these methods provide reasonable approximations to the price of the option. Keywords: Asian options, Basket options, Lower and Upper bounds, Volume-weighted average prices (VWAP), Levy processes.

q-fin.MF↗

arXiv2014

On moments of Pitman estimators: the case of fractional Brownian Motion

In some non-regular statistical estimation problems, the limiting likelihood processes are functionals of fractional Brownian motion (fBm) with Hurst's parameter H; 0 < H <=? 1. In this paper we present several analytical and numerical results on the moments of Pitman estimators represented in the form of integral functionals of fBm. We also provide Monte Carlo simulation results for variances of Pitman and asymptotic maximum likelihood estimators.

math.ST↗

arXiv2013

On lower and upper bounds for Asian-type options: a unified approach

In the context of dealing with financial risk management problems it is desirable to have accurate bounds for option prices in situations when pricing formulae do not exist in the closed form. A unified approach for obtaining upper and lower bounds for Asian-type options, including options on VWAP, is proposed in this paper. The bounds obtained are applicable to the continuous and discrete-time frameworks for the case of time-dependent interest rates. Numerical examples are provided to illustrate the accuracy of the bounds.

q-fin.PR↗

arXiv2007

Martingales and first passage times of AR(1) sequences

Using the martingale approach we find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences (AR(1)). Further, we prove a martingale identity to be used in obtaining explicit bounds for the expectation of first passage times.

math.PR↗