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Register a new userStock price formation: useful insights from a multi-agent reinforcement learning model
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In the past, financial stock markets have been studied with previous generations of multi-agent systems (MAS) that relied on zero-intelligence agents, and often the necessity to implement so-called noise traders to sub-optimally emulate price formation processes. However recent advances in the fields of neuroscience and machine learning have overall brought the possibility for new tools to the bottom-up statistical inference of complex systems. Most importantly, such tools allows for studying new fields, such as agent learning, which in finance is central to information and stock price estimation. We present here the results of a new generation MAS stock market simulator, where each agent autonomously learns to do price forecasting and stock trading via model-free reinforcement learning, and where the collective behaviour of all agents decisions to trade feed a centralised double-auction limit order book, emulating price and volume microstructures. We study here what such agents learn in detail, and how heterogenous are the policies they develop over time. We also show how the agents learning rates, and their propensity to be chartist or fundamentalist impacts the overall market stability and agent individual performance. We conclude with a study on the impact of agent information via random trading.
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The VSTOXX index tracks the expected 30-day volatility of the EURO STOXX 50 equity index. Futures on the VSTOXX index can, therefore, be used to hedge against economic uncertainty. We investigate the effect of trader inventory on the price of VSTOXX futures through a combination of stochastic processes and machine learning methods. We formulate a simple and efficient pricing methodology for VSTOXX futures, which assumes a Heston-type stochastic process for the underlying EURO STOXX 50 market. Under these dynamics, approximate analytical formulas for the implied volatility smile and the VSTOXX index have recently been derived. We use the EURO STOXX 50 option implied volatilities and the VSTOXX index value to estimate the parameters of this Heston model. Following the calibration, we calculate theoretical VSTOXX future prices and compare them to the actual market prices. While theoretical and market prices are usually in line, we also observe time periods, during which the market price does not agree with our Heston model. We collect a variety of market features that could potentially explain the price deviations and calibrate two machine learning models to the price difference: a regularized linear model and a random forest. We find that both models indicate a strong influence of accumulated trader positions on the VSTOXX futures price.
The three-state agent-based 2D model of financial markets as proposed by Giulia Iori has been extended by introducing increasing trust in the correctly predicting agents, a more realistic consultation procedure as well as a formal validation mechanism. This paper shows that such a model correctly reproduces the three fundamental stylised facts: fat-tail log returns, power-law volatility autocorrelation decay in time and volatility clustering.
Following Boukai (2021) we present the Generalized Gamma (GG) distribution as a possible RND for modeling European options prices under Hestons (1993) stochastic volatility (SV) model. This distribution is seen as especially useful in situations in which the spots price follows a negatively skewed distribution and hence, Black-Scholes based (i.e. the log-normal distribution) modeling is largely inapt. We apply the GG distribution as RND to modeling current market option data on three large market-index ETFs, namely the SPY, IWM and QQQ as well as on the TLT (an ETF that tracks an index of long term US Treasury bonds). The current option chain of each of the three market-index ETFs shows of a pronounced skew of their volatility `smile which indicates a likely distortion in the Black-Scholes modeling of such option data. Reflective of entirely different market expectations, this distortion appears not to exist in the TLT option data. We provide a thorough modeling of the available option data we have on each ETF (with the October 15, 2021 expiration) based on the GG distribution and compared it to the option pricing and RND modeling obtained directly from a well-calibrated Hestons (1993) SV model (both theoretically and empirically, using Monte-Carlo simulations of the spots price). All three market-index ETFs exhibit negatively skewed distributions which are well-matched with those derived under the GG distribution as RND. The inadequacy of the Black-Scholes modeling in such instances which involve negatively skewed distribution is further illustrated by its impact on the hedging factor, delta, and the immediate implications to the retail trader. In contrast, for the TLT ETF, which exhibits no such distortion to the volatility `smile, the three pricing models (i.e. Hestons, Black-Scholes and Generalized Gamma) appear to yield similar results.
Traders in a stock market exchange stock shares and form a stock trading network. Trades at different positions of the stock trading network may contain different information. We construct stock trading networks based on the limit order book data and classify traders into $k$ classes using the $k$-shell decomposition method. We investigate the influences of trading behaviors on the price impact by comparing a closed national market (A-shares) with an international market (B-shares), individuals and institutions, partially filled and filled trades, buyer-initiated and seller-initiated trades, and trades at different positions of a trading network. Institutional traders professionally use some trading strategies to reduce the price impact and individuals at the same positions in the trading network have a higher price impact than institutions. We also find that trades in the core have higher price impacts than those in the peripheral shell.
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