An Analysis of the Heston Stochastic Volatility Model: Implementation and Calibration Using Matlab

Crisóstomo, Ricardo

doi:10.2139/ssrn.2527818

Cited by 10 publications

(10 citation statements)

References 7 publications

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“…Terdapat beberapa model yang telah diusulkan untuk memodelkan perilaku volatilitas, antara lain model dari Anderson dan Brotherton-Ratcliffe [5], model yang mengasumsikan bahwa volatilitas mengikuti proses acak [6], dan model volatilitas stokastik [7]- [9]. Berdasarkan hasil penelitian Crisostomo [10] model Heston memiliki keunggulan dibandingkan model stokastik lain, yaitu memberikan solusi bentuk tertutup untuk penetapan harga opsi Eropa dan memodelkan perubahan aset dasar yang dapat memperhitungkan asimetri dan kurtosis berlebih yang biasanya diamati dalam return aset keuangan. Penelitian mengenai model volatilitas stokastik sebelumnya juga telah dilakukan oleh beberapa peneliti, di antaranya Wang [11] untuk menentukan harga opsi yang rentan terhadap volatilitas stokastik, Biswas [12] untuk menentukan harga opsi dengan regime switching stochastic volatility models, Tian [13] untuk menentukan harga opsi Eropa dengan biaya transaksi.…”

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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“…where ψ w ( ) F ln T denotes the characteristic function of F ln( ) T , ⋅ Re[ ] is the real operator and k are the strikes prices (see Crisóstomo, 2014Crisóstomo, , 2017.…”

Section: Risk-neutral Densitiesmentioning

confidence: 99%

Estimating real‐world probabilities: A forward‐looking behavioral framework

Crisóstomo

2021

Journal of Futures Markets

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We show that disentangling sentiment-induced biases from fundamental expectations significantly improves the accuracy and consistency of probabilistic forecasts. Using data from 1994 to 2017, we analyze 15 stochastic models and risk-preference combinations and in all possible cases a simple behavioral transformation delivers substantial forecast gains. Our results are robust across different evaluation methods, risk-preference hypotheses, and sentiment calibrations, demonstrating that behavioral effects can be effectively used to forecast asset prices. We also implement a trading strategy that shows how behavioral biases can be exploited to generate trading profits. Further analyses confirm that our real-world densities outperform forecasts recalibrated to avoid past mistakes and improve predictive models where risk aversion is dynamically estimated from option prices.

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“…The set of parameters is calibrated to market data from [55] with r = 0 and a short maturity T = 0.1:…”

Section: Heston Stochastic Volatility Modelmentioning

confidence: 99%

Option pricing with Legendre polynomials

Hok¹,

Chan

2017

Journal of Computational and Applied Mathematics

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Here we develop an option pricing method based on Legendre series expansion of the density function.The key insight, relying on the close relation of the characteristic function with the series coefficients, allows to recover the density function rapidly and accurately. Based on this representation for the density function, approximations formulas for pricing European type options are derived. To obtain highly accurate result for European call option, the implementation involves integrating high degree Legendre polynomials against exponential function. Some numerical instabilities arise because of serious subtractive cancellations in its formulation (96) in proposition 7.1. To overcome this difficulty, we rewrite this quantity as solution of a second-order linear difference equation and solve it using a robust and stable algorithm from Olver. Derivation of the pricing method has been accompanied by an error analysis. Errors bounds have been derived and the study relies more on smoothness properties which are not provided by the payoff functions, but rather by the density function of the underlying stochastic models. This is particularly relevant for options pricing where the payoffs of the contract are generally not smooth functions. The numerical experiments on a class of models widely used in quantitative finance show exponential convergence.

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An Analysis of the Heston Stochastic Volatility Model: Implementation and Calibration Using Matlab

Cited by 10 publications

References 7 publications

Penentuan Harga Opsi Dengan Volatilitas Stokastik Menggunakan Metode Monte Carlo

Penentuan Harga Opsi Dengan Volatilitas Stokastik Menggunakan Metode Monte Carlo

Estimating real‐world probabilities: A forward‐looking behavioral framework

Option pricing with Legendre polynomials

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