Deeply Learning Derivatives

  title={Deeply Learning Derivatives},
  author={Ryan Ferguson and Andrew Green},
  journal={CompSciRN: Artificial Intelligence (Topic)},
  • Ryan Ferguson, Andrew Green
  • Published 6 September 2018
  • Economics, Computer Science, Mathematics
  • CompSciRN: Artificial Intelligence (Topic)
This paper uses deep learning to value derivatives. The approach is broadly applicable, and we use a call option on a basket of stocks as an example. We show that the deep learning model is accurate and very fast, capable of producing valuations a million times faster than traditional models. We develop a methodology to randomly generate appropriate training data and explore the impact of several parameters including layer width and depth, training data quality and quantity on model speed and… Expand
Deep calibration of rough stochastic volatility models
This work showcases a direct comparison of different potential approaches to the learning stage and presents algorithms that provide a suffcient accuracy for practical use and provides a first neural network-based calibration method for rough volatility models for which calibration can be done on the y. Expand
Deep Learning Volatility
A neural network based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface and brings several numerical pricers and model families within the scope of applicability in industry practice. Expand
Deep Learning for Exotic Option Valuation
This work considers an alternative approach where the structure of the user’s preferred model is preserved but points on the volatility are features input to a neural network and shows that VFA can be expected to outperform MCA for the volatility surfaces encountered in practice. Expand
Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models
A neural network-based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface, and stochastic volatility models (classical and rough) can be handled in great generality as the framework also allows taking the forward variance curve as an input. Expand
Gradient boosting for quantitative finance
This paper discusses how tree-based machine learning techniques can be used in the context of derivatives pricing, and illustrates this methodology by reducing computation times for pricing exotic derivative products and American options. Expand
Accuracy of deep learning in calibrating HJM forward curves
A new class of volatility operators is introduced which map the square integrable noise into the Filipovi\'{c} space of forward curves, and a deterministic parametrized version of it is specified. Expand
Black-Box Model Risk in Finance
Machine learning models are increasingly used in a wide variety of financial settings. The difficulty of understanding the inner workings of these systems, combined with their wide applicability, hasExpand
The CV Makes the Difference – Control Variates for Neural Networks
We consider the application of a control variate technique for Deep Learning. In analogy to applications for Monte Carlo simulation or Fourier integration methods, this technique improves the qualityExpand
Deep Option Pricing - Term Structure Models
This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options within the setting of interest rate term structure models. This aims toExpand
Neural Networks for Option Pricing and Hedging: A Literature Review
This note intends to provide a comprehensive review of neural networks as a nonparametric method for option pricing and hedging since the early 1990s in terms of input features, output variables, benchmark models, performance measures, data partition methods, and underlying assets. Expand


Machine Learning in Finance : The Case of Deep Learning for Option Pricing
Modern advancements in mathematical analysis, computational hardware and software, and availability of big data have made possible commoditized machines that can learn to operate as investmentExpand
Deep Primal-Dual Algorithm for BSDEs: Applications of Machine Learning to CVA and IM
A primal-dual method for solving BSDEs based on the use of neural networks, stochastic gradient descent and a dual formulation of stochastics control problems is introduced. Expand
A Fast Learning Algorithm for Deep Belief Nets
A fast, greedy algorithm is derived that can learn deep, directed belief networks one layer at a time, provided the top two layers form an undirected associative memory. Expand
Learning representations by back-propagating errors
Back-propagation repeatedly adjusts the weights of the connections in the network so as to minimize a measure of the difference between the actual output vector of the net and the desired output vector, which helps to represent important features of the task domain. Expand
Chebyshev interpolation for parametric option pricing
The Chebyshev method turns out to be more efficient than parametric multilevel Monte Carlo and its combination with Monte Carlo simulation and the effect of (stochastic) approximations of the interpolation is analyzed. Expand
Adam: A Method for Stochastic Optimization
This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Expand
Forecasting Foreign Exchange Rates Using Recurrent Neural Networks
  • P. Tenti
  • Computer Science
  • Appl. Artif. Intell.
  • 1996
The use of recurrent neural networks in order to forecast foreign exchange rates is proposed and the methods described here which have obtained promising results in real time trading are applicable to other markets. Expand
Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations
We study a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, which is based on an analogy between theExpand
On Characterizing the Capacity of Neural Networks using Algebraic Topology
This paper reframe the problem of architecture selection as understanding how data determines the most expressive and generalizable architectures suited to that data, beyond inductive bias, and provides the first empirical characterization of the topological capacity of neural networks. Expand
Approximation capabilities of multilayer feedforward networks
  • K. Hornik
  • Mathematics, Computer Science
  • Neural Networks
  • 1991
Abstract We show that standard multilayer feedforward networks with as few as a single hidden layer and arbitrary bounded and nonconstant activation function are universal approximators with respectExpand