Deep Learning Volatility

Horvath, Blanka; Muguruza, Aitor; Tomas, Mehdi

doi:10.2139/ssrn.3322085

Cited by 39 publications

(43 citation statements)

References 52 publications

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“…Further future improvements include combining gradient-based optimization with the DE, since the gradient information is readily accessible. It is also feasible to employ a small neural network to reduce the computing time, like in the paper (Horvath et al, 2019) which builds a three-hidden-layers ANNs and each layer has 30 nodes during the calibration.…”

Section: Resultsmentioning

confidence: 99%

“…In a financial context, e.g., in the pricing and risk management of financial derivative contracts, asset model calibration aims at recovering the model Secondly, there is inherent parallelism in our ANN approach, so we will also take advantage of modern processing units (like GPUs). The paper (Horvath et al, 2019) also presented a neural network-based method to compute and calibrate rough volatility models. Our CaNN however incorporates a parallel global search method for calibration.…”

Section: Introductionmentioning

confidence: 99%

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A neural network-based framework for financial model calibration

et al. 2019

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A data-driven approach called CaNN (Calibration Neural Network) is proposed to calibrate financial asset price models using an Artificial Neural Network (ANN). Determining optimal values of the model parameters is formulated as training hidden neurons within a machine learning framework, based on available financial option prices. The framework consists of two parts: a forward pass in which we train the weights of the ANN offline, valuing options under many different asset model parameter settings; and a backward pass, in which we evaluate the trained ANN-solver on-line, aiming to find the weights of the neurons in the input layer. The rapid online learning of implied volatility by ANNs, in combination with the use of an adapted parallel global optimization method, tackles the computation bottleneck and provides a fast and reliable technique for calibrating model parameters while avoiding, as much as possible, getting stuck in local minima. Numerical experiments confirm that this machine-learning framework can be employed to calibrate parameters of high-dimensional stochastic volatility models efficiently and accurately.parameters of the underlying stochastic differential equations (SDEs) from observed market data. In other words, in the case of stocks and financial options, the calibration aims to determine the stock model parameters such that heavily traded, liquid option prices can be recovered by the mathematical model. The calibrated asset models are subsequently used to either determine a suitable price for over-the-counter (OTC) exotic financial derivatives products, or for hedging and risk management purposes.Calibrating financial models is a critical subtask within finance, and may need to be performed numerous times every day. Relevant issues in this context include accuracy, speed and robustness of the calibration. Real-time pricing and risk management require a fast and accurate calibration process. Repeatedly computing the values using mathematical models and at the same time fitting the parameters may be a computationally heavy burden, especially when dealing with multi-dimensional asset price models. The calibration problem is furthermore not necessarily a convex optimization problem, and it often gives rise to multiple local minima.A generic, robust calibration framework may be based on a global optimization technique in combination with a highly efficient pricing method, in a parallel computing environment. To meet these requirements, we will employ the machine learning technology and develop an artificial neural network (ANN) solution method for a generic calibration framework.The proposed ANN-based framework comprises three phases, i.e., training, prediction and calibration. During the training phase, the hidden layer parameters of the ANNs are optimized by means of supervised learning. This training phase builds a mapping between the model parameters and the output of interest. During the prediction phase, the hidden layers are kept unchanged (frozen) to compute the output quantities (e.g.,opt...

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A neural network-based framework for financial model calibration

et al. 2019

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“…These series could then be used to estimate the smoothness of volatility in fMRI data using models such as the rBergomi. [28,14,26]; F. Demeaned BOLD signal from voxel [12,27,30]; G. Demeaned BOLD signal from voxel [17,36,24]; H. Demeaned BOLD signal from voxel [37,19,15]. All returns data is from the Oxford-Man database https://realized.oxford-man.ox.ac.uk/.…”

Section: Introductionmentioning

confidence: 99%

Sailing in rough waters: examining volatility of fMRI noise

Leppänen

Stone

Lythgoe

et al. 2020

Preprint

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1.AbstractBackgroundFunctional resonance magnetic imaging (fMRI) noise is usually assumed to have constant volatility. However this assumption has been recently challenged in a few studies examining heteroscedasticity arising from head motion and physiological noise. However, to our knowledge no studies have studied heteroscedasticity in scanner noise. Thus the aim of this study was to estimate the smoothness of fMRI scanner noise using latest methods from the field of financial mathematics.MethodsA multi-echo fMRI scan was performed on a phantom using two 3 tesla MRI units. The echo times were used as intra-time point data to estimate realised volatility. Smoothness of the realised volatility processes is examined by estimating the Hurst parameter, a parameter H ∈ (0, 1) governing the roughness (Hölder continuity) of paths in the rough Bergomi model, introduced in [2]. The rough Bergomi model a member of the family of rough stochastic volatility models. A family of models which was recently popularised in mathematical finance by observations indicating that volatility in financial markets is best described by stochastic models where volatility can be modulated by the Hurst parameter H, which usually calibrates to values H ∈ (0, 0.5) (the rough case), hence inspiring the name of the model family. In this work, calibration of the Hurst parameter H is performed pathwise, using recently developed neural network calibration tools.ResultsIn all experiments the volatility calibrates to values well within the rough case H < 0.5 and on average fMRI scanner noise was very rough with H ≈ 0.03. Substantial variability was also observed, which was caused by edge effects, whereby H was larger near the edges of the phantoms.DiscussionThe findings challenge the assumption that fMRI scanner noise has constant volatility (in fact, the lower the value of H, the more pronounced the oscillations of the volatility, and hence the more “severe” is the violation of the constant volatility assumption) and add to the steady accumulation of studies suggesting implementing methods to model heteroscedasticity may improve fMRI data analysis. Additionally, the present findings add to previous work showing that the mean and normality of fMRI noise processes show edge effects, such that signal near the edges of the images is less likely to meet the assumptions of current modelling methods.

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“…On the practical side, competitive simulation methods are developed in Bennedsen, Lunde and Pakkanen [BLP15], Horvath, Jacquier and Muguruza [HJM17] and McCrickerd and Pakkanen [MP18]. Moreover, recent developments by Stone [Sto19] and Horvath, Muguruza and Tomas [HMT19] allow the use of neural networks for calibration; their calibration schemes are considerably faster and more accurate than existing methods for rough volatility models.…”

Section: Introductionmentioning

confidence: 99%

Asymptotics for Volatility Derivatives in Multi-Factor Rough Volatility Models

2019

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We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and robust numerical recipes to compute the rate function; the backbone of our theoretical framework. Based on our results, we further develop approximation schemes for the density of RV, which in turn allows to express the volatility swap in close-form. Lastly, we investigate different constructions of multi-factor models and how each of them affects the convexity of the implied volatility smile. Interestingly, we identify the class of models that generate non-linear smiles around-the-money.Date: March 25, 2019.2010 Mathematics Subject Classification. Primary 60F10, 60G22; Secondary 91G20, 60G15, 91G60. ε > 0, P ε is the joint law and, for each δ > 0, the set ω :and lim sup ε↓0 h ε log P ε (Γ δ ) = −∞, where Γ δ := {(ỹ, y) : d(ỹ, y) > δ} ⊂ Y × Y. Theorem D.2. Let X and Y be topological spaces and f : X → Y a continuous function. Consider a good rate function I : X → [0, ∞]. For each y ∈ Y, define I (y) := inf{I(x) : x ∈ X , y = f (x)}. Then, if I controls the LDP associated with a family of probability measures {µ ε } on X , the I controls the LDP associated with the family of probability measures {µ ε • f −1 } on Y and I is a good rate function on Y.

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Deep Learning Volatility

Cited by 39 publications

References 52 publications

A neural network-based framework for financial model calibration

A neural network-based framework for financial model calibration

Sailing in rough waters: examining volatility of fMRI noise

Asymptotics for Volatility Derivatives in Multi-Factor Rough Volatility Models

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