Pricing Options and Computing Implied Volatilities using Neural Networks

Liu, Shuaiqiang; Oosterlee, Cornelis W.; Bohté, Sander M.

doi:10.3390/risks7010016

Cited by 102 publications

(70 citation statements)

References 26 publications

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“…For example, in order to approximate the Black-Scholes implied volatilities based on the Heston input parameters, two numerical methods are required, i.e., the COS method to calculate the Heston option prices and Brent's root-finding algorithm to determine the corresponding implied volatility, as presented in Figure 1. Using two separate ANNs to map the Heston parameters to implied volatility has been applied in Liu et al (2019). In the present paper, we merge these two ANNs, see Figure 1.…”

Section: The Forward Pass: Learning the Solution With Annsmentioning

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: The Forward Pass: Learning the Solution With Annsmentioning

confidence: 99%

“…The global structure is depicted in Figure 6. More details on the ANN solver can be founded in (Liu et al, 2019). As a data-driven method, the samples from the parameter set for which the ANN is trained are randomly generated for the pricing of European put options.…”

Section: The Forward Passmentioning

confidence: 99%

A neural network-based framework for financial model calibration

et al. 2019

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“…Concerning the second problem, the inverse of the call function does not have an analytical representation and therefore the problem can only be approached by numerical methods (Newton-Raphson and other iterative schemes) and, in some instances, even those methods may fail for technical reasons (Orlando and Taglialatela 2017;Dura and Moşneagu 2010;Lorig et al 2014;Liu et al 2019). Recently, Liu et al (2019) and Cao et al (2019) suggested new numerical methods to reconstruct the volatility through neural networks.…”

Section: N (X)mentioning

confidence: 99%

Challenges in approximating the Black and Scholes call formula with hyperbolic tangents

Mininni

Orlando

Taglialatela

2020

Decisions Econ Finan

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In this paper, we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. Differently from other solutions proposed in the literature, this formula is invertible; hence, it is useful for pricing and risk management as well as for extracting the implied volatility from quoted options. The latter is of particular importance since it indicates the risk of the underlying and it is the main component of the option’s price. That is what trading desks focus on. Further we estimate numerically the approximating error of the suggested solution and, by comparing our results in computing the implied volatility with the most common methods available in the literature, we discuss the challenges of this approach.

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“…MLP able to solve non-linear problems while maintaining the original structure of perceptron of feedforward layered [25]. Neural network has been demonstrated to successfully employed in various field of studies such as medical [26], [27], agriculture [28], [29], industrial [30], [31] and finance [32], [33].…”

Section: A Neural Networkmentioning

confidence: 99%

Data Pre-Processing Algorithm for Neural Network Binary Classification Model in Bank Tele-Marketing

Halim*¹,

Jaya²,

Fadzil³

2020

IJITEE

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Tele-marketing presents a huge challenge in identifying potential customers with lack of effective marketing strategy may led a company to succumbs to problems such as prolonged marketing campaign. Various attempts to improve the performance of binary classification model for bank tele-marketing data. Previous researches indicate that the neural network is the most common algorithms being employed and able to produce commendable results with higher accuracy percentages compared to other algorithms. Despite several attempts to improve the model through treatment of imbalance dataset and features selection, this research argues that they are incomplete. Therefore, this research proposes a data pre-processing algorithm for bank tele-marketing binary classification neural network. Three datasets have been employed (19, 16, and 20 features) to evaluate the performance of the algorithm towards the classification model. The data pre-processing algorithm is divided into three phases; data cleaning, data imbalance treatment and finally data normalization. In this paper, the result indicated that binary classification model complemented with data cleaning techniques such as Missing common (MC) and Tomek Links (TL) shows a better result compared to Ignore Missing (IM). In terms of data normalization, techniques such as MaxAbsScaler (MAS) and MinMaxScaler (MMS) consistently indicated better performance from other normalization techniques. The classification model employed in this paper utilize data pre-processing algorithm combination of MC-TL-MMS. The algorithm using this approach able to record an area of the receiver operating characteristic curve (AUC) of 0.9129 and 0.9464 by using 16 features and 20 features respectively. This result presents the highest figure in terms of performance accuracy compared to other previous researches

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Pricing Options and Computing Implied Volatilities using Neural Networks

Cited by 102 publications

References 26 publications

A neural network-based framework for financial model calibration

A neural network-based framework for financial model calibration

Challenges in approximating the Black and Scholes call formula with hyperbolic tangents

Data Pre-Processing Algorithm for Neural Network Binary Classification Model in Bank Tele-Marketing

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