Roman Makarov

• PhD
• Professor at Wilfrid Laurier University

We analyze how the sentiment of financial news can be used to predict stock returns and build profitable trading strategies. Combining the textual analysis of financial news headlines and statistical methods, we build multi-class classification models to predict the stock return. The main contribution of this paper is twofold. Firstly, we develop a...

We explore a multi-asset jump-diffusion pricing model, combining a systemic risk asset with several conditionally independent ordinary assets. Our approach allows for analyzing and modeling a portfolio that integrates high-activity security, such as an exchange trading fund (ETF) tracking a major market index (e.g., S&P500), along with several low-...

We study two credit risk models with occupation time and liquidation barriers: the structural model and the hybrid model with hazard rate. The defaults within the models are characterized in accordance with Chapter 7 (a liquidation process) and Chapter 11 (a reorganization process) of the U.S. Bankruptcy Code. The models assume that credit events t...

By employing a randomisation procedure on the variance parameter of the standard geometric Brownian motion (GBM) model, we construct new families of analytically tractable asset pricing models. In particular, we develop two explicit families of processes that are respectively referred to as the randomised gamma (G) and randomised inverse gamma (IG)...

Credit risk is concerned with analyzing financial losses occurring due to changes in the credit quality of a firm. A rare occurrence of such sort is the default event that often leads to bankruptcy or liquidation, resulting in large financial losses to investors. In structural credit risk models, the asset value is compared to firm’s liabilities at...

This paper is concerned with the statistical modelling of the high-frequency dynamics of financial markets. We study whether a systemic component in a multi-asset price model can explain all jumps in the market’s dynamics. By performing statistical analysis of high-frequency data from Wharton Research Data Services (WRDS), we detect disjoint and co...

In this paper, we present a new multivariate jump-diffusion model for modelling financial securities that have missing or asynchronous data in time series of historical prices. The proposed model allows us to analyze a portfolio that combines a high-activity asset such as a market index (or an exchange-traded fund tracking a market index) and sever...

In this paper, we propose a new method that allows an investor to rank available financial securities such as equities and exchange-traded funds (ETFs) in accordance with his or her risk preferences. We have demonstrated that using a linear combination of several risk measures and performance metrics as a ranking function can help us to select the...

This book focuses on the recent development of methodologies and computation methods in mathematical and statistical modelling, computational science and applied mathematics. It emphasizes the development of theories and applications, and promotes interdisciplinary endeavour among mathematicians, statisticians, scientists, engineers and researchers...

We live in an incredible age. Due to extraordinary advances in sciences and engineering, we better understand the world around us. At the same time, we witness profound changes in the technology, environment, societal organization, and economic well-being. We face new challenges never experienced by humans before. To efficiently address these chall...

In this paper, we propose a new method that allows an investor to rank available financial securities such as equities and exchange-traded funds (ETFs) in accordance with his or her risk preferences. We use a combination of several risk and performance metrics as a ranking function and then apply three different methods to evaluate the long-term va...

In this paper, we present a new multivariate jump-diffusion model for modelling financial securities that have missing or asynchronous data in time series of historical prices. The proposed model allows us to analyze a portfolio that combines a high-activity asset such as a market index (or an exchange-traded fund tracking a market index) and sever...

We present new extensions to a method for constructing families of solvable one-dimensional time-homogeneous diffusions whose transition densities and other related quantities are obtainable in analytically closed form. Our approach is based on a dual application of the so-called diffusion canonical transformation method that combines a smooth mono...

In this paper, we develop a new structural model that allows for a distinction between default and liquidation to be made. Default occurs when firm’s asset value process crosses a bankruptcy barrier. Here, we do not assume that default immediately triggers liquidation. Instead, the firm is allowed to continue operating even if it is in default. Liq...

We develop a new structural model that allows for a distinction between default and liquidation to be made. Default occurs when firm's asset value process crosses a bankruptcy barrier. Here, we do not assume that default immediately triggers liquidation. Instead, the firm is allowed to continue operating even if it is in default. Liquidation is tri...

We introduce a hybrid stochastic volatility model where the asset price process follows the Heston model and interest rates are governed by a two-factor stochastic model. Two cases are considered. First, it is assumed that interest rates and asset prices are uncorrelated. The characteristic function method is used to derive semi-analytical pricing...

Focusing on five main groups of interdisciplinary problems, this book covers a wide range of topics in mathematical modeling, computational science and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions bet...

In this chapter, we study three asset pricing models for valuing financial derivatives; namely, the constant elasticity of variance (CEV) model, the Bessel-K model, derived from the squared Bessel (SQB) process, and the unbounded Ornstein–Uhlenbeck (UOU) model, derived from the standard OU process. All three models are diffusion processes with line...

This paper develops a semi-analytic pricing formula, easily implemented via quadrature, for a structural model based on occupation times that contains both the Merton and Black–Cox models as limiting cases. In the model liquidation is triggered as soon as the firm’s asset value has spent a prespecified amount of time below the default barrier. Surp...

The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and t...

Versatile for Several Interrelated Courses at the Undergraduate and Graduate Levels Financial Mathematics: A Comprehensive Treatment provides a unified, self-contained account of the main theory and application of methods behind modern-day financial mathematics. Tested and refined through years of the authors' teaching experiences, the book encompa...

We consider a special family of occupation-time derivatives, namely proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96 (1999)]. We develop new closed-form spectral expansions for pricing such options under a class of nonlinear volatility diffusion processes which includes the constant-elasticity-of-variance (CEV) model as...

We present some further developments in the construction and classification of new solvable one-dimensional diffusion models having transition densities, and other quantities that are fundamental to derivatives pricing, representable in analytically closed form. Our approach is based on so-called diffusion canonical transformations that produce a l...

A novel algorithm for the exact simulation of occupation times for Brownian processes and jump-diffusion processes with finite jump intensity is constructed. Our approach is based on sampling from the distribution function of occupation times of a Brownian bridge. For more general diffusions we propose an approximation procedure based on the Browni...

In this paper we present a new multi-asset pricing model, which is built upon newly developed families of solvable multi-parameter single-asset diffusions with a nonlinear smile-shaped volatility and an affine drift. Our multi-asset pricing model arises by employing copula methods. In particular, all discounted single-asset price processes are mode...

We study arecently developed adaptive path-integration technique for pricing financial derivatives. Themethod is based on therearrangement and splitting of path-integral variables to apply acombination of bridge sampling, adaptive methods of numerical integration, and thequasi-Monte Carlo method. We study thesubregion adaptive Vegas-type method Sua...

We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale transformation, and/or change...

We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale transformation, and/or change...

We present new extensions to a method for constructing several families of solvable one-dimensional time-homogeneous diffusions whose transition densities are obtainable in analytically closed-form. Our approach is based on a dual application of the so-called diffusion canonical transformation method that combines smooth monotonic mappings and meas...

We present a method for constructing new families of solvable one-dimensional diffusions with linear drift and nonlinear diffusion coefficient functions, whose transition densities are obtainable in analytically closed-form. Our approach is based on the so-called diffusion canonical transformation method that allows us to uncover new multiparameter...

Path integral algorithms are developed for evaluating European-style Asian options within three new families of multi-parameter local volatility models. The forward price process is a martingale under an assumed risk-neutral measure and the transition probability densities for such models are given in analytically closed form. Implied volatility su...

This paper develops bridge sampling path integral algorithms for pricing path-dependent options under a new class of nonlinear state dependent volatility models. Path-dependent option pricing is considered within a new (dual) Bessel family of semimartingale diffusion models, as well as the constant elasticity of variance (CEV) diffusion model, aris...

Here we construct two new functional Monte Carlo algorithms for the numerical solution of three-dimensional Dirichlet boundary value problems for the linear and nonlinear Helmholtz equations. These algorithms are based on estimating the solution and, if necessary, its partial derivatives at grid nodes using first Monte Carlo methods followed by an...

With the principal goal of developing an alternative, relatively simple and tractable pricing framework for accurately reproducing a market implied volatility surface, this paper presents two new asset price return models for option pricing and calibration. We consider a class of hidden Markov models based on Markov switching and a mixture model th...

In this paper, we consider the problem of numerical solution of the system of forward-backward stochastic differential equations and its Cauchy problem for a quasilinear parabolic equation. We propose a layer method of solving the Cauchy problem with simultaneous estimation of the solution gradient, which is based on the probabilistic representatio...

In this work we construct new algorithms of the method of statistical simulation for the numerical solution of the third boundary value problem for a parabolic-type equation. They are based on a combination of the probabilistic representation of the solution and the difference approximation of the boundary condition. We derive the estimate of the s...

We study a new approach to the approximation of solutions of stochastic differential equations (SDEs) with reflection at a boundary for multidimensional domains with sufficiently smooth boundary. The approach is based on an arbitrary numerical method of solving SDEs with reflection from the hyperplane and on the Ito formula. Simultaneously with the...

In this paper we construct a new algorithm for solving the third boundary value problem with a nonlinear equation of the form Δu = u + u2 by the Monte Carlo method. The estimate of the Monte Carlo method is constructed for a special chain of 'random walk by spheres and balls' with branching. In addition, we obtain new estimates of the Monte Carlo m...

In this paper we consider two ways of obtaining the estimates of the solutions of boundary value problems of the second and third kinds for the Helmholtz multidimensional equation Delta u - cu = -g. In the framework of both approaches we obtain the global estimates of the solutions and the estimates of the solutions at a single point. We prove that...

In this paper we present two new multivariate nonlinear diffusion pricing models for valuing path-dependent financial derivatives. These models are built upon a newly developed asset price model UOU (see Campolieti and Makarov (2006b;c)), which is constructed from an underlying Ornstein-Uhlenbeck diffusion process by transforming variables and chan...