A Comparative Study of Support Vector Machine and Artificial Neural Network for Predicting Option Price

Abstract

Prediction of Option Price accurately is a difficult task. Significantly accurate option price in any market helps decision maker to take proper decision for developing better financial management. Since the market is always dynamic and it has an impact on financial and different kinds of political affair. For this reason, different types of model are developed for predicting option price with the advancement of technology. So, it is a big matter to predict option price accurately.

This report presents the comparative study of Support Vector Machine and Artificial Neural Network for predicting option price accurately with the advent of machine learning.

This study is performed by optimizing the parameter of Artificial Neural Network model and Support Vector Machine by finding the smallest error between actual and predicted. The data set has been collected from the spy option of Yahoo finance 2015 for testing and training for both cases. After used in testing phase, we obtain RMSE of the Artificial Neural Network model was 0.

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274418 and for Support Vector Machine 0.409254.

The result shows that the Artificial Neural Network model is better than Support Vector Machine by having the smallest RMSE of the Artificial Neural Network model. Finally, this comparison provides contribution to knowledge where Artificial Neural Network makes impressive performance than Support Vector Machine for production quantity prediction. The testing and training process have been done by MATLAB 2018a language and hence it cannot exactly be determined if other languages or software’s may give better results.

Introduction

Financial market could be a propellant market.

The relationships between money markets and also the country economy is complicated. Understanding these relationships is one amongst the key parts for any money decision-making system [1,2,3]. within the previous days choice worth prediction became one amongst the key fields of analysis thanks to its wide domain of economic applications. Choice worth prediction field was developed to be dynamic, sophisticated and chaotic in nature [4]. Several researchers have worked on to enhance prediction mistreatment several ancient and innovative techniques. They need shown several characteristics and method that created them onerous to predict thanks to the necessity for ancient method. In line with the previous analysis we will make a case for this in 2 ways that by watching these problems.

These square measures applied mathematics primarily based approaches like regression, auto-regression and auto-regression moving average. There square measure variety of assumptions got to be thought-about whereas mistreatment these models like one-dimensionality and writing paper of the money time-series knowledge. Such non-realistic assumptions will degrade the standard of prediction results [5]. Soft computing could be a term that covers mimic biological processes. These techniques embrace Artificial Neural Networks, mathematical logic, Support Vector Machines, particle swarm improvement and lots of others.

ANNs legendary to be one amongst the with success developed ways that was wide employed in resolution several prediction issues in diversity of applications [6,7,8]. ANNs won't to solve type of issues in money statistic statement. as an example, prediction of stock worth movement was explored in [9]. Authors provided 2 models for the daily Istanbul stock market (ISE) National a hundred index mistreatment ANN and SVM. Another sort of ANN, the radial basis function (RBF) neural network was to forecast the indicant of the Shanghai stock market. In [10], ANNs were trained with stock knowledge from data system, DJIA and STI index. The rumored results indicated that increased ANN models with commercialism volumes will improve statement performance in each medium-and long-run horizons.

A comparison between SVM and Backpropagation ANN in statement six major Asian stock markets was rumored in [11]. different soft computing techniques like mathematical logic are to solve several stock exchange statement issues. biological process computation was additionally explored to unravel the prediction downside for the S&P five hundred indicant. Genetic Algorithms was to at the same time optimize all of a Radial Basis function network parameter such associate degree economical time-series is intended and used for business statement applications. In [12], author provided a replacement prediction model for the S&P five hundred mistreatment multigene symbolic regression genetic programming. Multigene general practitioner shows additional strong results particularly within the validation/testing case than ANN.

This study presents option price prediction model that combines ANN and SVM to predict option prices. In these approaches, the residuals between the actual prices and the Black-Scholes model are fed into the SVM and ANN model, and they conducted to further reduce the prediction errors. Empirical results of this study established that the model of ANN and Support Vector Machine. The empirical results shown that the ANN is better than the SVM for predict option price.

Related Work

A variety of educational studies have examined the relative performance of choices worth in many countries, few of the studies area unit mentioned here. Settler etal. [13] in 1994 used neural network for possibility valuation and compared its performance with Black Scholes model. The planned model performed fairly well. M. Liu [14] in 1996, Yaoetal. [15] in 2000 and Andreou [16] in 2008 with success applied neural network in possibility valuation. Saxena [17] studied European-style CNX keen choices listed at National exchange of India.

He combined the Black Sholes model and Artificial Neural Networks (ANNs), for possibility valuation and complete that hybrid model will improve the valuation performance of choices below all market conditions and Mitra [18] in 2012 studied keen choices in India and forecasted it exploitation neural network. Lajbcygieretal. [19] improved the Hybrid Neural Network exploitation bootstrap strategies to scale back bias in existing model. Rafiuletal [20] painted because the simplest theorem network, the Hidden Markov Model is combined with Artificial Neural Network and Genetic formula to forecast the financial market behavior.

ANN is employed to convert the daily stock values to a group of input arrays that area unit fed into the Hidden Markov Model. Genetic formula is employed to primarily optimize the primary set of parameters. HMM is employed to scoop out comparable patterns from previous knowledge. the value distinction for serial days at every juncture is calculated so as to search out a weighted average. This worth is employed to arrange the forecast. Kyoung [21] shows support vector machines area unit the methodologies with greatest results once it involves money statistic.

This paper compares Back propagation neural networks moreover to indicate however promising an alternate SVM is popping intent on. A structural Risk reduction principle is developed so as to attenuate classification error or a minimum of attempt to revent deviation from the particular linear stock costs.

One large advantage of SVM is that it provides a globally optimized resolution. This paper additionally compares case based mostly resoning and ANN with SVM. Akiraetal. [22] shows that the area unit varied factors that influence the choice of investors, among these additionally includes CPI, worth earnings quantitative relation, newspaper opinions and additionally tips by brokers. Despite psychological info additionally wide impacting the trends, utmost effort and care are taken that solely numerical info be wont to predict patterns and trends. the foremost recent Neural Network, the Deep Belief Neural Network has up to be used extensively in pattern mining. it's able to construct helpful info from large amounts of information which nearly exactly what's required for stock and market predictions.

In this paper Support Vector Machine and Artificial Neural Network are applying to predict the option price. The paper is structured as follows. First introduce the theoretical analysis of Black-Scholes, Artificial Neural Network (ANN), Support vector machine (SVM). In second, this report discusses about the data structure and algorithm on each type of option pricing dataset. Then result and discussion with table and figure is described then conclusion is presented and finally references are mentioned in the last section.

Related Literature Review

Neural Network

Neural Network (ANN) can be defined as a reasoning model based on the human brain. The brain consists of interrelated nerve cells named neurons. The human brain includes nearly 10 billion neurons and 60 trillion connections, synapses, between them16. A nerve cell neuron consists of three parts, namely: the summing function (summing function), activation function (activation function), and output (output).

The term ‘Neural’ is evolved from the human (animal) nervous system’s basic functional unit ‘neuron’ or nerve cells which are exist in the brain and other parts of the human (animal) body. A neuron with its different parts is given in the following figure:

The typical nerve cell of human brain constitutes of mainly three parts (Dendrite, Cell body, Axon). But there is also another important part, that is Synapses.

Dendrite:  It receives signals from other neurons.

Cell body (Soma): It sums all the incoming signals to generate input.

Axon:  When the sum reaches a threshold value, neuron fires and the signal travels down the axon to the other neurons.

Synapses:  The point of interconnection of one neuron with other neurons. The amount of signal transmitted depend upon the strength (synaptic weights) of the connections. The connections can be preclusive (decreasing strength) or manifest (increasing strength) in nature.

So, neural network, in general, is a highly interconnected network of billions of neurons with trillion of interconnections between them.

Artificial Neural Network with Biological Neural Network

The dendrites in biological neural network is analogous to the weighted inputs based on their synaptic interconnection in artificial neural network. Cell body is analogous to the artificial neuron unit in artificial neural network which also comprises of summation and threshold unit. Axon carry output that is analogous to the output unit in case of artificial neural network. So, ANN are modelled using the working of basic biological neurons.

Artificial Neural Networks are the biologically inspired simulations performed on the computer to perform certain specific tasks like clustering, classification, pattern detection etc. Artificial Neural Networks, in general - is a biologically enthused network of artificial neurons organized to perform specific tasks. Artificial Neural Networks are networks which are created based on the strategy and act of the human brain’s neurons.

ANN’s are growing from Biology. They are non-linear and non-parametric units which process information, knowledge, intelligence, instruction etc. It is a computational method encouraged by studies of the brain and nervous system. It is an information-processing system designed to simulator the ability of the human brain to perceive relationships and patterns.

The project imitates the structure and operations of the three-dimensional lattice of network among brain cells (or neurons). The network learns by example. It learns by gradually smoothing the connections between electronic neurons in its system. The learning process of the network can be discussed as like as the following way, a child learns to recognize patterns, shapes and sounds, and discerns among them. For example, the child has to be illuminated to a number of examples of a particular type of animals for her to be capable to recognize that type of animal later on. In addition, the child has to be illuminated to different types of animals for her to be capable to differentiate among animals.

Support Vector Machine

Support Vector Machine (SVM) is a classification and regression forecast tool that uses to maximize predictive accuracy while automatically avoiding over-fit to the data. It is a supervised learning algorithm which is also known as Support vector network. Vladimir N. Vapnik and Alexey Ya. Chervonenkis invented the original SVM algorithm in 1963. Depending on the nature of the data, such a separation might be linear or non-linear.

Let us consider a linear classifier (or, hyperplane) where represents weight vector, is the input feature vector and represents the position of the hyperplane. Here,

1.  if the input vector is 2-dimensional, the linear equation will represent a straight line.
2.  if the input vector is 3-dimensional, the linear equation will represent a plane.
3.  if input vector more than 3-dimension, the linear equation will represent a hyperplane.

The SVM algorithm is to find an optimal hyperplane for classification of two classes. Assume that the equation of hyperplane is . The distance between and is the margin of this hyperplane. By applying the distance rule between two straight lines, we get the margin,

For non-linear classifier SVM use kernel function to separate the data points. Obtain a nonlinear SVM regression model by replacing the dot product with a nonlinear kernel function where, is a transformation that maps to a high-dimensional space.

Polynomial kernel function: where and are support vector where support vector is the input vectors that just touch the boundary of the margin. Simply, support vectors are the data points that lie closest to the decision surface (or hyperplane).

Data Structure and Methodology

Financial data offer an excellent source of difficult and challenging problems to the computing community. We collect the data from the spy option of yahoo finance 2015. Using this data, we will predict the accuracy of the option price. In the original data, we modified some of the dimensions of the variable.

Table 1: Option price data of market value

In Fig. 3. Show methodology of predicting option price by Artificial Neural Network and Support Vector Machine. The aim of this research is to investigate the best learning method for option price prediction. As shown in figure. 3 input data set contains training data set and also testing dataset. The dataset will be transformed to get the relevant attributes according with the format of the input Artificial Neural Network and Support Vector Machine. We used experiment by trial and error to get the minimum error in this procedure. First of all, we need to know architecture of Support Vector Machine. For output of the Support Vector Machine we use the input variable as shown in table 2. For predicting option price, we use different kind of kernel function to minimize the error.

Sl.Parameter

Description

1. Spot price of the security
2. Exercise price of call option
3. Risk free rate of interest
4. Time left until option expiry (date in year fraction)
5. A measure of implied volatility (calculated as standard deviation)
6. Table 2: Input Parameters

Secondly, we determine the architecture ANN using feed forward neural network with one hidden layer. Firstly, to develop a ANN model, there are several stages. The first stage is the determination of training cycles. For minimizing the error, we use the weight vector arbitrarily with input variables. Also, we use different kind of activation function to minimize error. Training cycles are selected based on the result of smallest Root Mean Square Error (RMSE). After training cycle are obtained, learning rate is determined conducting a test input value. Learning rate also selects based on the result of smallest RMSE.

Experimental Result and Discussion

For learning proses of model ANN and SVM, we split the data into two parts: training data and testing data using cross-validation. Cross validation is used because it became standard method in practical terms. Cross-validation makes proses training performed 15 times because divided training data into 15 equal parts. And for prediction performance evaluation as accuracy indicator in our experiment are used RMSE. The experimental result of artificial neural network is reported in table 3. The best results in the experiment is one hidden layer, 5 inputs parameter with regarded weight and 4 neuron size with the smallest RMSE are produced 1.743, with six attributes of the input and one output.

Table 3: Result Parameter of Neural Network Model

The concept of SVM modeling can be given as considering a data set , where is thedimensional input space and is the corresponding output. In dot function is defined by it is inner product of and. Parameter of C being a regularization constant, determines the trade-off between the empirical risk and the regularization term. Parameter of Epsilon is specifying the insensitivity constant. No loss if the prediction lies this close to true value. This parameter is part of the loss function.

Table 4: Result Parameter of SVM Model

RMSE Result

0.409254

0.274418

In the table. 4 are reported the results of experiments in determining parameter SVM are C is 0.1 and epsilon 0.5. By getting the best parameters, it can be concluded that the results of experiments using support vector machine method to get the smallest RMSE is 1.752. From these two models we can get prediction based on ANN and SVM model that show in table 5 comparison result of production quantity prediction.

Finally, to verify a significant difference between these two methods (ANN and SVM), the result of both methods is compared using statistical technique t-Test. We can compare the result of comparison using statistical t-test analysis If P-Values is less than the predetermined significant level (α), it shows that the result has no significant deferent. Otherwise if P-Values more than predetermined significant level (α), it shows that the result has significant deferent. And the result show in table 6. That ANN and SVM that has significance difference in training result.

Figure 4 shows the scattered plot of actual and predicted price for SVM and ANN. From figure 4 we have that ANN can predict more than SVM with actual price.

Therefore, we can conclude that neural network makes an impressive performance in prediction rather than SVM for production quantity prediction.

Conclusions

Artificial Neural Network and Support Vector Machine model have been established for option price prediction. A good performance of the ANN and SVM was achieved with coefficient of determination (RMSE) value between the model prediction and actual values were 1.743 and 1.752 on training phase and RMSE in testing phase is 0.274418 and 0.409254, respectively. Based on results, neural network show that have good performance rather than SVM for production quantity prediction. So, for further prediction we can use artificial neural network to achieve good performance.

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