Quantitative Finance
We consider the dynamics and the interactions of multiple reinforcement learning optimal execution trading agents interacting with a reactive Agent-Based Model (ABM) of a financial market in event time. The model represents a market ecology…
This paper explores the mechanisms behind extreme financial events, specifically market crashes, by employing the theoretical framework of phase transitions. We focus on endogenous crashes, driven by internal market dynamics, and model…
This paper provides the first and second order derivatives of any risk measures, including VaR and ES for continuous and discrete portfolio loss random variable variables. Also, we give asymptotic results of the first and second order…
We extend a Discrete Time Random Walk (DTRW) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. Here using random walks with Sibuya waiting times to include a time-dependent stochastic…
In this paper we demonstrate both theoretically as well as numerically that neural networks can detect model-free static arbitrage opportunities whenever the market admits some. Due to the use of neural networks, our method can be applied…
Explainable machine learning methods have been accompanied by substantial development. Despite their success, the existing approaches focus more on the general framework with no prior domain expertise. High-stakes financial sectors have…
In this paper we introduce a method for significantly improving the signal to noise ratio in financial data. The approach relies on combining a target variable with different context variables and use auto-encoders (AEs) to learn…
This thesis explores the historical progression and theoretical constructs of financial mathematics, with an in-depth exploration of Stochastic Calculus as showcased in the Binomial Asset Pricing Model and the Continuous-Time Models. A…
We propose a novel data-driven network framework for forecasting problems related to E-mini S\&P 500 and CBOE Volatility Index futures, in which products with different expirations act as distinct nodes. We provide visual demonstrations of…
This study presents a Reinforcement Learning (RL)-based portfolio management model tailored for high-risk environments, addressing the limitations of traditional RL models and exploiting market opportunities through two-sided transactions…
This paper establishes a new and comprehensive theoretical analysis for the application of reinforcement learning (RL) in high-frequency market making. We bridge the modern RL theory and the continuous-time statistical models in…
The M6 Competition assessed the performance of competitors using a ranked probability score and an information ratio (IR). While these metrics do well at picking the winners in the competition, crucial questions remain for investors with…
We present closed analytical approximations for the pricing of basket options, also applicable to Asian options with discrete averaging under the Black-Scholes model with time-dependent parameters. The formulae are obtained by using a…
In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor.…
Mean-deviation models, along with the existing theory of coherent risk measures, are well studied in the literature. In this paper, we characterize monotonic mean-deviation (risk) measures from a general mean-deviation model by applying a…
Volatility forecasts play a central role among equity risk measures. Besides traditional statistical models, modern forecasting techniques based on machine learning can be employed when treating volatility as a univariate, daily…
Market information events are generated intermittently and disseminated at high speeds in real-time. Market participants consume this high-frequency data to build limit order books, representing the current bids and offers for a given…
This research examines whether sentiments conveyed in the State Bank of Pakistan's (SBP) communications impact financial market expectations and can act as a monetary policy tool. To achieve our goal, we first use sentiment analysis…
We use random walks to simulate the fluid limit of two coupled diffusive limit order books to model correlation emergence. The model implements the arrival, cancellation and diffusion of orders coupled by a pairs trader profiting from the…
We revisit the classical topic of quadratic and linear mean-variance equilibria with both financial and real assets. The novelty of our results is that they are the first allowing for equilibrium prices driven by general semimartingales and…