Computational Intelligence Applications to Option Pricing, Volatility Forecasting and Value at Risk

Mostafa, Fahed; Dillon, Tharam S.; Chang, Elizabeth

doi:10.1007/978-3-319-51668-4

Cited by 11 publications

(13 citation statements)

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“…Namun pada kenyataannya fluktuasi harga saham yang terjadi di bursa menyebabkan investor mengalami kesulitan dalam menentukan harga jual opsi yang optimal. Metode penentuan harga opsi Black-Scholes Merton (BSM) yang dikembangkan oleh Fisher Black dan Myron Scholes pada tahun 1973 merupakan metode yang terkenal untuk menghitung harga pasar opsi Eropa, metode ini berhasil mengungkapkan masalah penetapan harga opsi sebagai persamaan diferensial parsial [4]. Namun model ini memiliki asumsi yang secara praktis tidak dapat dipenuhi, salah satunya nilai volatilitas dari harga aset adalah konstan.…”

Section: Pendahuluanunclassified

Penentuan Harga Opsi Dengan Volatilitas Stokastik Menggunakan Metode Monte Carlo

Chalimatusadiah¹,

Lesmana²,

Budiarti³

2021

Jambura J. Math

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ABSTRAKHal yang utama dalam perdagangan opsi adalah penentuan harga jual opsi yang optimal. Namun pada kenyataan sebenarnya fluktuasi harga aset yang terjadi di pasar menandakan bahwa volatilitas dari harga aset tidaklah konstan, hal ini menyebabkan investor mengalami kesulitan dalam menentukan harga opsi yang optimal. Artikel ini membahas tentang penentuan harga opsi tipe Eropa yang optimal dengan volatilitas stokastik menggunakan metode Monte Carlo dan pengaruh harga saham awal, harga strike, dan waktu jatuh tempo terhadap harga opsi Eropa. Adapun model volatilitas stokastik yang digunakan dalam penelitian ini adalah model Heston, yang mengasumsikan bahwa proses harga saham (St) mengikuti distribusi log-normal, dan proses volatilitas saham (Vt) mengikuti Proses Cox-Ingersoll-Ross. Hal pertama yang dilakukan dalam penelitian ini adalah mengestimasi parameter model Heston untuk mendapatkan harga saham dengan menggunakan metode ordinary least square dan metode numerik Euler-Maruyama. Langkah kedua adalah melakukan estimasi harga saham untuk mendapatkan harga opsi tipe Eropa menggunakan metode Monte Carlo. Hasil dari penelitian ini menunjukkan bahwa penggunaan metode Monte Carlo dalam penentuan harga opsi tipe Eropa dengan volatilitas stokastik model Heston menghasilkan solusi yang cukup baik karena memiliki nilai error yang kecil dan akan konvergen ke solusi eksaknya dengan semakin banyak simulasi. Selain itu, simulasi Monte Carlo memberikan kesimpulan bahwa parameter harga strike, harga saham awal dan waktu jatuh tempo memiliki pengaruh terhadap harga opsi yang konsisten dengan teori harga opsi. ABSTRACTWhat is important in options trading is determining the optimal selling price. However, in real market conditions, fluctuations in asset prices that occur in the market indicate that the volatility of asset prices is not constant, this causes investors to experience difficulty in determining the optimal option price. This article discusses the optimal determination of the European type option price with stochastic volatility using the Monte Carlo method and the effect of the initial stock price, strike price, and expiration date on European option prices. The stochastic volatility model used in this study is the Heston model, which assumes that the stock price process (S) follows the normal log distribution, and the stock volatility process (V) follows the Ingersoll-Ross Cox Process. The first thing to do in this study is to estimate the parameters of the Heston model to get stock prices using the ordinary least square method and the Euler-Maruyama numerical method. The second step is to estimate the share price to get the European type option price using a Monte Carlo Simulation. This study indicates that using the Monte Carlo method in determining the price of European type options with the Heston model of stochastic volatility produces a fairly good solution because it has a small error value and will converge to the exact solution with more simulations. Also, the Monte Carlo simulation concludes that the parameters of the strike price, initial stock price, and maturity date influence the option price, which is consistent with the option price theory.

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Section: Pendahuluanunclassified

Penentuan Harga Opsi Dengan Volatilitas Stokastik Menggunakan Metode Monte Carlo

Chalimatusadiah¹,

Lesmana²,

Budiarti³

2021

Jambura J. Math

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“…Meanwhile, the architecture of each neural network model is shown in Table 2. There are different approaches in deciding the number of hidden neurons in the neural network [23,24]. In this study, the number of hidden neurons is set as 2n+1 where n is the number of input neurons [25].…”

Section: Training Parametersmentioning

confidence: 99%

Empirical Mode Decomposition Couple with Artificial Neural Network for Water Level Prediction

Loh¹,

Ismail²,

Khamis³

2019

cea

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Natural disaster brings massive destruction towards properties and human being and flood is one of them. In order for the government to take earlier action to reduce the damages, an accurate flood prediction is necessary. In Malaysia, Kelantan is categorized as a high flood risk area, thus this study focuses on Kelantan flood prediction. This study is to investigate the effect of decomposition for water level prediction by applying Artificial Neural Network (ANN) forecasting model. In this study, Empirical Mode Decomposition (EMD) is used as the decomposition method. The best Intrinsic Mode Function (IMF) for each input variable is selected using correlation-based selection method. The results showed that the performance of hybrid EMD and ANN is superior compared to other models, especially classic ANN model. The reason for this outcome is that through decomposition methods, ANN is able to capture more in-depth information of the Kelantan hydrological time series data. The resulting model provides new insights for government and hydrologist in Kelantan to have better prediction towards flood occurrence.

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“…The study specified an econometric model to remove linear dependence and used the residuals of this mean equation to test for ARCH effects. ARMA modes are the best in capturing the deterministic component of the series but they cannot capture the time changing variance and other key stylized facts of the return time series [13]. Various ARMA models were fitted to the differenced series and the best fit selected (one with the lowest AIC) to test for ARCH effects.…”

Section: Arma Modelsmentioning

confidence: 99%

Modelling Volatility of the US Dollar Against the Kenyan Shilling Exchange Rate and Investigating the Effect of Kenyan Inflation Rates on this Volatility in Kenya

Nandwa¹

2018

IJSDA

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Exchange rates and monetary policies are key tools in economic management and in the stabilization and adjustment process in developing countries, where low inflation rates and international competitiveness have become major policy targets. The study modelled the volatility of the US dollar against the Kenyan shilling (USD/KES) exchange rate and investigated the effect of inflation rates in Kenya on this volatility for the years 2005 to 2017. The data for this research was obtained from secondary sources: Central Bank of Kenya and the Kenya National Bureau of Statistics. The results indicated that the USD/KES exchange rate exhibited persistent signs of volatility. A number of heteroscedasticity models were then tested and the GARCH family (ARMA (1, 3)/EGARCH (1, 2)) model was concluded to be the best model to fit the volatility of the USD/KES exchange rate. The study tested the forecasting power of this model by comparing in-sample and out of sample observations and comprehensive conclusions were made that the model was the best fit to forecast the volatility of the USD/KES exchange rate. The volatility figures of the USD/KES exchange rate were extracted from the EGARCH model and further tests were conducted to investigate the effect of Kenyan inflation rates on them. Weighted Least Squares regression was conducted on the Kenyan inflation rates and volatility of the USD/KES exchange rate and comprehensive conclusions were made that there existed a significant relationship between the Kenyan inflation rates and the volatility of the USD/KES.

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Computational Intelligence Applications to Option Pricing, Volatility Forecasting and Value at Risk

Cited by 11 publications

References 0 publications

Penentuan Harga Opsi Dengan Volatilitas Stokastik Menggunakan Metode Monte Carlo

Penentuan Harga Opsi Dengan Volatilitas Stokastik Menggunakan Metode Monte Carlo

Empirical Mode Decomposition Couple with Artificial Neural Network for Water Level Prediction

Modelling Volatility of the US Dollar Against the Kenyan Shilling Exchange Rate and Investigating the Effect of Kenyan Inflation Rates on this Volatility in Kenya

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