|
on Market Microstructure |
| By: | Joseph Jerome; Leandro Sanchez-Betancourt; Rahul Savani; Martin Herdegen |
| Abstract: | Within the mathematical finance literature there is a rich catalogue of mathematical models for studying algorithmic trading problems -- such as market-making and optimal execution -- in limit order books. This paper introduces \mbtgym, a Python module that provides a suite of gym environments for training reinforcement learning (RL) agents to solve such model-based trading problems. The module is set up in an extensible way to allow the combination of different aspects of different models. It supports highly efficient implementations of vectorized environments to allow faster training of RL agents. In this paper, we motivate the challenge of using RL to solve such model-based limit order book problems in mathematical finance, we explain the design of our gym environment, and then demonstrate its use in solving standard and non-standard problems from the literature. Finally, we lay out a roadmap for further development of our module, which we provide as an open source repository on GitHub so that it can serve as a focal point for RL research in model-based algorithmic trading. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.07823&r= |
| By: | Bernhard K Meister |
| Abstract: | Investors trade shifting prices, portfolio values, and in turn their ability to borrow. Concentrated ownership, high price impact and low collateral requirements are propitious for arbitrage. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.05360&r= |
| By: | Qi Guo; Anatoliy Swishchuk; Bruno R\'emillard |
| Abstract: | 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. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.07621&r= |
| By: | Maria Elvira Mancino; Tommaso Mariotti; Giacomo Toscano |
| Abstract: | The main contribution of the paper is proving that the Fourier spot volatility estimator introduced in [Malliavin and Mancino, 2002] is consistent and asymptotically efficient if the price process is contaminated by microstructure noise. Specifically, in the presence of additive microstructure noise we prove a Central Limit Theorem with the optimal rate of convergence $n^{1/8}$. The result is obtained without the need for any manipulation of the original data or bias correction. Moreover, we complete the asymptotic theory for the Fourier spot volatility estimator in the absence of noise, originally presented in [Mancino and Recchioni, 2015], by deriving a Central Limit Theorem with the optimal convergence rate $n^{1/4}$. Finally, we propose a novel feasible adaptive method for the optimal selection of the parameters involved in the implementation of the Fourier spot volatility estimator with noisy high-frequency data and provide support to its accuracy both numerically and empirically. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.08967&r= |
| By: | Jin Hong Kuan |
| Abstract: | The standard approach for compensating liquidity providers on many decentralized exchanges (DEX) for serving as counter-party to swaps is through charging a small percentage of fees. The expected payoff from the cash flow of this mode of market making has yet to be mathematically formulated in terms of volatility in the existing literature. We provide here a preliminary derivation of the payoff formula, by making the standard set of assumptions for efficient markets, namely geometric Brownian price movements and zero arbitrage. Trading volume, conventionally taken as an exogenous variable for fees calculation, becomes a function of volatility and available liquidity in this formulation. In doing so, we show that it is a near-linear function of the volatility of the underlying risky asset. Since hedging instruments with such a property are highly sought after, we discuss the potential of securitizing the cash flow of liquidity fees to serve as a volatility product in its own right. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.01653&r= |
| By: | Frederik Bossaerts; Nitin Yadav; Peter Bossaerts; Chad Nash; Torquil Todd; Torsten Rudolf; Rowena Hutchins; Anne-Louise Ponsonby; Karl Mattingly |
| Abstract: | Prediction markets are a popular, prominent, and successful structure for a collective intelligence platform. However the exact mechanism by which information known to the participating traders is incorporated into the market price is unknown. Kyle (1985) detailed a model for price formation in continuous auctions with information distributed heterogeneously amongst market participants. This paper demonstrates a novel method derived from the Kyle model applied to data from a field experiment prediction market. The method is able to identify traders whose trades have price impact that adds a significant amount of information to the market price. Traders who are not identified as informed in aggregate have price impact consistent with noise trading. Results are reproduced on other prediction market datasets. Ultimately the results provide strong evidence in favor of the Kyle model in a field market setting, and highlight an under-discussed advantage of prediction markets over alternative group forecasting mechanisms: that the operator of the market does not need to have information on the distribution of information amongst participating traders. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.08778&r= |