arXiv · arXiv q-fin · 2022
This article analytically characterizes the impermanent loss of concentrated liquidity provision for automatic market makers in decentralised markets such as Uniswap. We propose two static replication formulas for the impermanent loss by a combination of European calls or puts with strike prices supported on the liquidity provision price interval. It facilitates liquidity providers to hedge permanent loss by trading …
Jun Deng, Hua Zong, Yun Wang
arXiv · arXiv q-fin · 2026
We derive the stochastic price process for tokens whose sole price discovery mechanism is a constant-product automated market maker (AMM). When the net flow into the pool follows a diffusion, the token price follows a constant elasticity of variance (CEV) process, nesting Black-Scholes as the limiting case of infinite liquidity. We obtain closed-form European option prices and introduce liquidity-adjusted Greeks. The…
Philip Z. Maymin
arXiv · arXiv q-fin · 2019
Since decades, the data science community tries to propose prediction models of financial time series. Yet, driven by the rapid development of information technology and machine intelligence, the velocity of today's information leads to high market efficiency. Sound financial theories demonstrate that in an efficient marketplace all information available today, including expectations on future events, are represented…
Giovanni Mariani, Yada Zhu, Jianbo Li, Florian Scheidegger, Roxana Istrate
arXiv · arXiv q-fin · 2022
Over the decades, the Markowitz framework has been used extensively in portfolio analysis though it puts too much emphasis on the analysis of the market uncertainty rather than on the trend prediction. While generative adversarial network (GAN) and conditional GAN (CGAN) have been explored to generate financial time series and extract features that can help portfolio analysis. The limitation of the CGAN framework sta…
Jun Lu, Shao Yi
arXiv · arXiv q-fin · 2018
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility would indicate market inefficiency. Using minute-by-minute data on S&P 500 index options, we provide evidence regarding delayed and gradual movements in implied volatility after t…
Juho Kanniainen, Martin Magris
arXiv · arXiv q-fin · 2014
We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous-time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of non-equivalent multiple priors. We solve the problem completely by identifying the worst--case measure. Our setup also allows to consider interest rate uncertainty; we show that un…
Qian Lin, Frank Riedel
arXiv · arXiv q-fin · 2021
This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers the modeling of the liability liquidity risk (or funding liquidity), the second dimension is dedicated to the modeling of the asset liquidity risk (or market liquidity), whereas the third dimension considers the management of the asset-liability liquidi…
Thierry Roncalli
arXiv · arXiv q-fin · 2007
In this work, we aim to gain a better understanding of the volatility smile observed in options markets through microsimulation (MS). We adopt two types of active traders in our MS model: speculators and arbitrageurs, and call and put options on one underlying asset. Speculators make decisions based on their expectations of the asset price at the option expiration time. Arbitrageurs trade at different arbitrage oppor…
G. Qiu, D. Kandhai, P. M. A. Sloot
arXiv · arXiv q-fin · 2025
We explore credit risk pricing by modeling equity as a call option and debt as the difference between the firm's asset value and a put option, following the structural framework of the Merton model. Our approach proceeds in two stages: first, we calibrate the asset volatility using the Black-Scholes-Merton (BSM) formula; second, we recover implied mean return and probability surfaces under the physical measure. To ac…
Jagdish Gnawali, Abootaleb Shirvani, Svetlozar T. Rachev
arXiv · arXiv q-fin · 2021
We explore online inductive transfer learning, with a feature representation transfer from a radial basis function network formed of Gaussian mixture model hidden processing units to a direct, recurrent reinforcement learning agent. This agent is put to work in an experiment, trading the major spot market currency pairs, where we accurately account for transaction and funding costs. These sources of profit and loss, …
Gabriel Borrageiro, Nick Firoozye, Paolo Barucca
arXiv · arXiv q-fin · 2021
We develop a dynamic trading strategy in the Linear Quadratic Regulator (LQR) framework. By including a price mean-reversion signal into the optimization program, in a trading environment where market impact is linear and stage costs are quadratic, we obtain an optimal trading curve that reacts opportunistically to price changes while retaining its ability to satisfy smooth or hard completion constraints. The optimal…
Simon Clinet, Jean-François Perreton, Serge Reydellet
arXiv · arXiv q-fin · 2020
We explain in a nontechnical fashion why dollar-neutral quant trading strategies, such as equities Statistical Arbitrage, suffered substantial losses (drawdowns) during the COVID-19 market selloff. We discuss: (i) why these strategies work during "normal" times; (ii) the market regimes when they work best; and (iii) their limitations and the reasons for why they "break" during extreme market events. An accompanying a…
Zura Kakushadze
arXiv · arXiv q-fin · 2018
This paper derives a robust on-line equity trading algorithm that achieves the greatest possible percentage of the final wealth of the best pairs rebalancing rule in hindsight. A pairs rebalancing rule chooses some pair of stocks in the market and then perpetually executes rebalancing trades so as to maintain a target fraction of wealth in each of the two. After each discrete market fluctuation, a pairs rebalancing r…
Alex Garivaltis
arXiv · arXiv q-fin · 2017
Market timing is an investment technique that tries to continuously switch investment into assets forecast to have better returns. What is the likelihood of having a successful market timing strategy? With an emphasis on modeling simplicity, I calculate the feasible set of market timing portfolios using index mutual fund data for perfectly timed (by hindsight) all or nothing quarterly switching between two asset clas…
Guy Metcalfe
arXiv · arXiv q-fin · 2016
In structural credit risk models, default events and the ensuing losses are both derived from the asset values at maturity. Hence it is of utmost importance to choose a distribution for these asset values which is in accordance with empirical data. At the same time, it is desirable to still preserve some analytical tractability. We achieve both goals by putting forward an ensemble approach for the asset correlations.…
Thilo A. Schmitt, Rudi Schäfer, Thomas Guhr
arXiv · arXiv q-fin · 2016
Market impact has become a subject of increasing concern among academics and industry experts. We put forward a price impact model which considers the heteroscedasticity of price in the time dimension and dependency between permanent impact and temporary impact. We discuss and derive the extremum of the expectation of permanent impact and realized impact by constructing several special trading trajectories. Given our…
Shiyu Han, Lan Wu, Yuan Cheng
arXiv · arXiv q-fin · 2015
We analyze a negative-parameter variant of the diversity-weighted portfolio studied by Fernholz, Karatzas, and Kardaras (Finance Stoch 9(1):1-27, 2005), which invests in each company a fraction of wealth inversely proportional to the company's market weight (the ratio of its capitalization to that of the entire market). We show that this strategy outperforms the market with probability one, under a non-degeneracy ass…
Alexander Vervuurt, Ioannis Karatzas
arXiv · arXiv q-fin · 2014
We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset price hits a certain level) is exponentially distributed. We obtain explicit optimal stopping rules in various cases one of which is interestingly complex because of an unexpected disc…
Sigurd Assing, Yufan Zhao