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Anatoliy Swishchuk

Publications and source records attributed to Anatoliy Swishchuk.

At least 19 recordsLinked to original sources
arXiv2026

Market Simulation under Adverse Selection

In this paper, we study the effects of fill probabilities and adverse fills on the trading strategy simulation process. We specifically focus on a stochastic optimal control market-making problem and test the strategy on ES (E-mini S\&P 500), NQ (E-mini Nasdaq 100), CL (Crude Oil) and ZN (10-Year Treasury Note), which are some of the most liquid futures contracts listed on the CME (Chicago Mercantile Exchange). We provide empirical evidence that shows how fill probabilities and adverse fills can significantly affect performance and propose a more prudent simulation framework to deal with this. Many previous works aim to measure different types of adverse selection in the limit order book (LOB), however, they often simulate price processes and market orders independently. This has the ability to largely inflate the performance of a short-term style trading strategy. Our studies show that using more realistic fill probabilities and tracking adverse fills in the strategy simulation process more accurately shows how these types of trading strategies would perform in reality.

q-fin.CP↗
arXiv2025

Self-Exciting Random Evolutions (SEREs) and their Applications (Version 2)

This paper is devoted to the study of a new class of random evolutions (RE), so-called self-exciting random evolutions (SEREs), and their applications. We also introduce a new random process $x(t)$ such that it is based on a superposition of a Markov chain $x_n$ and a Hawkes process $N(t),$ i.e., $x(t):=x_{N(t)}.$ We call this process self-walking imbedded semi-Hawkes process (Swish Process or SwishP). Then the self-exciting REs (SEREs) can be constructed in similar way as, e.g., semi-Markov REs, but instead of semi-Markov process $x(t)$ we have SwishP. We give classifications and examples of self-exciting REs (SEREs). Then we consider two limit theorems for SEREs such as averaging (Theorem 1) and diffusion approximation (Theorem 2). Applications of SEREs are devoted to the so-called self-exciting traffic/transport process and self-exciting summation on a Markov chain, which are examples of continuous and discrete SERE. From these processes we can construct many other self-exciting processes, e.g., such as impulse traffic/transport process, self-exciting risk process, general compound Hawkes process for a stock price, etc. We present averaged and diffusion approximation of self-exciting processes. The novelty of the paper associated with new models, such as $x(t)$ and SERE, and also new features of SEREs and their many applications, namely, self-exciting and clustering effects.

math.PR↗
arXiv2025

Algorithmic and High-Frequency Trading Problems for Semi-Markov and Hawkes Jump-Diffusion Models

This paper introduces a jump-diffusion pricing model specifically designed for algorithmic trading and high-frequency trading (HFT). The model incorporates independent jump and diffusion processes, providing a more precise representation of the limit order book (LOB) dynamics within a scaling-limit framework. Given that algorithmic and HFT strategies now dominate major financial markets, accurately modeling LOB dynamics is crucial for developing effective trading algorithms. Recent research has shown that LOB data often exhibit non-Markovian properties, reinforcing the need for models that better capture its evolution. In this paper, we address acquisition and liquidation problems under more general compound semi-Markov and Hawkes jump-diffusion models. We first develop jump-diffusion frameworks to capture these dynamics and then apply diffusion approximations to the jump components so that robust solutions can be given. Optimal trading strategies are formulated using stochastic optimal control (SOC) and solved numerically. Finally, we present strategy simulations analyzing price paths, inventory evolution, trading speed, and average execution prices. This study provides insights into how these models can improve execution strategies under more general price dynamics.

q-fin.MF↗
arXiv2025

Event-Based Limit Order Book Simulation under a Neural Hawkes Process: Application in Market-Making

In this paper, we propose an event-driven Limit Order Book (LOB) model that captures twelve of the most observed LOB events in exchange-based financial markets. To model these events, we propose using the state-of-the-art Neural Hawkes process, a more robust alternative to traditional Hawkes process models. More specifically, this model captures the dynamic relationships between different event types, particularly their long- and short-term interactions, using a Long Short-Term Memory neural network. Using this framework, we construct a midprice process that captures the event-driven behavior of the LOB by simulating high-frequency dynamics like how they appear in real financial markets. The empirical results show that our model captures many of the broader characteristics of the price fluctuations, particularly in terms of their overall volatility. We apply this LOB simulation model within a Deep Reinforcement Learning Market-Making framework, where the trading agent can now complete trade order fills in a manner that closely resembles real-market trade execution. Here, we also compare the results of the simulated model with those from real data, highlighting how the overall performance and the distribution of trade order fills closely align with the same analysis on real data.

q-fin.CP↗
arXiv2024

Reinforcement Learning in Non-Markov Market-Making

We develop a deep reinforcement learning (RL) framework for an optimal market-making (MM) trading problem, specifically focusing on price processes with semi-Markov and Hawkes Jump-Diffusion dynamics. We begin by discussing the basics of RL and the deep RL framework used, where we deployed the state-of-the-art Soft Actor-Critic (SAC) algorithm for the deep learning part. The SAC algorithm is an off-policy entropy maximization algorithm more suitable for tackling complex, high-dimensional problems with continuous state and action spaces like in optimal market-making (MM). We introduce the optimal MM problem considered, where we detail all the deterministic and stochastic processes that go into setting up an environment for simulating this strategy. Here we also give an in-depth overview of the jump-diffusion pricing dynamics used, our method for dealing with adverse selection within the limit order book, and we highlight the working parts of our optimization problem. Next, we discuss training and testing results, where we give visuals of how important deterministic and stochastic processes such as the bid/ask, trade executions, inventory, and the reward function evolved. We include a discussion on the limitations of these results, which are important points to note for most diffusion models in this setting.

q-fin.CP↗
arXiv2024

Variance-Hawkes Process and its Application to Energy Markets

We define a new model using a Hawkes process as a subordinator in a standard Brownian motion. We demonstrate that this Hawkes subordinated Brownian motion or more succinctly, variance-Hawkes process can be fit to 2018 and 2019 natural gas and crude oil front-month futures log returns. This variance-Hawkes process allows financial models to easily have clustering effects encoded into their behaviour in a simple and tractable way. We also compare the simulations of a square of a variance Hawkes process with its Ito formula. We simulate both processes and compare their distributions, trajectories, and percent errors across multiple runs. We derive the generator relating to this Hawkes subordinated Brownian motion, calculate several moments, and conjecture its distribution. We also provide explicit solutions to the second moments of the Hawkes process and its intensity as well as the cross moment between the Hawkes process and its intensity in the case of an exponential kernel.

q-fin.MF↗
arXiv2022

Multivariate Hawkes-based Models in LOB: European, Spread and Basket Option Pricing

In this paper, we consider pricing of European options and spread options for Hawkes-based model for the limit order book. We introduce multivariate Hawkes process and the multivariable general compound Hawkes process. Exponential multivariate general compound Hawkes processes and limit theorems for them, namely, LLN and FCLT, are considered then. We also consider a special case of one-dimensional EMGCHP and its limit theorems. Option pricing with $1D$ EGCHP in LOB, hedging strategies, and numerical example are presented. We also introduce greeks calculations for those models. Margrabe's spread options valuations with Hawkes-based models for two assets and numerical example are presented. Also, Margrabe's spread option pricing with two $2D$ EMGCHP and numerical example are included. Basket options valuations with numerical example are included. We finally discuss the implied volatility and implied order flow. It reveals the relationship between stock volatility and the order flow in the limit order book system. In this way, the Hawkes-based model can provide more market forecast information than the classical Black-Scholes model.

q-fin.MF↗
arXiv2021

Merton Investment Problems in Finance and Insurance for the Hawkes-based Models

We show how to solve Merton optimal investment stochastic control problem for Hawkes-based models in finance and insurance, i.e., for a wealth portfolio X(t) consisting of a bond and a stock price described by general compound Hawkes process (GCHP), and for a capital R(t) of an insurance company with the amount of claims described by the risk model based on GCHP. The novelty of the results consists of the new Hawkes-based models and in the new optimal investment results in finance and insurance for those models.

q-fin.PM↗
arXiv2020

Practical Option Valuations of Futures Contracts with Negative Underlying Prices

Here we propose two alternatives to Black 76 to value European option future contracts in which the underlying market prices can be negative or mean reverting. The two proposed models are Ornstein-Uhlenbeck (OU) and continuous time GARCH (generalized autoregressive conditionally heteroscedastic). We then analyse the values and compare them with Black 76, the most commonly used model, when the underlying market prices are positive

q-fin.MF↗
arXiv2020

Multivariate General Compound Point Processes in Limit Order Books

In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the Hawkes process. Law of large numbers (LLN) and two functional central limit theorems (FCLTs) for the MGCPP were proved in this work. Applications of the MGCPP in the limit order market were also considered. We provided numerical simulations and comparisons for the MGCPP and MGCHP by applying Google, Apple, Microsoft, Amazon, and Intel trading data.

q-fin.MF↗
arXiv2018

General Compound Hawkes Processes in Limit Order Books

In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regards to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit Theorems (FCLT) for several specific variations. We apply several of these FCLTs to limit order books to study the link between price volatility and order flow, where the volatility in mid-price changes is expressed in terms of parameters describing the arrival rates and mid-price process.

q-fin.TR↗
arXiv2017

Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models

In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation technique and Laplace transform method to evaluate volatility strikes and estimate VIX future prices. In empirical study, we use Markov chain Monte Carlo algorithm for model calibration based on S&P 500 historical data, evaluate the effect of adding jumps into asset price processes on volatility derivatives pricing, and compare the performance of different pricing approaches.

q-fin.MF↗
arXiv2017

Compound Hawkes Processes in Limit Order Books

In this paper we introduce two new Hawkes processes, namely, compound and regime-switching compound Hawkes processes, to model the price processes in limit order books. We prove Law of Large Numbers and Functional Central Limit Theorems (FCLT) for both processes. The two FCLTs are applied to limit order books where we use these asymptotic methods to study the link between price volatility and order flow in our two models by using the diffusion limits of these price processes. The volatilities of price changes are expressed in terms of parameters describing the arrival rates and price changes. We also present some numerical examples.

q-fin.MF↗
arXiv2017

General Compound Hawkes Processes in Limit Order Books

In this paper, we study various new Hawkes processes, namely, so-called general compound and regime-switching general compound Hawkes processes to model the price processes in the limit order books. We prove Law of Large Numbers (LLN) and Functional Central Limit Theorems (FCLT) for these processes. The latter two FCLTs are applied to limit order books where we use these asymptotic methods to study the link between price volatility and order flow in our two models by studying the diffusion limits of these price processes. The volatilities of price changes are expressed in terms of parameters describing the arrival rates and price changes.

q-fin.MF↗
arXiv2017

Risk Model Based on General Compound Hawkes Process

In this paper, we introduce a new model for the risk process based on general compound Hawkes process (GCHP) for the arrival of claims. We call it risk model based on general compound Hawkes process (RMGCHP). The Law of Large Numbers (LLN) and the Functional Central Limit Theorem (FCLT) are proved. We also study the main properties of this new risk model, net profit condition, premium principle and ruin time (including ultimate ruin time) applying the LLN and FCLT for the RMGCHP. We show, as applications of our results, similar results for risk model based on compound Hawkes process (RMCHP) and apply them to the classical risk model based on compound Poisson process (RMCPP).

q-fin.RM↗
arXiv2016

General Semi-Markov Model for Limit Order Books: Theory, Implementation and Numerics

The paper considers a general semi-Markov model for Limit Order Books with two states, which incorporates price changes that are not fixed to one tick. Furthermore, we introduce an even more general case of the semi-Markov model for LimitOrder Books that incorporates an arbitrary number of states for the price changes. For both cases the justifications, diffusion limits, implementations and numerical results are presented for different Limit Order Book data: Apple, Amazon, Google, Microsoft, Intel on 2012/06/21 and Cisco, Facebook, Intel, Liberty Global, Liberty Interactive, Microsoft, Vodafone from 2014/11/03 to 2014/11/07.

q-fin.TR↗
arXiv2016

A Semi-Markovian Modeling of Limit Order Markets

R. Cont and A. de Larrard (SIAM J. Finan. Math, 2013) introduced a tractable stochastic model for the dynamics of a limit order book, computing various quantities of interest such as the probability of a price increase or the diffusion limit of the price process. As suggested by empirical observations, we extend their framework to 1) arbitrary distributions for book events inter-arrival times (possibly non-exponential) and 2) both the nature of a new book event and its corresponding inter-arrival time depend on the nature of the previous book event. We do so by resorting to Markov renewal processes to model the dynamics of the bid and ask queues. We keep analytical tractability via explicit expressions for the Laplace transforms of various quantities of interest. We justify and illustrate our approach by calibrating our model to the five stocks Amazon, Apple, Google, Intel and Microsoft on June 21^{st} 2012. As in R. Cont and A. de Larrard, the bid-ask spread remains constant equal to one tick, only the bid and ask queues are modeled (they are independent from each other and get reinitialized after a price change), and all orders have the same size.

q-fin.MF↗