Filtering a nonlinear stochastic volatility model

Elliott, Robert J.; Siu, Tak Kuen; Fung, Eric S.

doi:10.1007/s11071-011-0069-4

Cited by 14 publications

(3 citation statements)

References 28 publications

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“…The extrusion force between the ring die and the roller is random and not predetermined, so only the probabilistic method is used to describe its change rule. The stochastic volatility model is a time-series analysis method [13] that regards volatility as an implicit variable. The extrusion force of ring die is established by the stochastic volatility model, and its expression is as follows:…”

Section: External Excitation Analysismentioning

confidence: 99%

Random Dynamic Analysis of Ring Die Pellet Mill

Na¹,

Liu²,

Cen³

2019

IJPE

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Ring die pellet mills are widely applied in feed and biomass fuel. Particles are formed by rotating ring die, so torsional vibration is essential. Because the material has randomness in the extrusion process, the torsional vibration of ring die pellet mills is random, which affects the life, stability, and reliability. Using Lagrange equations and the lump-mass method, the torsional dynamic model of the ring die pellet mill is established. Based on the stochastic volatility model, the extrusion force is created. The dynamic equation of the ring die pellet mill is solved using the Runge-Kutta integration method, and the results show that the torsional vibration is related to the extrusion force, rotational speed, errors in installation, and fabrication. The torsional vibration and the torque of the ring die have similar changes in trend. The error affects the torsional vibration when it reaches a certain level.

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Section: External Excitation Analysismentioning

confidence: 99%

Random Dynamic Analysis of Ring Die Pellet Mill

Na¹,

Liu²,

Cen³

2019

IJPE

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“…The result is that the taxymmetric GARCH model shows better estimation results than the symmetric GARCH model. Elliott et al [5] introduced a class of stochastic volatility models and developed a nonlinear filter with discrete-time to estimate hidden volatility based on observed returns. Burtnyak and Malytska [6] develop a method to forecast the option prices on assumption stochastic volatility.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Volatility Estimation of Stock Prices using the Ensemble Kalman Filter

Mahatma

Hadi

2021

InPrime:Ind.Jour.Pure.Applied.Math

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Volatility plays important role in options trading. In their seminal paper published in 1973, Black and Scholes assume that the stock price volatility, which is the underlying security volatility of a call option, is constant. But thereafter, researchers found that the return volatility was not constant but conditional to the information set available at the computation time. In this research, we improve a methodology to estimate volatility and interest rate using Ensemble Kalman Filter (EnKF). The price of call and put option used in the observation and the forecasting step of the EnKF algorithm computed using the solution of Black-Scholes PDE. The state-space used in this method is the augmented state space, which consists of static variables: volatility and interest rate, and dynamic variables: call and put option price. The numerical experiment shows that the EnKF algorithm is able to estimate accurately the estimated volatility and interest rates with an RMSE value of 0.0506.Keywords: stochastic volatility; call option; put option; Ensemble Kalman Filter. AbstrakVolatilitas adalah faktor penting dalam perdagangan suatu opsi. Dalam makalahnya yang dipublikasikan tahun 1973, Black dan Scholes mengasumsikan bahwa volatilitas harga saham, yang merupakan volatilitas sekuritas yang mendasari opsi beli, adalah konstan. Akan tetapi, para peneliti menemukan bahwa volatilitas pengembalian tidaklah konstan melainkan tergantung pada kumpulan informasi yang dapat digunakan pada saat perhitungan. Pada penelitian ini dikembangkan metodologi untuk mengestimasi volatilitas dan suku bunga menggunakan metode Ensembel Kalman Filter (EnKF). Harga opsi beli dan opsi jual yang digunakan pada observasi dan pada tahap prakiraan pada algoritma EnKF dihitung menggunakan solusi persamaan Black-Scholes. Ruang keadaan yang digunakan adalah ruang keadaan yang diperluas yang terdiri dari variabel statis yaitu volatilitas dan suku bunga, dan variabel dinamis yaitu harga opsi beli dan harga opsi jual. Eksperimen numerik menunjukkan bahwa algoritma ENKF dapat secara akurat mengestimasi volatiltas dan suku bunga dengan RMSE 0.0506.Kata kunci: volatilitas stokastik; opsi beli; opsi jual; Ensembel Kalman Filter.

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“…For the past few years, a lot of valuable researches have been conducted on oil prices, including relationship between oil prices and stock markets from different regions [ 5 ], multiscale entropy analysis of crude oil price dynamics [ 6 ], and forecasting of crude oil price with neural networks [ 7 ], etc. Among them, the exploration of return volatility dynamic is a significant subject for investors and decision makers, because it is a matter of great account in evaluating risks, modeling market dynamics and enabling portfolios to be optimized [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. Specifically, investors in energy markets are always faced with the problem of choosing the optimal portfolios, while unpredictable volatility behaviors are often the main investment risks.…”

Section: Introductionmentioning

confidence: 99%

Complexity Synchronization of Energy Volatility Monotonous Persistence Duration Dynamics

Jia

Wang

2019

Entropy

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A new concept named volatility monotonous persistence duration (VMPD) dynamics is introduced into the research of energy markets, in an attempt to describe nonlinear fluctuation behaviors from a new perspective. The VMPD sequence unites the maximum fluctuation difference and the continuous variation length, which is regarded as a novel indicator to evaluate risks and optimize portfolios. Further, two main aspects of statistical and nonlinear empirical research on the energy VMPD sequence are observed: probability distribution and autocorrelation behavior. Moreover, a new nonlinear method named the cross complexity-invariant distance (CID) FuzzyEn (CCF) which is composed of cross-fuzzy entropy and complexity-invariant distance is firstly proposed to study the complexity synchronization properties of returns and VMPD series for seven representative energy items. We also apply the ensemble empirical mode decomposition (EEMD) to resolve returns and VMPD sequence into the intrinsic mode functions, and the degree that they follow the synchronization features of the initial sequence is investigated.

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Filtering a nonlinear stochastic volatility model

Cited by 14 publications

References 28 publications

Random Dynamic Analysis of Ring Die Pellet Mill

Random Dynamic Analysis of Ring Die Pellet Mill

Stochastic Volatility Estimation of Stock Prices using the Ensemble Kalman Filter

Complexity Synchronization of Energy Volatility Monotonous Persistence Duration Dynamics

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