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Register a new userDeep Investing in Kyles Single Period Model
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The Kyle model describes how an equilibrium of order sizes and security prices naturally arises between a trader with insider information and the price providing market maker as they interact through a series of auctions. Ever since being introduced by Albert S. Kyle in 1985, the model has become important in the study of market microstructure models with asymmetric information. As it is well understood, it serves as an excellent opportunity to study how modern deep learning technology can be used to replicate and better understand equilibria that occur in certain market learning problems. We model the agents in Kyles single period setting using deep neural networks. The networks are trained by interacting following the rules and objectives as defined by Kyle. We show how the right network architectures and training methods lead to the agents behaviour converging to the theoretical equilibrium that is predicted by Kyles model.
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The dynamics of financial markets are driven by the interactions between participants, as well as the trading mechanisms and regulatory frameworks that govern these interactions. Decision-makers would rather not ignore the impact of other participants on these dynamics and should employ tools and models that take this into account. To this end, we demonstrate the efficacy of applying opponent-modeling in a number of simulated market settings. While our simulations are simplified representations of actual market dynamics, they provide an idealized playground in which our techniques can be demonstrated and tested. We present this work with the aim that our techniques could be refined and, with some effort, scaled up to the full complexity of real-world market scenarios. We hope that the results presented encourage practitioners to adopt opponent-modeling methods and apply them online systems, in order to enable not only reactive but also proactive decisions to be made.
We implement and test kernel averaging Non-Uniform Fast Fourier Transform (NUFFT) methods to enhance the performance of correlation and covariance estimation on asynchronously sampled event-data using the Malliavin-Mancino Fourier estimator. The methods are benchmarked for Dirichlet and Fej{e}r Fourier basis kernels. We consider test cases formed from Geometric Brownian motions to replicate synchronous and asynchronous data for benchmarking purposes. We consider three standard averaging kernels to convolve the event-data for synchronisation via over-sampling for use with the Fast Fourier Transform (FFT): the Gaussian kernel, the Kaiser-Bessel kernel, and the exponential of semi-circle kernel. First, this allows us to demonstrate the performance of the estimator with different combinations of basis kernels and averaging kernels. Second, we investigate and compare the impact of the averaging scales explicit in each averaging kernel and its relationship between the time-scale averaging implicit in the Malliavin-Mancino estimator. Third, we demonstrate the relationship between time-scale averaging based on the number of Fourier coefficients used in the estimator to a theoretical model of the Epps effect. We briefly demonstrate the methods on Trade-and-Quote (TAQ) data from the Johannesburg Stock Exchange to make an initial visualisation of the correlation dynamics for various time-scales under market microstructure.
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In this paper we derive semi-closed form prices of barrier (perhaps, time-dependent) options for the Hull-White model, ie., where the underlying follows a time-dependent OU process with a mean-reverting drift. Our approach is similar to that in (Carr and Itkin, 2020) where the method of generalized integral transform is applied to pricing barrier options in the time-dependent OU model, but extends it to an infinite domain (which is an unsolved problem yet). Alternatively, we use the method of heat potentials for solving the same problems. By semi-closed solution we mean that first, we need to solve numerically a linear Volterra equation of the first kind, and then the option price is represented as a one-dimensional integral. Our analysis shows that computationally our method is more efficient than the backward and even forward finite difference methods (if one uses them to solve those problems), while providing better accuracy and stability.
In this article, we show how the scaling symmetry of the SABR model can be utilized to efficiently price European options. For special kinds of payoffs, the complexity of the problem is reduced by one dimension. For more generic payoffs, instead of solving the 1+2 dimensional SABR PDE, it is sufficient to solve $N_V$ uncoupled 1+1 dimensional PDEs, where $N_V$ is the number of points used to discretize one dimension. Furthermore, the symmetry argument enables us to obtain prices of multiple options, whose payoffs are related to each other by convolutions, by valuing one of them. The results of the method are compared with the Monte Carlo simulation.
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