Quantitative Finance

Amini, Hamed; Bichuch, Maxim; Feinstein, Zachary

doi: 10.48550/arxiv.2307.08768pmid: N/A

Abstract:Prediction markets allow traders to bet on potential future outcomes. These markets exist for weather, political, sports, and economic forecasting. Within this work we consider a decentralized framework for prediction markets using automated market makers (AMMs). Specifically, we construct a liquidity-based AMM structure for prediction markets that, under reasonable axioms on the underlying utility function, satisfy meaningful financial properties on the cost of betting and the resulting pricing oracle. Importantly, we study how liquidity can be pooled or withdrawn from the AMM and the resulting implications to the market behavior. In considering this decentralized framework, we additionally propose financially meaningful fees that can be collected for trading to compensate the liquidity providers for their vital market function.

Fang, Zhou; Xu, Haiqing

doi: 10.48550/arxiv.2307.01814pmid: N/A

Abstract:Market making of options with different maturities and strikes is a challenging problem due to its highly dimensional nature. In this paper, we propose a novel approach that combines a stochastic policy and reinforcement learning-inspired techniques to determine the optimal policy for posting bid-ask spreads for an options market maker who trades options with different maturities and strikes.

Guo, Ivan; Jin, Shijia; Nam, Kihun

doi: 10.48550/arxiv.2307.14129pmid: N/A

Abstract:We propose a macroscopic market making model à la Avellaneda-Stoikov, using continuous processes for orders instead of discrete point processes. The model intends to bridge the gap between market making and optimal execution problems, while shedding light on the influence of order flows on the optimal strategies. We demonstrate our model through three problems. The study provides a comprehensive analysis from Markovian to non-Markovian noises and from linear to non-linear intensity functions, encompassing both bounded and unbounded coefficients. Mathematically, the contribution lies in the existence and uniqueness of the optimal control, guaranteed by the well-posedness of the strong solution to the Hamilton-Jacobi-Bellman equation and the (non-)Lipschitz forward-backward stochastic differential equation. Finally, the model's applications to price impact and optimal execution are discussed.

Qian, Shuaijie; Yang, Chen

doi: 10.48550/arxiv.2307.02178pmid: N/A

Abstract:This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and proportional transaction costs, in which the commonly used concavification principle for terminal value is no longer applicable. We establish a proper theoretical characterization of this problem via a two-step procedure. First, we examine the asymptotic terminal behavior of the value function, which implies that any transaction close to maturity only provides a marginal contribution to the utility. Second, we establish the theoretical foundation in terms of the discontinuous viscosity solution, incorporating the proper characterization of the terminal condition. Via extensive numerical analyses involving several types of utility functions, we find that the introduction of transaction costs into non-concave utility maximization problems can make it optimal for investors to hold on to a larger long position in the risky asset compared to the frictionless case, or hold on to a large short position in the risky asset despite a positive risk premium.

Galindo-Silva, Hector; Herrera-Idárraga, Paula

doi: 10.48550/arxiv.2307.08869pmid: N/A

Abstract:This study investigates the impact of integrating gender equality into the Colombian constitution of 1991 on attitudes towards gender equality, experiences of gender-based discrimination, and labor market participation. Using a difference-in-discontinuities framework, we compare individuals exposed to mandatory high school courses on the Constitution with those who were not exposed. Our findings show a significant increase in labor market participation, primarily driven by women. Exposure to these courses also shapes attitudes towards gender equality, with men demonstrating greater support. Women report experiencing less gender-based discrimination. Importantly, our results suggest that women's increased labor market participation is unlikely due to reduced barriers from male partners. A disparity in opinions regarding traditional gender norms concerning household domains is observed between men and women, highlighting an ongoing power struggle within the home. However, the presence of a younger woman in the household appears to influence men's more positive view of gender equality, potentially indicating a desire to empower younger women in their future lives. These findings highlight the crucial role of cultural shocks and the constitutional inclusion of women's rights in shaping labor market dynamics.

Azmoodeh, Ehsan; Hür, Ozan

doi: 10.48550/arxiv.2307.08651pmid: N/A

Abstract:Introduced by Müller et al. in their seminal paper \cite{muller}, fractional stochastic dominance (SD) offers a nuanced approach to ordering distributions. In this paper, we propose a fundamentally new framework by replacing the fixed parameter $\gamma \in [0,1]$ in fractional SD with a function $\boldsymbol{\gamma}: \mathbb{R} \to [0,1]$. This yields two novel families, multi-fractional stochastic dominance (MFSD) and functional fractional stochastic dominance (FFSD). They enable the ranking of a broader range of distributions and incorporate a more informative utility class, including those with local non-concavities whose steepness varies depending on the location. Furthermore, our framework introduces the concept of partial greediness, which dynamically captures how behaviour of decision makers adapts to changes in wealth. We also extend this framework to encompass almost stochastic dominance. We provide the mathematical foundations of our generalized framework and study how it offers a novel tool for ordering distributions across various settings.

Cartea, Álvaro; Drissi, Fayçal; Monga, Marcello

doi: 10.48550/arxiv.2307.03499pmid: N/A

Abstract:Automated market makers (AMMs) are a new prototype of decentralised exchanges which are revolutionising market interactions. The majority of AMMs are constant product markets (CPMs) where exchange rates are set by a trading function. This work studies optimal trading and statistical arbitrage in CPMs where balancing exchange rate risk and execution costs is key. Empirical evidence shows that execution costs are accurately estimated by the convexity of the trading function. These convexity costs are linear in the trade size and are nonlinear in the depth of liquidity and in the exchange rate. We develop models for when exchange rates form in a competing centralised exchange, in a CPM, or in both venues. Finally, we derive computationally efficient strategies that account for stochastic convexity costs and we showcase their out-of-sample performance.

Yeo, Christian

doi: 10.48550/arxiv.2307.04510pmid: N/A

Abstract:Linear regression, firstly introduced for the pricing of American-style options, has since been expanded to include swing options pricing. Swing options price may be viewed as the solution to a Backward Dynamic Programming Principle, which involves a conditional expectation known as the continuation value. The approximation of the continuation value using linear regression involves two levels of approximation. First, the continuation value is replaced by an orthogonal projection over a subspace spanned by a finite set of $m$ squared-integrable functions yielding a first approximation $V^m$ of the swing value function. In this paper, we prove that, with well-chosen regression functions, $V^m$ converges to the swing actual price $V$ as $m \to + \infty$. A similar result is proved when classic regression functions are replaced by neural networks. For both methods (linear regression and neural networks), we analyze the second level of approximation involving practical computation of the swing price using Monte Carlo simulations and yielding an approximation $V^{m, N}$ (where $N$ denotes the Monte Carlo sample size). Especially, we prove that $V^{m, N} \to V^m$ as $N \to + \infty$ for both methods and using a Hilbert basis assumption in the linear regression. Besides, a convergence rate of order $\mathcal{O}\big(\frac{1}{\sqrt{N}} \big)$ is proved in the linear regression case.