Supervised Deep Neural Networks (DNNs) for Pricing/Calibration of Vanilla/Exotic Options Under Various Different Processes

Hirsa, Ali; Karatas, Tugce; Oskoui, Amir

doi:10.48550/arxiv.1902.05810

Cited by 4 publications

(5 citation statements)

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“…First of all, the machine learning approach may significantly accelerate classical option pricing techniques, particularly when involved asset price models are of interest. Recently there has been increasing interest in applying machine-learning techniques for fast pricing and calibration, see (Liu et al, 2019;Poggio et al, 2017;Spiegeleer et al, 2018;Horvath et al, 2019;Dimitroff et al, 2018;Hernandez, 2016;Hirsa et al, 2019). For example, the paper (Spiegeleer et al, 2018) used Gaussian process regression methods for derivative pricing.…”

Section: Introductionmentioning

confidence: 99%

“…For example, the paper (Spiegeleer et al, 2018) used Gaussian process regression methods for derivative pricing. Other work, including this paper, employs artificial neural networks to learn the solution of the financial SDE system (Liu et al, 2019;Horvath et al, 2019;Hirsa et al, 2019), that do not suffer much from the curse of dimensionality.…”

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A neural network-based framework for financial model calibration

et al. 2019

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“…Further, it is noticeable in the literature that although similar approaches are adopted for the same model, the loss of test data differ considerably depending on the details of the training methods. This notion is validated via the mean squared fitting errors (MSFE) of Culkin and Das [9], Broström and Kristiansson [10], Liu et al [13], and Hirsa et al [14] for the Black-Scholes model in Table 1 and 2 . This association may be because the latter networks have narrower structures or learn from smaller data than the former.…”

Section: Introductionmentioning

confidence: 83%

“…Since the work of Hutchinson et al [5], many researchers have been studying artificial neural networks to predict the option prices c (or the implied volatilities σ I ) for particular parametric models, such as the Black-Scholes model [6], the Heston model [7], and the SABR model [8]. We selected six related studies [9,10,11,12,13,14] and summarized their approaches in Tables 1 and 2. Interestingly, we can observe similar propensities in the studies.…”

Section: Introductionmentioning

confidence: 99%

Extensive networks would eliminate the demand for pricing formulas

Jeon¹,

Park²,

Huh³

2021

Preprint

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In this study, we generate a large number of implied volatilities for the Stochastic Alpha Beta Rho (SABR) model using a graphics processing unit (GPU) based simulation and enable an extensive neural network to learn them. This model does not have any exact pricing formulas for vanilla options, and neural networks have an outstanding ability to approximate various functions. Surprisingly, the network reduces the simulation noises by itself, thereby achieving as much accuracy as the Monte-Carlo simulation. Extremely high accuracy cannot be attained via existing approximate formulas. Moreover, the network is as efficient as the approaches based on the formulas. When evaluating based on high accuracy and efficiency, extensive networks can eliminate the necessity of the pricing formulas for the SABR model. Another significant contribution is that a novel method is proposed to examine the errors based on nonlinear regression. This approach is easily extendable to other pricing models for which it is hard to induce analytic formulas.

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“…all the parameters in the model given labels generated by other pricing methods (see e.g. [3,10,19,27,21,2]). The neural network approach is fast in computing prices and volatilities once trained and thus it is a good choice for model calibration.…”

Section: Introductionmentioning

confidence: 99%

Solving barrier options under stochastic volatility using deep learning

Fu¹,

Hirsa²

2022

Preprint

Self Cite

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We develop an unsupervised deep learning method to solve the barrier options under the Bergomi model. The neural networks serve as the approximate option surfaces and are trained to satisfy the PDE as well as the boundary conditions. Two singular terms are added to the neural networks to deal with the non-smooth and discontinuous payoff at the strike and barrier levels so that the neural networks can replicate the asymptotic behaviors of barrier options at short maturities. After that, vanilla options and barrier options are priced in a single framework. Also, neural networks are employed to deal with the high dimensionality of the function input in the Bergomi model. Once trained, the neural network solution yields fast and accurate option values.

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Supervised Deep Neural Networks (DNNs) for Pricing/Calibration of Vanilla/Exotic Options Under Various Different Processes

Cited by 4 publications

References 0 publications

A neural network-based framework for financial model calibration

A neural network-based framework for financial model calibration

Extensive networks would eliminate the demand for pricing formulas

Solving barrier options under stochastic volatility using deep learning

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